1
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Zerba C, Kuhlenkamp C, Imamoğlu A, Knap M. Realizing Topological Superconductivity in Tunable Bose-Fermi Mixtures with Transition Metal Dichalcogenide Heterostructures. PHYSICAL REVIEW LETTERS 2024; 133:056902. [PMID: 39159121 DOI: 10.1103/physrevlett.133.056902] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2023] [Accepted: 06/21/2024] [Indexed: 08/21/2024]
Abstract
Heterostructures of two-dimensional transition metal dichalcogenides are emerging as a promising platform for investigating exotic correlated states of matter. Here, we propose to engineer Bose-Fermi mixtures in these systems by coupling interlayer excitons to doped charges in a trilayer structure. Their interactions are determined by the interlayer trion, whose spin-selective nature allows excitons to mediate an attractive interaction between charge carriers of only one spin species. Remarkably, we find that this causes the system to become unstable to topological p+ip superconductivity at low temperatures. We then demonstrate a general mechanism to develop and control this unconventional state by tuning the trion binding energy using a solid-state Feshbach resonance.
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Affiliation(s)
| | - Clemens Kuhlenkamp
- Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, 80799 München, Germany
- Institute for Quantum Electronics, ETH Zürich, CH-8093 Zürich, Switzerland
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2
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Wan Z, Qiu G, Ren H, Qian Q, Li Y, Xu D, Zhou J, Zhou J, Zhou B, Wang L, Yang TH, Sofer Z, Huang Y, Wang KL, Duan X. Unconventional superconductivity in chiral molecule-TaS 2 hybrid superlattices. Nature 2024; 632:69-74. [PMID: 38926586 DOI: 10.1038/s41586-024-07625-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2023] [Accepted: 05/29/2024] [Indexed: 06/28/2024]
Abstract
Chiral superconductors, a unique class of unconventional superconductors in which the complex superconducting order parameter winds clockwise or anticlockwise in the momentum space1, represent a topologically non-trivial system with intrinsic time-reversal symmetry breaking (TRSB) and direct implications for topological quantum computing2,3. Intrinsic chiral superconductors are extremely rare, with only a few arguable examples, including UTe2, UPt3 and Sr2RuO4 (refs. 4-7). It has been suggested that chiral superconductivity may exist in non-centrosymmetric superconductors8,9, although such non-centrosymmetry is uncommon in typical solid-state superconductors. Alternatively, chiral molecules with neither mirror nor inversion symmetry have been widely investigated. We suggest that an incorporation of chiral molecules into conventional superconductor lattices could introduce non-centrosymmetry and help realize chiral superconductivity10. Here we explore unconventional superconductivity in chiral molecule intercalated TaS2 hybrid superlattices. Our studies reveal an exceptionally large in-plane upper critical field Bc2,|| well beyond the Pauli paramagnetic limit, a robust π-phase shift in Little-Parks measurements and a field-free superconducting diode effect (SDE). These experimental signatures of unconventional superconductivity suggest that the intriguing interplay between crystalline atomic layers and the self-assembled chiral molecular layers may lead to exotic topological materials. Our study highlights that the hybrid superlattices could lay a versatile path to artificial quantum materials by combining a vast library of layered crystals of rich physical properties with the nearly infinite variations of molecules of designable structural motifs and functional groups11.
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Affiliation(s)
- Zhong Wan
- Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, CA, USA
| | - Gang Qiu
- Department of Electrical and Computer Engineering, University of California, Los Angeles, Los Angeles, CA, USA
| | - Huaying Ren
- Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, CA, USA
| | - Qi Qian
- Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, CA, USA
| | - Yaochen Li
- Department of Electrical and Computer Engineering, University of California, Los Angeles, Los Angeles, CA, USA
| | - Dong Xu
- Department of Materials Science and Engineering, University of California, Los Angeles, Los Angeles, CA, USA
| | - Jingyuan Zhou
- Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, CA, USA
| | - Jingxuan Zhou
- Department of Materials Science and Engineering, University of California, Los Angeles, Los Angeles, CA, USA
| | - Boxuan Zhou
- Department of Materials Science and Engineering, University of California, Los Angeles, Los Angeles, CA, USA
| | - Laiyuan Wang
- Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, CA, USA
| | - Ting-Hsun Yang
- Department of Electrical and Computer Engineering, University of California, Los Angeles, Los Angeles, CA, USA
| | - Zdeněk Sofer
- Department of Inorganic Chemistry, University of Chemistry and Technology Prague, Prague, Czech Republic
| | - Yu Huang
- Department of Materials Science and Engineering, University of California, Los Angeles, Los Angeles, CA, USA.
- California NanoSystems Institute, University of California, Los Angeles, Los Angeles, CA, USA.
| | - Kang L Wang
- Department of Electrical and Computer Engineering, University of California, Los Angeles, Los Angeles, CA, USA.
- California NanoSystems Institute, University of California, Los Angeles, Los Angeles, CA, USA.
- Department of Physics and Astronomy, University of California, Los Angeles, Los Angeles, CA, USA.
| | - Xiangfeng Duan
- Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, CA, USA.
- California NanoSystems Institute, University of California, Los Angeles, Los Angeles, CA, USA.
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3
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Le T, Pan Z, Xu Z, Liu J, Wang J, Lou Z, Yang X, Wang Z, Yao Y, Wu C, Lin X. Superconducting diode effect and interference patterns in kagome CsV 3Sb 5. Nature 2024; 630:64-69. [PMID: 38750364 DOI: 10.1038/s41586-024-07431-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2023] [Accepted: 04/16/2024] [Indexed: 06/07/2024]
Abstract
The interplay among frustrated lattice geometry, non-trivial band topology and correlation yields rich quantum states of matter in kagome systems1,2. A series of recent members in this family, AV3Sb5 (A = K, Rb or Cs), exhibit a cascade of symmetry-breaking transitions3, involving the 3Q chiral charge ordering4-8, electronic nematicity9,10, roton pair density wave11 and superconductivity12. The nature of the superconducting order is yet to be resolved. Here we report an indication of dynamic superconducting domains with boundary supercurrents in intrinsic CsV3Sb5 flakes. The magnetic field-free superconducting diode effect is observed with polarity modulated by thermal histories, suggesting that there are dynamic superconducting order domains in a spontaneous time-reversal symmetry-breaking background. Strikingly, the critical current exhibits double-slit superconductivity interference patterns when subjected to an external magnetic field. The characteristics of the patterns are modulated by thermal cycling. These phenomena are proposed as a consequence of periodically modulated supercurrents flowing along certain domain boundaries constrained by fluxoid quantization. Our results imply a time-reversal symmetry-breaking superconducting order, opening a potential for exploring exotic physics, for example, Majorana zero modes, in this intriguing topological kagome system.
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Affiliation(s)
- Tian Le
- Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science and Research Center for Industries of the Future, Westlake University, Hangzhou, People's Republic of China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, People's Republic of China
| | - Zhiming Pan
- Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science and Research Center for Industries of the Future, Westlake University, Hangzhou, People's Republic of China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, People's Republic of China
- Institute for Theoretical Sciences, Westlake University, Hangzhou, China
| | - Zhuokai Xu
- Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science and Research Center for Industries of the Future, Westlake University, Hangzhou, People's Republic of China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, People's Republic of China
| | - Jinjin Liu
- Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing, China
- Beijing Key Lab of Nanophotonics and Ultrafine Optoelectronic Systems, Beijing Institute of Technology, Beijing, China
| | - Jialu Wang
- Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science and Research Center for Industries of the Future, Westlake University, Hangzhou, People's Republic of China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, People's Republic of China
| | - Zhefeng Lou
- Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science and Research Center for Industries of the Future, Westlake University, Hangzhou, People's Republic of China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, People's Republic of China
| | - Xiaohui Yang
- Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science and Research Center for Industries of the Future, Westlake University, Hangzhou, People's Republic of China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, People's Republic of China
- Department of Physics, China Jiliang University, Hangzhou, People's Republic of China
| | - Zhiwei Wang
- Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing, China.
- Beijing Key Lab of Nanophotonics and Ultrafine Optoelectronic Systems, Beijing Institute of Technology, Beijing, China.
- Material Science Center, Yangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing, China.
| | - Yugui Yao
- Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing, China
- Beijing Key Lab of Nanophotonics and Ultrafine Optoelectronic Systems, Beijing Institute of Technology, Beijing, China
- Material Science Center, Yangtze Delta Region Academy of Beijing Institute of Technology, Jiaxing, China
| | - Congjun Wu
- Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science and Research Center for Industries of the Future, Westlake University, Hangzhou, People's Republic of China.
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, People's Republic of China.
- Institute for Theoretical Sciences, Westlake University, Hangzhou, China.
- New Cornerstone Science Laboratory, Department of Physics, School of Science, Westlake University, Hangzhou, China.
| | - Xiao Lin
- Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science and Research Center for Industries of the Future, Westlake University, Hangzhou, People's Republic of China.
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, People's Republic of China.
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4
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Zhang JL, Chen W, Liu HT, Li Y, Wang Z, Huang W. Quantum-Geometry-Induced Anomalous Hall Effect in Nonunitary Superconductors and Application to Sr_{2}RuO_{4}. PHYSICAL REVIEW LETTERS 2024; 132:136001. [PMID: 38613301 DOI: 10.1103/physrevlett.132.136001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2023] [Accepted: 03/01/2024] [Indexed: 04/14/2024]
Abstract
The polar Kerr effect and the closely related anomalous charge Hall effect are among the most distinguishing signatures of the superconducting state in Sr_{2}RuO_{4}, as well as in several other compounds. These effects are often thought to be derived from chiral superconducting pairing, and different mechanisms have been invoked for the explanation. However, the intrinsic mechanisms proposed previously often involve unrealistically strong interband Cooper pairing. We show in this Letter that, even without interband pairing, nonunitary superconducting states can support the intrinsic anomalous charge Hall effect, thanks to the quantum geometric properties of the Bloch electrons. The key here is to have a normal-state spin Hall effect, for which a nonzero spin-orbit coupling is essential. A finite charge Hall effect then naturally arises at the onset of a spin-polarized nonunitary superconducting pairing. It depends on both the spin polarization and the normal-state electron Berry curvature, the latter of which is the imaginary part of the quantum geometric tensor of the Bloch states. Applying our results to the weakly paired Sr_{2}RuO_{4} we conclude that, if the reported Kerr effect is of intrinsic origin, the superconducting state is most likely nonunitary and has odd parity. Our theory may be generalized to other superconductors that exhibit the polar Kerr effect.
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Affiliation(s)
- Jia-Long Zhang
- Department of Physics, The Hong Kong University of Science and Technology, Hong Kong SAR, China
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
| | - Weipeng Chen
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Hao-Tian Liu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yu Li
- Institute of Quantum Materials and Physics, Henan Academy of Sciences, Zhengzhou, Henan 450046, China
- Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Zhiqiang Wang
- Department of Physics and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| | - Wen Huang
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
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5
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Gassner S, Weber CS, Claassen M. Light-induced switching between singlet and triplet superconducting states. Nat Commun 2024; 15:1776. [PMID: 38413590 PMCID: PMC10899631 DOI: 10.1038/s41467-024-45949-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Accepted: 02/08/2024] [Indexed: 02/29/2024] Open
Abstract
While the search for topological triplet-pairing superconductivity has remained a challenge, recent developments in optically stabilizing metastable superconducting states suggest a new route to realizing this elusive phase. Here, we devise a testable theory of competing superconducting orders that permits ultrafast switching to an opposite-parity superconducting phase in centrosymmetric crystals with strong spin-orbit coupling. Using both microscopic and phenomenological models, we show that dynamical inversion symmetry breaking with a tailored light pulse can induce odd-parity (spin triplet) order parameter oscillations in a conventional even-parity (spin singlet) superconductor, which when driven strongly can send the system to a competing minimum in its free energy landscape. Our results provide new guiding principles for engineering unconventional electronic phases using light, suggesting a fundamentally non-equilibrium route toward realizing topological superconductivity.
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Affiliation(s)
- Steven Gassner
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, 19104, USA.
| | - Clara S Weber
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, 19104, USA
- Institut für Theorie der Statistischen Physik, RWTH Aachen and JARA - Fundamentals of Future Information Technology, D-52056, Aachen, Germany
| | - Martin Claassen
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, 19104, USA.
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6
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Tokarczyk P, Vidmar L, Łydżba P. Single-quasiparticle eigenstate thermalization. Phys Rev E 2024; 109:024102. [PMID: 38491661 DOI: 10.1103/physreve.109.024102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2023] [Accepted: 12/13/2023] [Indexed: 03/18/2024]
Abstract
Quadratic Hamiltonians that exhibit single-particle quantum chaos are called quantum-chaotic quadratic Hamiltonians. One of their hallmarks is single-particle eigenstate thermalization introduced in Łydżba et al. [Phys. Rev. B 104, 214203 (2021)2469-995010.1103/PhysRevB.104.214203], which describes statistical properties of matrix elements of observables in single-particle eigenstates. However, the latter has been studied only in quantum-chaotic quadratic Hamiltonians that obey the U(1) symmetry. Here, we focus on quantum-chaotic quadratic Hamiltonians that break the U(1) symmetry and, hence, their "single-particle" eigenstates are actually single-quasiparticle excitations introduced on the top of a many-body state. We study their wave functions and matrix elements of one-body observables, for which we introduce the notion of single-quasiparticle eigenstate thermalization. Focusing on spinless fermion Hamiltonians in three dimensions with local hopping, pairing, and on-site disorder, we also study the properties of disorder-induced near zero modes, which give rise to a sharp peak in the density of states at zero energy. Finally, we numerically show equilibration of observables in many-body eigenstates after a quantum quench. We argue that the latter is a consequence of single-quasiparticle eigenstate thermalization, in analogy to the U(1) symmetric case from Łydżba et al. [Phys. Rev. Lett. 131, 060401 (2023)0031-900710.1103/PhysRevLett.131.060401].
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Affiliation(s)
- Piotr Tokarczyk
- Institute of Theoretical Physics, Wroclaw University of Science and Technology, 50-370 Wrocław, Poland
| | - Lev Vidmar
- Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
| | - Patrycja Łydżba
- Institute of Theoretical Physics, Wroclaw University of Science and Technology, 50-370 Wrocław, Poland
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7
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Silber I, Mathimalar S, Mangel I, Nayak AK, Green O, Avraham N, Beidenkopf H, Feldman I, Kanigel A, Klein A, Goldstein M, Banerjee A, Sela E, Dagan Y. Two-component nematic superconductivity in 4Hb-TaS 2. Nat Commun 2024; 15:824. [PMID: 38280890 PMCID: PMC10821864 DOI: 10.1038/s41467-024-45169-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2022] [Accepted: 01/15/2024] [Indexed: 01/29/2024] Open
Abstract
Most superconductors have an isotropic, single component order parameter and are well described by the standard (BCS) theory for superconductivity. Unconventional, multiple-component superconductors are exceptionally rare and are much less understood. Here, we combine scanning tunneling microscopy and angle-resolved macroscopic transport for studying the candidate chiral superconductor, 4Hb-TaS2. We reveal quasi-periodic one-dimensional modulations in the tunneling conductance accompanied by two-fold symmetric superconducting critical field. The strong modulation of the in-plane critical field, Hc2, points to a nematic, unconventional order parameter. However, the imaged vortex core is isotropic at low temperatures. We suggest a model that reconciles this apparent discrepancy and takes into account previously observed spontaneous time-reversal symmetry breaking at low temperatures. The model describes a competition between a dominating chiral superconducting order parameter and a nematic one. The latter emerges close to the normal phase. Our results strongly support the existence of two-component superconductivity in 4Hb-TaS2 and can provide valuable insights into other systems with coexistent charge order and superconductivity.
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Affiliation(s)
- I Silber
- School of Physics and Astronomy, Tel - Aviv University, Tel Aviv, 69978, Israel
| | - S Mathimalar
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - I Mangel
- Physics Department, Technion-Israel Institute of Technology, Haifa, 32000, Israel
| | - A K Nayak
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - O Green
- School of Physics and Astronomy, Tel - Aviv University, Tel Aviv, 69978, Israel
| | - N Avraham
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - H Beidenkopf
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - I Feldman
- Physics Department, Technion-Israel Institute of Technology, Haifa, 32000, Israel
| | - A Kanigel
- Physics Department, Technion-Israel Institute of Technology, Haifa, 32000, Israel
| | - A Klein
- Department of Physics, Faculty of Natural Sciences, Ariel University, Ariel, 40700, Israel
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot, 76100, Israel
| | - M Goldstein
- School of Physics and Astronomy, Tel - Aviv University, Tel Aviv, 69978, Israel
| | - A Banerjee
- Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel
| | - E Sela
- School of Physics and Astronomy, Tel - Aviv University, Tel Aviv, 69978, Israel
| | - Y Dagan
- School of Physics and Astronomy, Tel - Aviv University, Tel Aviv, 69978, Israel.
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8
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Azari N, Yakovlev M, Rye N, Dunsiger SR, Sundar S, Bordelon MM, Thomas SM, Thompson JD, Rosa PFS, Sonier JE. Absence of Spontaneous Magnetic Fields due to Time-Reversal Symmetry Breaking in Bulk Superconducting UTe_{2}. PHYSICAL REVIEW LETTERS 2023; 131:226504. [PMID: 38101387 DOI: 10.1103/physrevlett.131.226504] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2023] [Accepted: 10/18/2023] [Indexed: 12/17/2023]
Abstract
We have investigated the low-temperature local magnetic properties in the bulk of molten salt-flux (MSF)-grown single crystals of the candidate odd-parity superconductor UTe_{2} by zero-field muon spin relaxation (μSR). In contrast to previous μSR studies of UTe_{2} single crystals grown by a chemical vapor transport method, we find no evidence of magnetic clusters or electronic moments fluctuating slow enough to cause a discernible relaxation of the zero-field μSR asymmetry spectrum. Consequently, our measurements on MSF-grown single crystals rule out the generation of spontaneous magnetic fields in the bulk that would occur near impurities or lattice defects if the superconducting state of UTe_{2} breaks time-reversal symmetry. This result suggests that UTe_{2} is characterized by a single-component superconducting order parameter.
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Affiliation(s)
- N Azari
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - M Yakovlev
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - N Rye
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - S R Dunsiger
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
- Centre for Molecular and Materials Science, TRIUMF, Vancouver, British Columbia V6T 2A3, Canada
| | - S Sundar
- Scottish Universities Physics Alliance, School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS, United Kingdom
| | - M M Bordelon
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - S M Thomas
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - J D Thompson
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - P F S Rosa
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - J E Sonier
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
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9
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Shang T, Svanidze E, Shiroka T. Probing the superconducting pairing of the La 4Be 33Pt 16alloy via muon-spin spectroscopy. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 36:105601. [PMID: 37988753 DOI: 10.1088/1361-648x/ad0e93] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2023] [Accepted: 11/21/2023] [Indexed: 11/23/2023]
Abstract
We report a study of the superconducting pairing of the noncentrosymmetric La4Be33Pt16alloy using muon-spin rotation and relaxation (µSR) technique. BelowTc=2.4 K, La4Be33Pt16exhibits bulk superconductivity (SC), here characterized by heat-capacity and magnetic-susceptibility measurements. The temperature dependence of the superfluid densityρsc(T), extracted from the transverse-fieldµSR measurements, reveals a nodeless SC in La4Be33Pt16. The best fit ofρsc(T)using ans-wave model yields a magnetic penetration depthλ0=542 nm and a superconducting gapΔ0=0.37 meV at zero Kelvin. The single-gapped superconducting state is further evidenced by the temperature-dependent electronic specific heatCe(T)/Tand the linear field-dependent electronic specific-heat coefficientγH(H). The zero-fieldµSR spectra collected in the normal- and superconducting states of La4Be33Pt16are almost identical, confirming the absence of an additional field-related relaxation and, thus, of spontaneous magnetic fields belowTc. The nodeless SC combined with a preserved time-reversal symmetry in the superconducting state proves that the spin-singlet pairing is dominant in La4Be33Pt16. This material represents yet another example of a complex system showing only a conventional behavior, in spite of a noncentrosymmetric structure and a sizeable spin-orbit coupling.
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Affiliation(s)
- Tian Shang
- Key Laboratory of Polar Materials and Devices (MOE), School of Physics and Electronic Science, East China Normal University, Shanghai 200241, People's Republic of China
- Chongqing Key Laboratory of Precision Optics, Chongqing Institute of East China Normal University, Chongqing 401120, People's Republic of China
| | - Eteri Svanidze
- Max Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany
| | - Toni Shiroka
- Laboratory for Muon-Spin Spectroscopy, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
- Laboratorium für Festkörperphysik, ETH-Hönggerberg, CH-8093 Zürich, Switzerland
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10
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Mandal M, Drucker NC, Siriviboon P, Nguyen T, Boonkird A, Lamichhane TN, Okabe R, Chotrattanapituk A, Li M. Topological Superconductors from a Materials Perspective. CHEMISTRY OF MATERIALS : A PUBLICATION OF THE AMERICAN CHEMICAL SOCIETY 2023; 35:6184-6200. [PMID: 37637011 PMCID: PMC10448998 DOI: 10.1021/acs.chemmater.3c00713] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Revised: 07/12/2023] [Indexed: 08/29/2023]
Abstract
Topological superconductors (TSCs) have garnered significant research and industry attention in the past two decades. By hosting Majorana bound states which can be used as qubits that are robust against local perturbations, TSCs offer a promising platform toward (nonuniversal) topological quantum computation. However, there has been a scarcity of TSC candidates, and the experimental signatures that identify a TSC are often elusive. In this Perspective, after a short review of the TSC basics and theories, we provide an overview of the TSC materials candidates, including natural compounds and synthetic material systems. We further introduce various experimental techniques to probe TSCs, focusing on how a system is identified as a TSC candidate and why a conclusive answer is often challenging to draw. We conclude by calling for new experimental signatures and stronger computational support to accelerate the search for new TSC candidates.
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Affiliation(s)
- Manasi Mandal
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, United States
| | - Nathan C. Drucker
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- School
of Engineering and Applied Sciences, Harvard
University, Cambridge, Massachusetts 02138, United States
| | - Phum Siriviboon
- Department
of Physics, MIT, Cambridge, Massachusetts 02139, United States
| | - Thanh Nguyen
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, United States
| | - Artittaya Boonkird
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, United States
| | - Tej Nath Lamichhane
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, United States
| | - Ryotaro Okabe
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Chemistry, MIT, Cambridge, Massachusetts 02139, United States
| | - Abhijatmedhi Chotrattanapituk
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Electrical Engineering and Computer Science, MIT, Cambridge, Massachusetts 02139, United States
| | - Mingda Li
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, United States
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11
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Crépel V, Guerci D, Cano J, Pixley JH, Millis A. Topological Superconductivity in Doped Magnetic Moiré Semiconductors. PHYSICAL REVIEW LETTERS 2023; 131:056001. [PMID: 37595206 DOI: 10.1103/physrevlett.131.056001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2023] [Accepted: 07/06/2023] [Indexed: 08/20/2023]
Abstract
We show that topological superconductivity may emerge upon doping of transition metal dichalcogenide heterobilayers above an integer-filling magnetic state of the topmost valence moiré band. The effective attraction between charge carriers is generated by an electric p-wave Feshbach resonance arising from interlayer excitonic physics and has a tunable strength, which may be large. Together with the low moiré carrier densities reachable by gating, this robust attraction enables access to the long-sought p-wave BEC-BCS transition. The topological protection arises from an emergent time reversal symmetry occurring when the magnetic order and long wavelength magnetic fluctuations do not couple different valleys. The resulting topological superconductor features helical Majorana edge modes, leading to half-integer quantized spin-thermal Hall conductivity and to charge currents induced by circularly polarized light or other time-reversal symmetry-breaking fields.
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Affiliation(s)
- Valentin Crépel
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Daniele Guerci
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Jennifer Cano
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
- Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
| | - J H Pixley
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
- Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Andrew Millis
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
- Department of Physics, Columbia University, New York, New York 10027, USA
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12
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Broyles C, Rehfuss Z, Siddiquee H, Zhu JA, Zheng K, Nikolo M, Graf D, Singleton J, Ran S. Revealing a 3D Fermi Surface Pocket and Electron-Hole Tunneling in UTe_{2} with Quantum Oscillations. PHYSICAL REVIEW LETTERS 2023; 131:036501. [PMID: 37540859 DOI: 10.1103/physrevlett.131.036501] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Revised: 06/20/2023] [Accepted: 06/22/2023] [Indexed: 08/06/2023]
Abstract
Spin triplet superconductor UTe_{2} is widely believed to host a quasi-two-dimensional Fermi surface, revealed by first-principles calculations, photoemission, and quantum oscillation measurements. An outstanding question still remains as to the existence of a three-dimensional Fermi surface pocket, which is crucial for our understanding of the exotic superconducting and topological properties of UTe_{2}. This 3D Fermi surface pocket appears in various theoretical models with different physics origins, but has not been unambiguously detected in experiment. Here for the first time we provide concrete evidence for a relatively isotropic, small Fermi surface pocket of UTe_{2} via quantum oscillation measurements. In addition, we observed high frequency quantum oscillations corresponding to electron-hole tunneling between adjacent electron and hole pockets. The coexistence of 2D and 3D Fermi surface pockets, as well as the breakdown orbits, provide a test bed for theoretical models and aid the realization of a unified understanding of the superconducting state of UTe_{2} from the first-principles approach.
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Affiliation(s)
- Christopher Broyles
- Department of Physics, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | - Zack Rehfuss
- Department of Physics, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | - Hasan Siddiquee
- Department of Physics, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | - Jiahui Althena Zhu
- Department of Physics, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | - Kaiwen Zheng
- Department of Physics, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | - Martin Nikolo
- Department of Physics, Saint Louis University, St. Louis, Missouri 63103, USA
| | - David Graf
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA
| | - John Singleton
- National High Magnetic Field Laboratory, Pulse Field Facility, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Sheng Ran
- Department of Physics, Washington University in St. Louis, St. Louis, Missouri 63130, USA
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13
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Asrafusjaman M, Islam J, Rahman MA, Hossain AKMA. Investigation of the Influence of Pressure on the Physical Properties and Superconducting Transition Temperature of Chiral Noncentrosymmetric TaRh 2B 2 and NbRh 2B 2. ACS OMEGA 2023; 8:21813-21822. [PMID: 37360420 PMCID: PMC10286279 DOI: 10.1021/acsomega.3c01461] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/03/2023] [Accepted: 05/09/2023] [Indexed: 06/28/2023]
Abstract
TaRh2B2 and NbRh2B2 compounds exhibit noncentrosymmetric superconductivity with a chiral structure. Density functional theory-based ab-initio calculations have been executed to analyze the structural properties, mechanical stability, ductility/brittleness behaviors, Debye temperature, melting temperature, optical response to incident photon energy, electronic characteristics, and superconducting transition temperature of chiral TaRh2B2 and NbRh2B2 compounds under pressure up to 16 GPa. Both the chiral phases are mechanically stable and exhibit ductile nature under the studied pressure. The maximum value of the Pugh ratio (an indicator of ductile/brittle behaviors) is observed to be 2.55 (for NbRh2B2) and 2.52 (for TaRh2B2) at 16 GPa. The lowest value of the Pugh ratio is noticed at 0 GPa for both these chiral compounds. The analysis of reflectivity spectra suggests that both the chiral compounds can be used as efficient reflecting materials in the visible energy region. At 0 GPa, the calculated densities of states (DOSs) at the Fermi level are found to be 1.59 and 2.13 states eV-1 per formula unit for TaRh2B2 and NbRh2B2, respectively. The DOS values of both the chiral phases do not alter significantly with applied pressure. The shape of the DOS curve of both compounds remains almost invariant with applied pressure. The pressure-induced variation of Debye temperatures of both compounds is observed, which may cause the alternation of the superconducting transition temperature, Tc, with applied pressure. The probable changing of Tc with pressure has been analyzed from the McMillan equation.
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Affiliation(s)
- Mohammad Asrafusjaman
- Department of Physics, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh
| | - Jakiul Islam
- Department of Physics, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh
| | - M. Azizar Rahman
- Department of Physics, Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh
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14
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Gu Q, Carroll JP, Wang S, Ran S, Broyles C, Siddiquee H, Butch NP, Saha SR, Paglione J, Davis JCS, Liu X. Detection of a pair density wave state in UTe 2. Nature 2023; 618:921-927. [PMID: 37380691 DOI: 10.1038/s41586-023-05919-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2022] [Accepted: 03/03/2023] [Indexed: 06/30/2023]
Abstract
Spin-triplet topological superconductors should exhibit many unprecedented electronic properties, including fractionalized electronic states relevant to quantum information processing. Although UTe2 may embody such bulk topological superconductivity1-11, its superconductive order parameter Δ(k) remains unknown12. Many diverse forms for Δ(k) are physically possible12 in such heavy fermion materials13. Moreover, intertwined14,15 density waves of spin (SDW), charge (CDW) and pair (PDW) may interpose, with the latter exhibiting spatially modulating14,15 superconductive order parameter Δ(r), electron-pair density16-19 and pairing energy gap17,20-23. Hence, the newly discovered CDW state24 in UTe2 motivates the prospect that a PDW state may exist in this material24,25. To search for it, we visualize the pairing energy gap with μeV-scale energy resolution using superconductive scanning tunnelling microscopy (STM) tips26-31. We detect three PDWs, each with peak-to-peak gap modulations of around 10 μeV and at incommensurate wavevectors Pi=1,2,3 that are indistinguishable from the wavevectors Qi=1,2,3 of the prevenient24 CDW. Concurrent visualization of the UTe2 superconductive PDWs and the non-superconductive CDWs shows that every Pi:Qi pair exhibits a relative spatial phase δϕ ≈ π. From these observations, and given UTe2 as a spin-triplet superconductor12, this PDW state should be a spin-triplet PDW24,25. Although such states do exist32 in superfluid 3He, for superconductors, they are unprecedented.
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Affiliation(s)
- Qiangqiang Gu
- LASSP, Department of Physics, Cornell University, Ithaca, NY, USA
| | - Joseph P Carroll
- LASSP, Department of Physics, Cornell University, Ithaca, NY, USA
- Department of Physics, University College Cork, Cork, Ireland
| | - Shuqiu Wang
- LASSP, Department of Physics, Cornell University, Ithaca, NY, USA.
- Clarendon Laboratory, University of Oxford, Oxford, UK.
| | - Sheng Ran
- Department of Physics, Washington University in St. Louis, St. Louis, MO, USA
| | - Christopher Broyles
- Department of Physics, Washington University in St. Louis, St. Louis, MO, USA
| | - Hasan Siddiquee
- Department of Physics, Washington University in St. Louis, St. Louis, MO, USA
| | - Nicholas P Butch
- Maryland Quantum Materials Center, University of Maryland, College Park, MD, USA
- NIST Center for Neutron Research, Gaithersburg, MD, USA
| | - Shanta R Saha
- Maryland Quantum Materials Center, University of Maryland, College Park, MD, USA
| | - Johnpierre Paglione
- Maryland Quantum Materials Center, University of Maryland, College Park, MD, USA
- Canadian Institute for Advanced Research, Toronto, Ontario, Canada
| | - J C Séamus Davis
- LASSP, Department of Physics, Cornell University, Ithaca, NY, USA.
- Department of Physics, University College Cork, Cork, Ireland.
- Clarendon Laboratory, University of Oxford, Oxford, UK.
- Max Planck Institute for Chemical Physics of Solids, Dresden, Germany.
| | - Xiaolong Liu
- LASSP, Department of Physics, Cornell University, Ithaca, NY, USA.
- Department of Physics and Astronomy, University of Notre Dame, Notre Dame, IN, USA.
- Stavropoulos Center for Complex Quantum Matter, University of Notre Dame, Notre Dame, IN, USA.
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15
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Ishihara K, Roppongi M, Kobayashi M, Imamura K, Mizukami Y, Sakai H, Opletal P, Tokiwa Y, Haga Y, Hashimoto K, Shibauchi T. Chiral superconductivity in UTe 2 probed by anisotropic low-energy excitations. Nat Commun 2023; 14:2966. [PMID: 37221184 DOI: 10.1038/s41467-023-38688-y] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2023] [Accepted: 05/08/2023] [Indexed: 05/25/2023] Open
Abstract
Chiral spin-triplet superconductivity is a topologically nontrivial pairing state with broken time-reversal symmetry, which can host Majorana quasiparticles. The heavy-fermion superconductor UTe2 exhibits peculiar properties of spin-triplet pairing, and the possible chiral state has been actively discussed. However, the symmetry and nodal structure of its order parameter in the bulk, which determine the Majorana surface states, remains controversial. Here we focus on the number and positions of superconducting gap nodes in the ground state of UTe2. Our magnetic penetration depth measurements for three field orientations in three crystals all show the power-law temperature dependence with exponents close to 2, which excludes single-component spin-triplet states. The anisotropy of low-energy quasiparticle excitations indicates multiple point nodes near the ky- and kz-axes in momentum space. These results can be consistently explained by a chiral B3u + iAu non-unitary state, providing fundamentals of the topological properties in UTe2.
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Affiliation(s)
- Kota Ishihara
- Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba, 277-8561, Japan.
| | - Masaki Roppongi
- Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba, 277-8561, Japan
| | - Masayuki Kobayashi
- Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba, 277-8561, Japan
| | - Kumpei Imamura
- Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba, 277-8561, Japan
| | - Yuta Mizukami
- Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba, 277-8561, Japan
- Department of Physics, Graduate School of Science, Tohoku University, 6-3, Aramaki Aza-Aoba, Aoba-ku, Sendai, 980-8578, Japan
| | - Hironori Sakai
- Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki, 319-1195, Japan
| | - Petr Opletal
- Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki, 319-1195, Japan
| | - Yoshifumi Tokiwa
- Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki, 319-1195, Japan
| | - Yoshinori Haga
- Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki, 319-1195, Japan
| | - Kenichiro Hashimoto
- Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba, 277-8561, Japan
| | - Takasada Shibauchi
- Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba, 277-8561, Japan.
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16
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Iguchi Y, Man H, Thomas SM, Ronning F, Rosa PFS, Moler KA. Microscopic Imaging Homogeneous and Single Phase Superfluid Density in UTe_{2}. PHYSICAL REVIEW LETTERS 2023; 130:196003. [PMID: 37243629 DOI: 10.1103/physrevlett.130.196003] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2022] [Revised: 12/21/2022] [Accepted: 04/04/2023] [Indexed: 05/29/2023]
Abstract
Odd-parity superconductor UTe_{2} shows spontaneous time-reversal symmetry breaking and multiple superconducting phases, which imply chiral superconductivity, but only in a subset of samples. Here we microscopically observe a homogeneous superfluid density n_{s} on the surface of UTe_{2} and an enhanced superconducting transition temperature near the edges. We also detect vortex-antivortex pairs even at zero magnetic field, indicating the existence of a hidden internal field. The temperature dependence of n_{s}, determined independent of sample geometry, does not support point nodes along the b axis for a quasi-2D Fermi surface and provides no evidence for multiple phase transitions in UTe_{2}.
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Affiliation(s)
- Yusuke Iguchi
- Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
| | - Huiyuan Man
- Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
- Stanford Nano Shared Facilities, Stanford University, Stanford, California 94305, USA
| | - S M Thomas
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Filip Ronning
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | | | - Kathryn A Moler
- Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
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17
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Volkov PA, Wilson JH, Lucht KP, Pixley JH. Current- and Field-Induced Topology in Twisted Nodal Superconductors. PHYSICAL REVIEW LETTERS 2023; 130:186001. [PMID: 37204877 DOI: 10.1103/physrevlett.130.186001] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2021] [Revised: 12/06/2022] [Accepted: 03/13/2023] [Indexed: 05/21/2023]
Abstract
We show that interlayer current induces topological superconductivity in twisted bilayers of nodal superconductors. A bulk gap opens and achieves its maximum near a "magic" twist angle θ_{MA}. Chiral edge modes lead to a quantized thermal Hall effect at low temperatures. Furthermore, we show that an in-plane magnetic field creates a periodic lattice of topological domains with edge modes forming low-energy bands. We predict their signatures in scanning tunneling microscopy. Estimates for candidate materials indicate that twist angles θ∼θ_{MA} are optimal for observing the predicted effects.
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Affiliation(s)
- Pavel A Volkov
- Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Department of Physics, University of Connecticut, Storrs, Connecticut 06269, USA
| | - Justin H Wilson
- Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA
- Department of Physics and Astronomy, and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA
| | - Kevin P Lucht
- Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA
| | - J H Pixley
- Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA
- Physics Department, Princeton University, Princeton, New Jersey 08544, USA
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18
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Kong JT, Yan ZX, Song W, Li WL, X Y, Xu WY, Cheng Q, Li DX. Emergent Majorana zero-modes in an intrinsic anti-ferromagnetic topological superconductor Mn 2B 2 monolayer. Phys Chem Chem Phys 2023; 25:6963-6969. [PMID: 36807355 DOI: 10.1039/d2cp05523f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
Topological superconductors (TSCs) are an exotic field due to the existence of Majorana zero-modes (MZM) in the edge states that obey non-Abelian statistics and can be used to implement topological quantum computations, especially for two-dimensional (2D) materials. Here we predict manganese diboride (Mn2B2) as an intrinsic 2D anti-ferromagnetic (AFM) TSC based on the magnetic and electronic structures of Mn and B atoms. Once Mn2B2 ML enters a superconducting state, MZM will be induced by the spin-polarized helical gapless edge states. The Z2 topological non-trivial properties are confirmed by Wannier charge centers (WCC) and the platform of the spin Hall conductivity near the Fermi level. Phonon-electron coupling (EPC) implies s-wave superconductivity and the critical temperature (Tc) is 6.79 K.
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Affiliation(s)
- J T Kong
- College of Science, Xi'an University of Science and Technology, Xi'an 710054, China.
| | - Z X Yan
- College of Science, Xi'an University of Science and Technology, Xi'an 710054, China.
| | - W Song
- College of Science, Xi'an University of Science and Technology, Xi'an 710054, China.
| | - W L Li
- College of Science, Xi'an University of Science and Technology, Xi'an 710054, China.
| | - You X
- College of Science, Xi'an University of Science and Technology, Xi'an 710054, China.
| | - W Y Xu
- College of Science, Xi'an University of Science and Technology, Xi'an 710054, China.
| | - Q Cheng
- College of Science, Xi'an University of Science and Technology, Xi'an 710054, China.
| | - D X Li
- College of Science, Xi'an University of Science and Technology, Xi'an 710054, China.
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19
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Topological Structure of the Order Parameter of Unconventional Superconductors Based on d- and f- Elements. Symmetry (Basel) 2023. [DOI: 10.3390/sym15020376] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
The superconducting order parameter (SOP) of a triplet superconductor UTe2 was constructed using the topological space group approach, in which, in contrast to phenomenological and topological approaches, the single pair function and phase winding in condensate are different quantities. The connection between them is investigated for the D2h point group and the m′m′m magnetic group. It is shown how a non-unitary pair function of UTe2 can be constructed using one-dimensional real irreducible representations and Ginzburg–Landau phase winding. It is also shown that the total phase winding is non-zero in magnetic symmetry only. Experimental data on the superconducting order parameter of topological superconductors UPt3, Sr2RuO4, LaPt3P, and UTe2 are considered and peculiarities of their nodal structures are connected with the theoretical results of the topological space group approach.
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20
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Shang T, Zhao J, Hu LH, Ma J, Gawryluk DJ, Zhu X, Zhang H, Zhen Z, Yu B, Xu Y, Zhan Q, Pomjakushina E, Shi M, Shiroka T. Unconventional superconductivity in topological Kramers nodal-line semimetals. SCIENCE ADVANCES 2022; 8:eabq6589. [PMID: 36306356 PMCID: PMC9616505 DOI: 10.1126/sciadv.abq6589] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/24/2022] [Accepted: 09/09/2022] [Indexed: 06/16/2023]
Abstract
Crystalline symmetry is a defining factor of the electronic band topology in solids, where many-body interactions often induce a spontaneous breaking of symmetry. Superconductors lacking an inversion center are among the best systems to study such effects or even to achieve topological superconductivity. Here, we demonstrate that TRuSi materials (with T a transition metal) belong to this class. Their bulk normal states behave as three-dimensional Kramers nodal-line semimetals, characterized by large antisymmetric spin-orbit couplings and by hourglass-like dispersions. Our muon-spin spectroscopy measurements show that certain TRuSi compounds spontaneously break the time-reversal symmetry at the superconducting transition, while unexpectedly showing a fully gapped superconductivity. Their unconventional behavior is consistent with a unitary (s + ip) pairing, reflecting a mixture of spin singlets and spin triplets. By combining an intrinsic time-reversal symmetry-breaking superconductivity with nontrivial electronic bands, TRuSi compounds provide an ideal platform for investigating the rich interplay between unconventional superconductivity and the exotic properties of Kramers nodal-line/hourglass fermions.
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Affiliation(s)
- Tian Shang
- Key Laboratory of Polar Materials and Devices (MOE), School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Jianzhou Zhao
- Co-Innovation Center for New Energetic Materials, Southwest University of Science and Technology, Mianyang 621010, China
| | - Lun-Hui Hu
- Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA
| | - Junzhang Ma
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong
| | - Dariusz Jakub Gawryluk
- Laboratory for Multiscale Materials Experiments, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
| | - Xiaoyan Zhu
- Key Laboratory of Polar Materials and Devices (MOE), School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Hui Zhang
- Key Laboratory of Polar Materials and Devices (MOE), School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Zhixuan Zhen
- Key Laboratory of Polar Materials and Devices (MOE), School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Bocheng Yu
- Key Laboratory of Polar Materials and Devices (MOE), School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Yang Xu
- Key Laboratory of Polar Materials and Devices (MOE), School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Qingfan Zhan
- Key Laboratory of Polar Materials and Devices (MOE), School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
| | - Ekaterina Pomjakushina
- Laboratory for Multiscale Materials Experiments, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
| | - Ming Shi
- Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
| | - Toni Shiroka
- Laboratory for Muon-Spin Spectroscopy, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
- Laboratorium für Festkörperphysik, ETH Zürich, CH-8093 Zürich, Switzerland
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21
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Huang GH, Xu ZF, Wu Z. Intrinsic Anomalous Hall Effect in a Bosonic Chiral Superfluid. PHYSICAL REVIEW LETTERS 2022; 129:185301. [PMID: 36374672 DOI: 10.1103/physrevlett.129.185301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Revised: 08/25/2022] [Accepted: 10/11/2022] [Indexed: 06/16/2023]
Abstract
The anomalous Hall effect has had a profound influence on the understanding of many electronic topological materials but is much less studied in their bosonic counterparts. We predict that an intrinsic anomalous Hall effect exists in a recently realized bosonic chiral superfluid, a p-orbital Bose-Einstein condensate in a 2D hexagonal boron nitride optical lattice [Wang et al., Nature (London) 596, 227 (2021)NATUAS0028-083610.1038/s41586-021-03702-0]. We evaluate the frequency-dependent Hall conductivity within a multi-orbital Bose-Hubbard model that accurately captures the real experimental system. We find that in the high frequency limit, the Hall conductivity is determined by finite loop current correlations on the s-orbital residing sublattice, the latter a defining feature of the system's chirality. In the opposite limit, the dc Hall conductivity can trace its origin back to the noninteracting band Berry curvature at the condensation momentum, although the contribution from atomic interactions can be significant. We discuss available experimental probes to observe this intrinsic anomalous Hall effect at both zero and finite frequencies.
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Affiliation(s)
- Guan-Hua Huang
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Zhi-Fang Xu
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Zhigang Wu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
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22
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Microstructure and Anisotropic Order Parameter of Boron-Doped Nanocrystalline Diamond Films. CRYSTALS 2022. [DOI: 10.3390/cryst12081031] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
Unconventional superconductivity in heavily boron-doped nanocrystalline diamond films (HBDDF) produced a significant amount of interest. However, the exact pairing mechanism has not been understood due to a lack of understanding of crystal symmetry, which is broken at the grain boundaries. The superconducting order parameter (Δ) of HBDDF is believed to be anisotropic since boron atoms form a complex structure with carbon and introduce spin-orbit coupling to the diamond system. From ultra-high resolution transmission electron microscopy, the internal symmetry of the grain boundary structure of HBDDF is revealed, which can explain these films’ unconventional superconducting transport features. Here, we show the signature of the anisotropic Δ in HBDDF by breaking the structural symmetry in a layered microstructure, enabling a Rashba-type spin-orbit coupling. The superlattice-like structure in diamond describes a modulation that explains strong insulator peak features observed in temperature-dependent resistance, a transition of the magnetic field-dependent resistance, and their oscillatory, as well as angle-dependent, features. Overall, the interface states of the diamond films can be explained by the well-known Shockley model describing the layers connected by vortex-like structures, hence forming a topologically protected system.
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23
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Wolf S, Di Sante D, Schwemmer T, Thomale R, Rachel S. Triplet Superconductivity from Nonlocal Coulomb Repulsion in an Atomic Sn Layer Deposited onto a Si(111) Substrate. PHYSICAL REVIEW LETTERS 2022; 128:167002. [PMID: 35522509 DOI: 10.1103/physrevlett.128.167002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2021] [Accepted: 03/29/2022] [Indexed: 06/14/2023]
Abstract
Atomic layers deposited on semiconductor substrates introduce a platform for the realization of the extended electronic Hubbard model, where the consideration of electronic repulsion beyond the on-site term is paramount. Recently, the onset of superconductivity at 4.7 K has been reported in the hole-doped triangular lattice of tin atoms on a silicon substrate. Through renormalization group methods designed for weak and intermediate coupling, we investigate the nature of the superconducting instability in hole-doped Sn/Si(111). We find that the extended Hubbard nature of interactions is crucial to yield triplet pairing, which is f-wave (p-wave) for moderate (higher) hole doping. In light of persisting challenges to tailor triplet pairing in an electronic material, our finding promises to pave unprecedented ways for engineering unconventional triplet superconductivity.
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Affiliation(s)
- Sebastian Wolf
- School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia
| | - Domenico Di Sante
- Department of Physics and Astronomy, University of Bologna, 40127 Bologna, Italy
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Tilman Schwemmer
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland Campus Süd, Würzburg 97074, Germany
| | - Ronny Thomale
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland Campus Süd, Würzburg 97074, Germany
| | - Stephan Rachel
- School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia
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24
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Aoki D, Brison JP, Flouquet J, Ishida K, Knebel G, Tokunaga Y, Yanase Y. Unconventional superconductivity in UTe 2. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:243002. [PMID: 35203074 DOI: 10.1088/1361-648x/ac5863] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2021] [Accepted: 02/24/2022] [Indexed: 06/14/2023]
Abstract
The novel spin-triplet superconductor candidate UTe2was discovered only recently at the end of 2018 and already attracted enormous attention. We review key experimental and theoretical progress which has been achieved in different laboratories. UTe2is a heavy-fermion paramagnet, but following the discovery of superconductivity, it has been expected to be close to a ferromagnetic instability, showing many similarities to the U-based ferromagnetic superconductors, URhGe and UCoGe. This view might be too simplistic. The competition between different types of magnetic interactions and the duality between the local and itinerant character of the 5fUranium electrons, as well as the shift of the U valence appear as key parameters in the rich phase diagrams discovered recently under extreme conditions like low temperature, high magnetic field, and pressure. We discuss macroscopic and microscopic experiments at low temperature to clarify the normal phase properties at ambient pressure for field applied along the three axis of this orthorhombic structure. Special attention will be given to the occurrence of a metamagnetic transition atHm= 35 T for a magnetic field applied along the hard magnetic axisb. Adding external pressure leads to strong changes in the magnetic and electronic properties with a direct feedback on superconductivity. Attention is paid on the possible evolution of the Fermi surface as a function of magnetic field and pressure. Superconductivity in UTe2is extremely rich, exhibiting various unconventional behaviors which will be highlighted. It shows an exceptionally huge superconducting upper critical field with a re-entrant behavior under magnetic field and the occurrence of multiple superconducting phases in the temperature-field-pressure phase diagrams. There is evidence for spin-triplet pairing. Experimental indications exist for chiral superconductivity and spontaneous time reversal symmetry breaking in the superconducting state. Different theoretical approaches will be described. Notably we discuss that UTe2is a possible example for the realization of a fascinating topological superconductor. Exploring superconductivity in UTe2reemphasizes that U-based heavy fermion compounds give unique examples to study and understand the strong interplay between the normal and superconducting properties in strongly correlated electron systems.
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Affiliation(s)
- D Aoki
- IMR, Tohoku University, Oarai, Ibaraki, 311-1313, Japan
| | - J-P Brison
- Univ. Grenoble Alpes, CEA, Grenoble INP, IRIG, PHELIQS, F-38000 Grenoble, France
| | - J Flouquet
- Univ. Grenoble Alpes, CEA, Grenoble INP, IRIG, PHELIQS, F-38000 Grenoble, France
| | - K Ishida
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
| | - G Knebel
- Univ. Grenoble Alpes, CEA, Grenoble INP, IRIG, PHELIQS, F-38000 Grenoble, France
| | - Y Tokunaga
- ASRC, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan
| | - Y Yanase
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
- Institute for Molecular Science, Okazaki 444-8585, Japan
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25
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Makarov D, Volkov OM, Kákay A, Pylypovskyi OV, Budinská B, Dobrovolskiy OV. New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2101758. [PMID: 34705309 PMCID: PMC11469131 DOI: 10.1002/adma.202101758] [Citation(s) in RCA: 22] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2021] [Revised: 05/16/2021] [Indexed: 06/13/2023]
Abstract
Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro- and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-ready prototypes and eventual products.
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Affiliation(s)
- Denys Makarov
- Helmholtz‐Zentrum Dresden ‐ Rossendorf e.V.Institute of Ion Beam Physics and Materials Research01328DresdenGermany
| | - Oleksii M. Volkov
- Helmholtz‐Zentrum Dresden ‐ Rossendorf e.V.Institute of Ion Beam Physics and Materials Research01328DresdenGermany
| | - Attila Kákay
- Helmholtz‐Zentrum Dresden ‐ Rossendorf e.V.Institute of Ion Beam Physics and Materials Research01328DresdenGermany
| | - Oleksandr V. Pylypovskyi
- Helmholtz‐Zentrum Dresden ‐ Rossendorf e.V.Institute of Ion Beam Physics and Materials Research01328DresdenGermany
- Kyiv Academic UniversityKyiv03142Ukraine
| | - Barbora Budinská
- Superconductivity and Spintronics LaboratoryNanomagnetism and MagnonicsFaculty of PhysicsUniversity of ViennaVienna1090Austria
| | - Oleksandr V. Dobrovolskiy
- Superconductivity and Spintronics LaboratoryNanomagnetism and MagnonicsFaculty of PhysicsUniversity of ViennaVienna1090Austria
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26
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Can O, Zhang XX, Kallin C, Franz M. Probing Time Reversal Symmetry Breaking Topological Superconductivity in Twisted Double Layer Copper Oxides with Polar Kerr Effect. PHYSICAL REVIEW LETTERS 2021; 127:157001. [PMID: 34677994 DOI: 10.1103/physrevlett.127.157001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2021] [Accepted: 08/23/2021] [Indexed: 06/13/2023]
Abstract
Recent theoretical work predicted the emergence of a chiral topological superconducting phase with spontaneously broken time reversal symmetry in a twisted bilayer composed of two high-T_{c} cuprate monolayers such as Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}. Here, we identify a large intrinsic Hall response that can be probed through the polar Kerr effect measurement as a convenient signature of the T-broken phase. Our modeling predicts the Kerr angle θ_{K} to be in the range of 10-100 μrad, which is a factor of 10^{3} to 10^{4} times larger than what is expected for the leading chiral superconductor candidate Sr_{2}RuO_{4}. In addition, we show that the optical Hall conductivity σ_{H}(ω) can be used to distinguish between the topological d_{x^{2}-y^{2}}±id_{xy} phase and the d_{x^{2}-y^{2}}±is phase, which is also expected to be present in the phase diagram but is topologically trivial.
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Affiliation(s)
- Oguzhan Can
- Department of Physics and Astronomy and Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
| | - Xiao-Xiao Zhang
- Department of Physics and Astronomy and Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
| | - Catherine Kallin
- Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Marcel Franz
- Department of Physics and Astronomy and Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada
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27
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Chiu SP, Tsuei CC, Yeh SS, Zhang FC, Kirchner S, Lin JJ. Observation of triplet superconductivity in CoSi 2/TiSi 2 heterostructures. SCIENCE ADVANCES 2021; 7:7/29/eabg6569. [PMID: 34272237 PMCID: PMC8284886 DOI: 10.1126/sciadv.abg6569] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2021] [Accepted: 06/03/2021] [Indexed: 05/22/2023]
Abstract
Unconventional superconductivity and, in particular, triplet superconductivity have been front and center of topological materials and quantum technology research. Here, we report our observation of triplet pairing in nonmagnetic CoSi2/TiSi2 heterostructures on silicon. CoSi2 undergoes a sharp superconducting transition at a critical temperature T c ≃ 1.5 K, while TiSi2 is a normal metal. We investigate conductance spectra of both two-terminal CoSi2/TiSi2 contact junctions and three-terminal T-shaped CoSi2/TiSi2 superconducting proximity structures. Below T c, we observe (i) a narrow zero-bias conductance peak on top of a broad hump, accompanied by two symmetric side dips in the contact junctions, (ii) a narrow zero-bias conductance peak in T-shaped structures, and (iii) hysteresis in the junction magnetoresistance. These three independent and complementary observations point to chiral p-wave pairing in CoSi2/TiSi2 heterostructures. The excellent fabrication compatibility of CoSi2 and TiSi2 with present-day silicon-based integrated-circuit technology suggests their potential use in scalable quantum-computing devices.
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Affiliation(s)
- Shao-Pin Chiu
- Institute of Physics and Center for Emergent Functional Matter Science, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan
| | - C C Tsuei
- IBM Thomas J. Watson Research Centers, Yorktown Heights, NY 10598, USA
- Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan
| | - Sheng-Shiuan Yeh
- Institute of Physics and Center for Emergent Functional Matter Science, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan
- International College of Semiconductor Technology, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan
| | - Fu-Chun Zhang
- Kavli Institute for Theoretical Sciences and CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Stefan Kirchner
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027, China.
- Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Juhn-Jong Lin
- Institute of Physics and Center for Emergent Functional Matter Science, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan.
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan
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28
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Bae S, Kim H, Eo YS, Ran S, Liu IL, Fuhrman WT, Paglione J, Butch NP, Anlage SM. Anomalous normal fluid response in a chiral superconductor UTe 2. Nat Commun 2021; 12:2644. [PMID: 33976162 PMCID: PMC8113495 DOI: 10.1038/s41467-021-22906-6] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2020] [Accepted: 04/06/2021] [Indexed: 11/13/2022] Open
Abstract
Chiral superconductors have been proposed as one pathway to realize Majorana normal fluid at its boundary. However, the long-sought 2D and 3D chiral superconductors with edge and surface Majorana normal fluid are yet to be conclusively found. Here, we report evidence for a chiral spin-triplet pairing state of UTe2 with surface normal fluid response. The microwave surface impedance of the UTe2 crystal was measured and converted to complex conductivity, which is sensitive to both normal and superfluid responses. The anomalous residual normal fluid conductivity supports the presence of a significant normal fluid response. The superfluid conductivity follows the temperature behavior predicted for an axial spin-triplet state, which is further narrowed down to a chiral spin-triplet state with evidence of broken time-reversal symmetry. Further analysis excludes trivial origins for the observed normal fluid response. Our findings suggest that UTe2 can be a new platform to study exotic topological excitations in higher dimension.
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Affiliation(s)
- Seokjin Bae
- Maryland Quantum Materials Center, Department of Physics, University of Maryland, College Park, MD, USA.
- Materials Research Laboratory, University of Illinois Urbana-Champaign, Urbana, IL, USA.
| | - Hyunsoo Kim
- Maryland Quantum Materials Center, Department of Physics, University of Maryland, College Park, MD, USA
- Department of Physics and Astronomy, Texas Tech University, Lubbock, TX, USA
| | - Yun Suk Eo
- Maryland Quantum Materials Center, Department of Physics, University of Maryland, College Park, MD, USA
| | - Sheng Ran
- Maryland Quantum Materials Center, Department of Physics, University of Maryland, College Park, MD, USA
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, USA
- Department of Physics, Washington University, St. Louis, MO, USA
| | - I-Lin Liu
- Maryland Quantum Materials Center, Department of Physics, University of Maryland, College Park, MD, USA
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, USA
| | - Wesley T Fuhrman
- Maryland Quantum Materials Center, Department of Physics, University of Maryland, College Park, MD, USA
| | - Johnpierre Paglione
- Maryland Quantum Materials Center, Department of Physics, University of Maryland, College Park, MD, USA
- The Canadian Institute for Advanced Research, Toronto, ON, Canada
| | - Nicholas P Butch
- Maryland Quantum Materials Center, Department of Physics, University of Maryland, College Park, MD, USA
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, USA
| | - Steven M Anlage
- Maryland Quantum Materials Center, Department of Physics, University of Maryland, College Park, MD, USA.
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29
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Biswas PK, Ghosh SK, Zhao JZ, Mayoh DA, Zhigadlo ND, Xu X, Baines C, Hillier AD, Balakrishnan G, Lees MR. Chiral singlet superconductivity in the weakly correlated metal LaPt 3P. Nat Commun 2021; 12:2504. [PMID: 33947862 PMCID: PMC8097077 DOI: 10.1038/s41467-021-22807-8] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2020] [Accepted: 03/30/2021] [Indexed: 11/09/2022] Open
Abstract
Chiral superconductors are novel topological materials with finite angular momentum Cooper pairs circulating around a unique chiral axis, thereby spontaneously breaking time-reversal symmetry. They are rather scarce and usually feature triplet pairing: a canonical example is the chiral p-wave state realized in the A-phase of superfluid He3. Chiral triplet superconductors are, however, topologically fragile with the corresponding gapless boundary modes only weakly protected against symmetry-preserving perturbations in contrast to their singlet counterparts. Using muon spin relaxation measurements, here we report that the weakly correlated pnictide compound LaPt3P has the two key features of a chiral superconductor: spontaneous magnetic fields inside the superconducting state indicating broken time-reversal symmetry and low temperature linear behaviour in the superfluid density indicating line nodes in the order parameter. Using symmetry analysis, first principles band structure calculation and mean-field theory, we unambiguously establish that the superconducting ground state of LaPt3P is a chiral d-wave singlet.
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Affiliation(s)
- P K Biswas
- ISIS Pulsed Neutron and Muon Source, STFC Rutherford Appleton Laboratory, Harwell Campus, Didcot, Oxfordshire, UK.
| | - S K Ghosh
- School of Physical Sciences, University of Kent, Canterbury, UK.
| | - J Z Zhao
- Co-Innovation Center for New Energetic Materials, Southwest University of Science and Technology, Mianyang, China
| | - D A Mayoh
- Physics Department, University of Warwick, Coventry, UK
| | - N D Zhigadlo
- Laboratory for Solid State Physics, ETH Zurich, Zurich, Switzerland.,CrystMat Company, Zurich, Switzerland
| | - Xiaofeng Xu
- Department of Applied Physics, Zhejiang University of Technology, Hangzhou, China
| | - C Baines
- Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, Villigen PSI, Switzerland
| | - A D Hillier
- ISIS Pulsed Neutron and Muon Source, STFC Rutherford Appleton Laboratory, Harwell Campus, Didcot, Oxfordshire, UK
| | | | - M R Lees
- Physics Department, University of Warwick, Coventry, UK
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30
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Samarawickrama P, Dulal R, Fu Z, Erugu U, Wang W, Ackerman J, Leonard B, Tang J, Chien T, Tian J. Two-Dimensional 2M-WS 2 Nanolayers for Superconductivity. ACS OMEGA 2021; 6:2966-2972. [PMID: 33553915 PMCID: PMC7860099 DOI: 10.1021/acsomega.0c05327] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/01/2020] [Accepted: 01/08/2021] [Indexed: 06/12/2023]
Abstract
Recently, a newly discovered VIB group transition metal dichalcogenide (TMD) material, 2M-WS2, has attracted extensive attention due to its interesting physical properties such as topological superconductivity, nodeless superconductivity, and anisotropic Majorana bound states. However, the techniques to grow high-quality 2M-WS2 bulk crystals and the study of their physical properties at the nanometer scale are still limited. In this work, we report a new route to grow high-quality 2M-WS2 single crystals and the observation of superconductivity in its thin layers. The crystal structure of the as-grown 2M-WS2 crystals was determined by X-ray diffraction (XRD) and scanning tunneling microscopy (STM). The chemical composition of the 2M-WS2 crystals was determined by energy dispersive X-ray spectroscopy (EDS) analysis. At 77 K, we observed the spatial variation of the local tunneling conductance (dI/dV) of the 2M-WS2 thin flakes by scanning tunneling spectroscopy (STS). Our low temperature transport measurements demonstrate clear signatures of superconductivity of a 25 nm-thick 2M-WS2 flake with a critical temperature (T C) of ∼8.5 K and an upper critical field of ∼2.5 T at T = 1.5 K. Our work may pave new opportunities in studying the topological superconductivity at the atomic scale in simple 2D TMD materials.
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Affiliation(s)
- Piumi Samarawickrama
- Department
of Physics & Astronomy, University of
Wyoming, Laramie, Wyoming 82071, United States
| | - Rabindra Dulal
- Department
of Physics & Astronomy, University of
Wyoming, Laramie, Wyoming 82071, United States
| | - Zhuangen Fu
- Department
of Physics & Astronomy, University of
Wyoming, Laramie, Wyoming 82071, United States
| | - Uppalaiah Erugu
- Department
of Physics & Astronomy, University of
Wyoming, Laramie, Wyoming 82071, United States
| | - Wenyong Wang
- Department
of Physics & Astronomy, University of
Wyoming, Laramie, Wyoming 82071, United States
| | - John Ackerman
- Department
of Chemical Engineering, University of Wyoming, Laramie, Wyoming 82071, United States
- Resonant
Sciences, Beavercreek, Ohio 45430, United
States
| | - Brian Leonard
- Department
of Chemistry, University of Wyoming, Laramie, Wyoming 82071, United States
| | - Jinke Tang
- Department
of Physics & Astronomy, University of
Wyoming, Laramie, Wyoming 82071, United States
| | - TeYu Chien
- Department
of Physics & Astronomy, University of
Wyoming, Laramie, Wyoming 82071, United States
| | - Jifa Tian
- Department
of Physics & Astronomy, University of
Wyoming, Laramie, Wyoming 82071, United States
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31
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Ghosh SK, Smidman M, Shang T, Annett JF, Hillier AD, Quintanilla J, Yuan H. Recent progress on superconductors with time-reversal symmetry breaking. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 33:033001. [PMID: 32721940 DOI: 10.1088/1361-648x/abaa06] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2019] [Accepted: 07/28/2020] [Indexed: 06/11/2023]
Abstract
Superconductivity and magnetism are adversarial states of matter. The presence of spontaneous magnetic fields inside the superconducting state is, therefore, an intriguing phenomenon prompting extensive experimental and theoretical research. In this review, we discuss recent experimental discoveries of unconventional superconductors which spontaneously break time-reversal symmetry and theoretical efforts in understanding their properties. We discuss the main experimental probes and give an extensive account of theoretical approaches to understand the order parameter symmetries and the corresponding pairing mechanisms, including the importance of multiple bands.
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Affiliation(s)
- Sudeep Kumar Ghosh
- Physics of Quantum Materials, School of Physical Sciences, University of Kent, Canterbury CT2 7NH, United Kingdom
| | - Michael Smidman
- Center for Correlated Matter and Department of Physics, Zhejiang University, Hangzhou 310058, People's Republic of China
- Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, People's Republic of China
| | - Tian Shang
- Laboratory for Multiscale Materials Experiments, Paul Scherrer Institut, Villigen CH-5232, Switzerland
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - James F Annett
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - Adrian D Hillier
- ISIS Facility, STFC Rutherford Appleton Laboratory, Harwell Science and Innovation Campus, Didcot OX11 0QX, United Kingdom
| | - Jorge Quintanilla
- Physics of Quantum Materials, School of Physical Sciences, University of Kent, Canterbury CT2 7NH, United Kingdom
| | - Huiqiu Yuan
- Center for Correlated Matter and Department of Physics, Zhejiang University, Hangzhou 310058, People's Republic of China
- Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, People's Republic of China
- State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou 310027, People's Republic of China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People's Republic of China
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32
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Wu X, Ming F, Smith TS, Liu G, Ye F, Wang K, Johnston S, Weitering HH. Superconductivity in a Hole-Doped Mott-Insulating Triangular Adatom Layer on a Silicon Surface. PHYSICAL REVIEW LETTERS 2020; 125:117001. [PMID: 32976011 DOI: 10.1103/physrevlett.125.117001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2020] [Accepted: 08/07/2020] [Indexed: 06/11/2023]
Abstract
Adsorption of one-third monolayer of Sn on an atomically clean Si(111) substrate produces a two-dimensional triangular adatom lattice with one unpaired electron per site. This dilute adatom reconstruction is an antiferromagnetic Mott insulator; however, the system can be modulation doped and metallized using heavily doped p-type Si(111) substrates. Here, we show that the hole-doped dilute adatom layer on a degenerately doped p-type Si(111) wafer is superconducting with a critical temperature of 4.7±0.3 K. While a phonon-mediated coupling scenario would be consistent with the observed T_{c}, Mott correlations in the Sn-derived dangling-bond surface state could suppress the s-wave pairing channel. The latter suggests that the superconductivity in this triangular adatom lattice may be unconventional.
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Affiliation(s)
- Xuefeng Wu
- Department of Physics, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China
| | - Fangfei Ming
- State Key Laboratory of Optoelectronic Materials and Technologies, School of Electronics and Information Technology and Guangdong Province Key Laboratory of Display Material and Technology, Sun Yat-sen University, Guangzhou 510275, China
| | - Tyler S Smith
- Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Guowei Liu
- Department of Physics, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China
| | - Fei Ye
- Department of Physics, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China
| | - Kedong Wang
- Department of Physics, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China
| | - Steven Johnston
- Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Hanno H Weitering
- Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA
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33
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Perfetto E, Stefanucci G. Floquet Topological Phase of Nondriven p-Wave Nonequilibrium Excitonic Insulators. PHYSICAL REVIEW LETTERS 2020; 125:106401. [PMID: 32955296 DOI: 10.1103/physrevlett.125.106401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2020] [Accepted: 08/14/2020] [Indexed: 06/11/2023]
Abstract
The nontrivial topology of p-wave superfluids makes these systems attractive candidates in information technology. In this work we report on the topological state of a p-wave nonequilibrium excitonic insulator (NEQ-EI) and show how to steer a nontopological band insulator with bright p excitons toward this state by a suitable laser pulse, thus achieving a dynamical topological phase transition. The underlying mechanism behind the transition is the broken gauge-symmetry of the NEQ-EI which causes self-sustained persistent oscillations of the excitonic condensate and hence a Floquet topological state for high enough exciton densities. We show the formation of Floquet Majorana modes at the boundaries of the open system and discuss unique topological spectral signatures for time-resolved ARPES experiments. We emphasize that the topological properties of a p-wave NEQ-EI arise exclusively from the electron-hole Coulomb interaction as the system is not driven by external fields.
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Affiliation(s)
- E Perfetto
- Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
- INFN, Sezione di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - G Stefanucci
- Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
- INFN, Sezione di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
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34
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Huang HL, Jeng HT. Orbital ordering and magnetism in layered Perovskite Ruthenate Sr 2RuO 4. Sci Rep 2020; 10:7089. [PMID: 32341446 PMCID: PMC7184627 DOI: 10.1038/s41598-020-63415-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2019] [Accepted: 03/31/2020] [Indexed: 11/17/2022] Open
Abstract
Local density approximation plus on-site Coulomb interaction U electronic structure calculations reveal that layered perovskite oxide Sr2RuO4 exhibits the ferromagnetic (FM) half-metallic ground state, which is nearly degenerate with the antiferromagnetic (AFM) phase with a slightly higher total energy. The nearly degenerate FM/AFM total energies provide a reasonable explanation for the experimentally observed spin-fluctuation. In addition, a dumbbell-shape 4d − t2g recombined dxz − dyz orbital ordering on the Ru sublattice is obtained owing to the on-site Coulomb interaction U associated with the elongated RuO6 octahedron local structure. The discovered orbital ordering is robust against the spin-orbit interaction as well as the surface terminations. Our findings unravel the on-site Coulomb correlation as the driving force of the Ru-4d orbital ordering as well as the inherent magnetic degeneracy.
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Affiliation(s)
- Hung-Lung Huang
- Department of Physics, National Tsing Hua University, Hsinchu, 30013, Taiwan
| | - Horng-Tay Jeng
- Department of Physics, National Tsing Hua University, Hsinchu, 30013, Taiwan. .,Physics Division, National Center for Theoretical Sciences, Hsinchu, 30013, Taiwan. .,Institute of Physics, Academia Sinica, Taipei, 11529, Taiwan.
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35
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Sharma R, Edkins SD, Wang Z, Kostin A, Sow C, Maeno Y, Mackenzie AP, Davis JCS, Madhavan V. Momentum-resolved superconducting energy gaps of Sr 2RuO 4 from quasiparticle interference imaging. Proc Natl Acad Sci U S A 2020; 117:5222-5227. [PMID: 32094178 PMCID: PMC7071898 DOI: 10.1073/pnas.1916463117] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Sr2RuO4 has long been the focus of intense research interest because of conjectures that it is a correlated topological superconductor. It is the momentum space (k-space) structure of the superconducting energy gap [Formula: see text] on each band i that encodes its unknown superconducting order parameter. However, because the energy scales are so low, it has never been possible to directly measure the [Formula: see text] of Sr2RuO4 Here, we implement Bogoliubov quasiparticle interference (BQPI) imaging, a technique capable of high-precision measurement of multiband [Formula: see text] At T = 90 mK, we visualize a set of Bogoliubov scattering interference wavevectors [Formula: see text] consistent with eight gap nodes/minima that are all closely aligned to the [Formula: see text] crystal lattice directions on both the α and β bands. Taking these observations in combination with other very recent advances in directional thermal conductivity [E. Hassinger et al., Phys. Rev. X 7, 011032 (2017)], temperature-dependent Knight shift [A. Pustogow et al., Nature 574, 72-75 (2019)], time-reversal symmetry conservation [S. Kashiwaya et al., Phys. Rev B, 100, 094530 (2019)], and theory [A. T. Rømer et al., Phys. Rev. Lett. 123, 247001 (2019); H. S. Roising, T. Scaffidi, F. Flicker, G. F. Lange, S. H. Simon, Phys. Rev. Res. 1, 033108 (2019); and O. Gingras, R. Nourafkan, A. S. Tremblay, M. Côté, Phys. Rev. Lett. 123, 217005 (2019)], the BQPI signature of Sr2RuO4 appears most consistent with [Formula: see text] having [Formula: see text] [Formula: see text] symmetry.
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Affiliation(s)
- Rahul Sharma
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, NY 14853
- Condensed Matter Physics and Material Science Department, Brookhaven National Laboratory, Upton, NY 11973
| | - Stephen D Edkins
- Department of Applied Physics, Stanford University, Stanford, CA 94305
| | - Zhenyu Wang
- Department of Physics, University of Illinois, Urbana, IL 61801
| | - Andrey Kostin
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, NY 14853
- Condensed Matter Physics and Material Science Department, Brookhaven National Laboratory, Upton, NY 11973
| | - Chanchal Sow
- Department of Physics, Kyoto University, 606-8502 Kyoto, Japan
- Department of Physics, Indian Institute of Technology-Kanpur, 208016 Uttar Pradesh, India
| | - Yoshiteru Maeno
- Department of Physics, Kyoto University, 606-8502 Kyoto, Japan
| | - Andrew P Mackenzie
- Physics of Quantum Materials Department, Max Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany
- School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews KY16 9SS, United Kingdom
| | - J C Séamus Davis
- Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University, Ithaca, NY 14853;
- Physics of Quantum Materials Department, Max Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany
- Clarendon Laboratory, University of Oxford, Oxford OX1 3PU, United Kingdom
- Department of Physics, University College Cork, T12R5C Cork, Ireland
| | - Vidya Madhavan
- Department of Physics, University of Illinois, Urbana, IL 61801;
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36
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Wu TC, Pal HK, Hosur P, Foster MS. Power-Law Temperature Dependence of the Penetration Depth in a Topological Superconductor Due to Surface States. PHYSICAL REVIEW LETTERS 2020; 124:067001. [PMID: 32109094 DOI: 10.1103/physrevlett.124.067001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2019] [Accepted: 01/27/2020] [Indexed: 06/10/2023]
Abstract
We study the temperature dependence of the magnetic penetration depth in a 3D topological superconductor (TSC), incorporating the paramagnetic current due to the surface states. A TSC is predicted to host a gapless 2D surface Majorana fluid. In addition to the bulk-dominated London response, we identify a T^{3} power-law-in-temperature contribution from the surface, valid in the low-temperature limit. Our system is fully gapped in the bulk, and should be compared to bulk nodal superconductivity, which also exhibits power-law behavior. Power-law temperature dependence of the penetration depth can be one indicator of topological superconductivity.
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Affiliation(s)
- Tsz Chun Wu
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Hridis K Pal
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Pavan Hosur
- Texas Center for Superconductivity and Department of Physics, University of Houston, Houston, Texas 77204, USA
| | - Matthew S Foster
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
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37
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Shomali Z, Asgari R. Spin transfer torque and exchange coupling in Josephson junctions with ferromagnetic superconductor reservoirs. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:035806. [PMID: 31585455 DOI: 10.1088/1361-648x/ab4b1d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
In this paper, the spin transfer torque (STT) and the exchange coupling of the Josephson junctions containing the interesting cases of diffusive/ballistic-triplet/singlet ferromagnetic superconductor (FS) materials are investigated. First, the diffusive FS1/F c /FS2 structures with F c being a junction consisting of ferromagnetic and normal metal parts as well as insulating barriers are investigated. Secondly, the ballistic Josephson junction containing the triplet chiral p/wave FS reservoirs is studied. Using the Nazarov quantum circuit theory for the diffusive structures, it is found that the antiparallel/parallel or vice versa parallel/antiparallel transition of the favorable exchange coupling takes place due to the appearance of the only out-of-plane STT. Furthermore, the analyze of the phase difference interval in which an interlayer length-induced antiparallel/parallel transition can be occurred, is performed. Afterward, the mentioned ballistic structure is dealt with solving the 16 [Formula: see text] 16 Bogoliubov-de-Gennes equation. It is found that although the exchange fields of the FS are laid in the z and y direction, the STT interestingly exists in all three directions of x, y and z. This exciting finding suggests that the favorable equilibrium configuration concerning the least exchange coupling occurs in the relative exchange field direction different from 0 or [Formula: see text].
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Affiliation(s)
- Zahra Shomali
- Department of Physics, Tarbiat Modares University, PO Box 14115-175, Tehran, Iran. School of Physics, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran
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38
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Li Y, Xu X, Lee MH, Chu MW, Chien CL. Observation of half-quantum flux in the unconventional superconductor β-Bi 2Pd. Science 2019; 366:238-241. [PMID: 31601768 DOI: 10.1126/science.aau6539] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2018] [Revised: 12/26/2018] [Accepted: 09/17/2019] [Indexed: 11/02/2022]
Abstract
Magnetic flux quantization is one of the defining properties of a superconductor. We report the observation of half-integer magnetic flux quantization in mesoscopic rings of superconducting β-Bi2Pd thin films. The half-quantum fluxoid manifests itself as a π phase shift in the quantum oscillation of the superconducting critical temperature. This result verifies unconventional superconductivity of β-Bi2Pd and is consistent with a spin-triplet pairing symmetry. Our findings may have implications for flux quantum bits in the context of quantum computing.
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Affiliation(s)
- Yufan Li
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA.
| | - Xiaoying Xu
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA
| | - M-H Lee
- Center for Condensed Matter Sciences and Center of Atomic Initiative for New Materials, National Taiwan University, Taipei 10617, Taiwan
| | - M-W Chu
- Center for Condensed Matter Sciences and Center of Atomic Initiative for New Materials, National Taiwan University, Taipei 10617, Taiwan
| | - C L Chien
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA. .,Institute of Physics, Academia Sinica, Taipei 11519, Taiwan.,Department of Physics, National Taiwan University, Taipei 10617, Taiwan
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39
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Abstract
The possibility of p-wave pairing in superconductors has been proposed more than five decades ago, but has not yet been convincingly demonstrated. One difficulty is that some p-wave states are thermodynamically indistinguishable from s-wave, while others are very similar to d-wave states. Here we studied the self-field critical current of NdFeAs(O,F) thin films in order to extract absolute values of the London penetration depth, the superconducting energy gap, and the relative jump in specific heat at the superconducting transition temperature, and find that all the deduced physical parameters strongly indicate that NdFeAs(O,F) is a bulk p-wave superconductor. Further investigation revealed that single atomic layer FeSe also shows p-wave pairing. In an attempt to generalize these findings, we re-examined the whole inventory of superfluid density measurements in iron-based superconductors and show quite generally that single-band weak-coupling p-wave superconductivity is exhibited in iron-based superconductors.
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40
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Schlawin F, Jaksch D. Cavity-Mediated Unconventional Pairing in Ultracold Fermionic Atoms. PHYSICAL REVIEW LETTERS 2019; 123:133601. [PMID: 31697538 DOI: 10.1103/physrevlett.123.133601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2019] [Indexed: 06/10/2023]
Abstract
We investigate long-range pairing interactions between ultracold fermionic atoms confined in an optical lattice which are mediated by the coupling to a cavity. In the absence of other perturbations, we find three degenerate pairing symmetries for a two-dimensional square lattice. By tuning a weak local atomic interaction via a Feshbach resonance or by tuning a weak magnetic field, the superfluid system can be driven from a topologically trivial s wave to topologically ordered, chiral superfluids containing Majorana edge states. Our work points out a novel path towards the creation of exotic superfluid states by exploiting the competition between long-range and short-range interactions.
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Affiliation(s)
- Frank Schlawin
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Dieter Jaksch
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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41
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Denisov KS, Rozhansky IV, Averkiev NS, Lähderanta E. Chiral spin ordering of electron gas in solids with broken time reversal symmetry. Sci Rep 2019; 9:10817. [PMID: 31346225 PMCID: PMC6658505 DOI: 10.1038/s41598-019-47274-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2019] [Accepted: 07/12/2019] [Indexed: 11/29/2022] Open
Abstract
In this work we manifest that an electrostatic disorder in conducting systems with broken time reversal symmetry universally leads to a chiral ordering of the electron gas giving rise to skyrmion-like textures in spatial distribution of the electron spin density. We describe a microscopic mechanism underlying the formation of the equilibrium chiral spin textures in two-dimensional systems with spin-orbit interaction and exchange spin splitting. We have obtained analytical expressions for spin-density response functions and have analyzed both local and non-local spin response to electrostatic perturbations for systems with parabolic-like and Dirac electron spectra. With the proposed theory we come up with a concept of controlling spin chirality by electrical means.
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Affiliation(s)
- K S Denisov
- Ioffe Institute, St.Petersburg, 194021, Russia.
- Lappeenranta-Lahti University of Technology, FI-53851, Lappeenranta, Finland.
| | - I V Rozhansky
- Ioffe Institute, St.Petersburg, 194021, Russia
- Lappeenranta-Lahti University of Technology, FI-53851, Lappeenranta, Finland
| | | | - E Lähderanta
- Lappeenranta-Lahti University of Technology, FI-53851, Lappeenranta, Finland
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42
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Daido A, Yoshida T, Yanase Y. Z_{4} Topological Superconductivity in UCoGe. PHYSICAL REVIEW LETTERS 2019; 122:227001. [PMID: 31283273 DOI: 10.1103/physrevlett.122.227001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2019] [Indexed: 06/09/2023]
Abstract
Topological nonsymmorphic crystalline superconductivity (TNCS) is an intriguing phase of matter, offering a platform to study the interplay between topology, superconductivity, and nonsymmorphic crystalline symmetries. Interestingly, some of TNCSs are classified into Z_{4} topological phases, which have unique surface states referred to as a Möbius strip or an hourglass, and they have not been achieved in symmorphic superconductors. However, material realization of Z_{4} TNCS has never been known, to the best of our knowledge. Here, we propose that the paramagnetic superconducting phase of UCoGe under pressure is a promising candidate of Z_{4}-nontrivial TNCS enriched by glide symmetry. We evaluate Z_{4} invariants of UCoGe by deriving the formulas relating Z_{4} invariants to the topology of Fermi surfaces. Applying the formulas and previous ab initio calculations, we clarify that three odd-parity representations out of four are Z_{4}-nontrivial TNCS, whereas the other is also Z_{2}-nontrivial TNCS. We also discuss possible Z_{4} TNCS in CrAs and related materials.
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Affiliation(s)
- Akito Daido
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Tsuneya Yoshida
- Department of Physics, University of Tsukuba, Ibaraki 305-8571, Japan
| | - Youichi Yanase
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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43
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Abstract
Recent work done on the time reversal symmetry (TRS) breaking superconductors is reviewed in this paper. The special attention is paid to Sr 2 RuO 4 believed to be spin triplet chiral p-wave superconductor which break TRS and is expected to posses non-trivial topological properties. The family of TRS breaking superconductors is growing relatively fast, with many of its newly discovered members being non-centrosymmetric. However not only Sr 2 RuO 4 but also many other superconductors which possess center of inversion also break TRS. The TRS is often identified by means of the muon spin relaxation ( μ SR) and the Kerr effect. Both methods effectively measure the appearance of the spontaneous bulk magnetic field below superconducting transition temperature. This compound provides an example of the material whose many band, multi-condensate modeling has enjoyed a number of successes, but the full understanding has not been achieved yet. We discuss in some details the properties of the material. Among them is the Kerr effect and by understanding has resulted in the discovery of the novel mechanism of the phenomenon. The mechanism is universal and thus applicable to all systems with multi-orbital character of states at the Fermi energy.
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44
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Steffens P, Sidis Y, Kulda J, Mao ZQ, Maeno Y, Mazin II, Braden M. Spin Fluctuations in Sr_{2}RuO_{4} from Polarized Neutron Scattering: Implications for Superconductivity. PHYSICAL REVIEW LETTERS 2019; 122:047004. [PMID: 30768293 DOI: 10.1103/physrevlett.122.047004] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2018] [Indexed: 06/09/2023]
Abstract
Triplet pairing in Sr_{2}RuO_{4} was initially suggested based on the hypothesis of strong ferromagnetic spin fluctuations. Using polarized inelastic neutron scattering, we accurately determine the full spectrum of spin fluctuations in Sr_{2}RuO_{4}. Besides the well-studied incommensurate magnetic fluctuations, we do find a sizable quasiferromagnetic signal, quantitatively consistent with all macroscopic and microscopic probes. We use this result to address the possibility of magnetically driven triplet superconductivity in Sr_{2}RuO_{4}. We conclude that, even though the quasiferromagnetic signal is stronger and sharper than previously anticipated, spin fluctuations alone are not enough to generate a triplet state strengthening the need for additional interactions or an alternative pairing scenario.
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Affiliation(s)
- P Steffens
- II. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, D-50937 Köln, Germany
- Institut Laue Langevin, 71 avenue des Martyrs, 38000 Grenoble, France
| | - Y Sidis
- Laboratoire Léon Brillouin, C.E.A./C.N.R.S., F-91191 Gif-sur-Yvette CEDEX, France
| | - J Kulda
- Institut Laue Langevin, 71 avenue des Martyrs, 38000 Grenoble, France
| | - Z Q Mao
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
- Department of Physics, Tulane University, New Orleans, Louisiana 70118, USA
- Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Y Maeno
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - I I Mazin
- Code 6393, Naval Research Laboratory, Washington, DC 20375, USA
| | - M Braden
- II. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, D-50937 Köln, Germany
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45
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Abstract
High-quality single crystals are essentially needed for the investigation of the novel bulk properties of unconventional superconductors. The availability of such crystals grown by the floating-zone method has helped to unveil the unconventional superconductivity of the layered perovskite Sr2RuO4, which is considered as a strong candidate of a topological spin-triplet superconductor. Yet, recent progress of investigations urges further efforts to obtain ultimately high-quality crystalline samples. In this paper, we focus on the method of preparation of feed rods for the floating-zone melting and report on the improvements of the crystal growth. We present details of the improved methods used to obtain crystals with superconducting transition temperatures Tc that are consistently as high as 1.4 K, as well as the properties of these crystals.
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46
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Ran S, Liu IL, Eo YS, Campbell DJ, Neves PM, Fuhrman WT, Saha SR, Eckberg C, Kim H, Graf D, Balakirev F, Singleton J, Paglione J, Butch NP. Extreme magnetic field-boosted superconductivity. NATURE PHYSICS 2019; 15:10.1038/s41567-019-0670-x. [PMID: 34131432 PMCID: PMC8201648 DOI: 10.1038/s41567-019-0670-x] [Citation(s) in RCA: 40] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2019] [Accepted: 08/21/2019] [Indexed: 05/31/2023]
Abstract
Applied magnetic fields underlie exotic quantum states, such as the fractional quantum Hall effect1 and Bose-Einstein condensation of spin excitations2. Superconductivity, however, is inherently antagonistic towards magnetic fields. Only in rare cases3-5 can these effects be mitigated over limited fields, leading to re-entrant superconductivity. Here, we report the coexistence of multiple high-field re-entrant superconducting phases in the spin-triplet superconductor UTe2 (ref. 6). We observe superconductivity in the highest magnetic field range identified for any re-entrant superconductor, beyond 65 T. Although the stability of superconductivity in these high magnetic fields challenges current theoretical models, these extreme properties seem to reflect a new kind of exotic superconductivity rooted in magnetic fluctuations7 and boosted by a quantum dimensional crossover8.
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Affiliation(s)
- Sheng Ran
- Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, MD, USA
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, USA
- Department of Materials Science and Engineering, University of Maryland, College Park, MD, USA
| | - I-Lin Liu
- Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, MD, USA
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, USA
- Department of Materials Science and Engineering, University of Maryland, College Park, MD, USA
| | - Yun Suk Eo
- Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, MD, USA
| | - Daniel J. Campbell
- Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, MD, USA
| | - Paul M. Neves
- Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, MD, USA
| | - Wesley T. Fuhrman
- Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, MD, USA
| | - Shanta R. Saha
- Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, MD, USA
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, USA
| | - Christopher Eckberg
- Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, MD, USA
| | - Hyunsoo Kim
- Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, MD, USA
| | - David Graf
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL, USA
| | - Fedor Balakirev
- National High Magnetic Field Laboratory, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - John Singleton
- National High Magnetic Field Laboratory, Los Alamos National Laboratory, Los Alamos, NM, USA
- Department of Physics, The Clarendon Laboratory, University of Oxford, Oxford, UK
| | - Johnpierre Paglione
- Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, MD, USA
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, USA
| | - Nicholas P. Butch
- Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, MD, USA
- NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, USA
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47
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Mi S, Burset P, Flindt C. Electron waiting times in hybrid junctions with topological superconductors. Sci Rep 2018; 8:16828. [PMID: 30442914 PMCID: PMC6237767 DOI: 10.1038/s41598-018-34776-y] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2018] [Accepted: 10/22/2018] [Indexed: 11/09/2022] Open
Abstract
We investigate the waiting time distributions (WTDs) of superconducting hybrid junctions, considering both conventional and topologically nontrivial superconductors hosting Majorana bound states at their edges. To this end, we employ a scattering matrix formalism that allows us to evaluate the waiting times between the transmissions and reflections of electrons or holes. Specifically, we analyze normal-metal–superconductor (NIS) junctions and NISIN junctions, where Cooper pairs are spatially split into different leads. The distribution of waiting times is sensitive to the simultaneous reflection of electrons and holes, which is enhanced by the zero-energy state in topological superconductors. For the NISIN junctions, the WTDs of trivial superconductors feature a sharp dependence on the applied voltage, while for topological ones they are mostly independent of it. This particular voltage dependence is again connected to the presence of topological edge states, showing that WTDs are a promising tool for identifying topological superconductivity.
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Affiliation(s)
- Shuo Mi
- Department of Applied Physics, Aalto University, 00076, Aalto, Finland. .,Univ. Grenoble Alpes, CEA, INAC-Pheliqs, 38000, Grenoble, France.
| | - Pablo Burset
- Department of Applied Physics, Aalto University, 00076, Aalto, Finland
| | - Christian Flindt
- Department of Applied Physics, Aalto University, 00076, Aalto, Finland
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48
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Yu ZM, Liu Y, Yao Y, Yang SA. Unconventional Pairing Induced Anomalous Transverse Shift in Andreev Reflection. PHYSICAL REVIEW LETTERS 2018; 121:176602. [PMID: 30411955 DOI: 10.1103/physrevlett.121.176602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2017] [Revised: 03/12/2018] [Indexed: 06/08/2023]
Abstract
Superconductors with unconventional pairings have been a fascinating subject of research, for which a central issue is to explore effects that can be used to characterize the pairing. The process of Andreev reflection-the reflection of an electron as a hole at a normal-metal-superconductor interface-offers a basic mechanism to probe the pairing. Here we predict that in Andreev reflection from unconventional superconductors, the reflected hole acquires an anomalous spatial shift normal to the plane of incidence, arising from the unconventional pairing. The transverse shift is sensitive to the superconducting gap structure, exhibiting characteristic features for each pairing type, and can be detected as voltage signals. Our work not only unveils a fundamentally new effect with a novel underlying mechanism, but also suggests a possible new technique capable of probing the structure of unconventional pairings.
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Affiliation(s)
- Zhi-Ming Yu
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
| | - Ying Liu
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
| | - Yugui Yao
- Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Shengyuan A Yang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
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49
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Huang W, Yao H. Possible Three-Dimensional Nematic Odd-Parity Superconductivity in Sr_{2}RuO_{4}. PHYSICAL REVIEW LETTERS 2018; 121:157002. [PMID: 30362809 DOI: 10.1103/physrevlett.121.157002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2018] [Indexed: 06/08/2023]
Abstract
The superconducting pairing in Sr_{2}RuO_{4} is widely considered to be chiral p wave with d[over →]_{k}∼(k_{x}+ik_{y})z[over ^], which belongs to the E_{u} representation of the crystalline D_{4h} group. However, this superconducting order appears hard to reconcile with a number of key experiments. In this Letter, based on symmetry analysis we discuss the possibility of odd-parity pairing with inherent three-dimensional character enforced by the interorbital interlayer coupling and the sizable spin-orbit coupling in the material. We focus on a yet unexplored E_{u} pairing, which contains finite (k_{z}x[over ^], k_{z}y[over ^]) component in the gap function. Under appropriate circumstances a novel time-reversal invariant nematic pairing can be realized. This nematic superconducting state could make contact with some puzzling observations on Sr_{2}RuO_{4}, such as the absence of spontaneous edge current and no evidence of split transitions under uniaxial strains.
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Affiliation(s)
- Wen Huang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Hong Yao
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
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Robins A, Brydon P. Time-reversal symmetry-breaking in noncentrosymmetric superconductors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:405602. [PMID: 30175970 DOI: 10.1088/1361-648x/aade6a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
In this paper we examine the appearance of time-reversal symmetry-breaking (TRSB) states in the bulk and at the surface of a noncentrosymmetric superconductor. We utilize a Ginzburg-Landau theory, with coefficients derived from a microscopic model of the superconductor. We show that suppression of the triplet order parameter at the surface stabilizes a TRSB state by locally tuning the system into the bulk TRSB phase. We compare these results with those from centrosymmetric systems, and examine the appearance of a magnetization at the surface.
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Affiliation(s)
- Allyn Robins
- Department of Physics and MacDiarmid Institute for Advanced Materials and Nanotechnology, University of Otago, PO Box 56, Dunedin 9054, New Zealand
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