1
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Zhou YZ, Chen J, Li ZX, Luo J, Yang J, Guo YF, Wang WH, Zhou R, Zheng GQ. Antiferromagnetic Spin Fluctuations and Unconventional Superconductivity in Topological Superconductor Candidate YPtBi Revealed by ^{195}Pt-NMR. PHYSICAL REVIEW LETTERS 2023; 130:266002. [PMID: 37450816 DOI: 10.1103/physrevlett.130.266002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Revised: 03/22/2023] [Accepted: 05/16/2023] [Indexed: 07/18/2023]
Abstract
We report ^{195}Pt nuclear magnetic resonance (NMR) measurements on topological superconductor candidate YPtBi, which has broken inversion symmetry and topological nontrivial band structures due to the strong spin-orbit coupling. In the normal state, we find that Knight shift K is field- and temperature independent, suggesting that the contribution from the topological bands is very small at low temperatures. However, the spin-lattice relaxation rate 1/T_{1} divided by temperature (T), 1/T_{1}T, increases with decreasing T, implying the existence of antiferromagnetic spin fluctuations. In the superconducting state, no Hebel-Slichter coherence peak is seen below T_{c} and 1/T_{1} follows T^{3} variation, indicating the unconventional superconductivity. The finite spin susceptibility at zero-temperature limit and the anomalous increase of the NMR linewidth below T_{c} point to a mixed state of spin-singlet and spin-triplet (or spin-septet) pairing.
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Affiliation(s)
- Y Z Zhou
- Institute of Physics, Chinese Academy of Sciences, and Beijing National Laboratory for Condensed Matter Physics, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - J Chen
- Institute of Physics, Chinese Academy of Sciences, and Beijing National Laboratory for Condensed Matter Physics, Beijing 100190, China
| | - Z X Li
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - J Luo
- Institute of Physics, Chinese Academy of Sciences, and Beijing National Laboratory for Condensed Matter Physics, Beijing 100190, China
| | - J Yang
- Institute of Physics, Chinese Academy of Sciences, and Beijing National Laboratory for Condensed Matter Physics, Beijing 100190, China
| | - Y F Guo
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- ShanghaiTech Laboratory for Topological Physics, Shanghai 201210, China
| | - W H Wang
- Institute of Physics, Chinese Academy of Sciences, and Beijing National Laboratory for Condensed Matter Physics, Beijing 100190, China
| | - R Zhou
- Institute of Physics, Chinese Academy of Sciences, and Beijing National Laboratory for Condensed Matter Physics, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Guo-Qing Zheng
- Department of Physics, Okayama University, Okayama 700-8530, Japan
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2
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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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3
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Oh H, Agterberg DF, Moon EG. Using Disorder to Identify Bogoliubov Fermi-Surface States. PHYSICAL REVIEW LETTERS 2021; 127:257002. [PMID: 35029417 DOI: 10.1103/physrevlett.127.257002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Accepted: 11/16/2021] [Indexed: 06/14/2023]
Abstract
We argue that a superconducting state with a Fermi surface of Bogoliubov quasiparticles, a Bogoliubov Fermi surface (BG-FS), can be identified by the dependence of physical quantities on disorder. In particular, we show that a linear dependence of the residual density of states at weak disorder distinguishes a BG-FS state from other nodal superconducting states. We further demonstrate the stability of supercurrent against impurities and a characteristic Drude-like behavior of the optical conductivity. Our results can be directly applied to electron irradiation experiments on candidate materials of BG-FSs, including Sr_{2}RuO_{4}, FeSe_{1-x}S_{x}, and UBe_{13}.
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Affiliation(s)
- Hanbit Oh
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea
| | - Daniel F Agterberg
- Department of Physics, University of Wisconsin, Milwaukee, Wisconsin 53201, USA
| | - Eun-Gook Moon
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea
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4
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Jiang YF, Yao H, Yang F. Possible Superconductivity with a Bogoliubov Fermi Surface in a Lightly Doped Kagome U(1) Spin Liquid. PHYSICAL REVIEW LETTERS 2021; 127:187003. [PMID: 34767423 DOI: 10.1103/physrevlett.127.187003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2020] [Revised: 05/22/2021] [Accepted: 09/30/2021] [Indexed: 06/13/2023]
Abstract
Whether the doped t-J model on the Kagome lattice supports exotic superconductivity has not been decisively answered. In this Letter, we propose a new class of variational states for this model and perform a large-scale variational Monte Carlo simulation on it. The proposed variational states are parameterized by the SU(2)-gauge rotation angles, as the SU(2)-gauge structure hidden in the Gutzwiller-projected mean-field Ansatz for the undoped model is broken upon doping. These variational doped states smoothly connect to the previously studied U(1) π-flux or 0-flux states, and energy minimization among them yields a chiral noncentrosymmetric nematic superconducting state with 2×2-enlarged unit cell. Moreover, this pair density wave state possesses a finite Fermi surface for the Bogoliubov quasiparticles. We further study experimentally relevant properties of this intriguing pairing state.
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Affiliation(s)
- Yi-Fan Jiang
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, Menlo Park, California 94025, USA
| | - Hong Yao
- Institute of Advanced Study, Tsinghua University, Beijing 100084, China
- State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Fan Yang
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
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5
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Xie YM, Gao XJ, Xu XY, Zhang CP, Hu JX, Gao JZ, Law KT. Kramers nodal line metals. Nat Commun 2021; 12:3064. [PMID: 34031382 PMCID: PMC8144424 DOI: 10.1038/s41467-021-22903-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2020] [Accepted: 04/06/2021] [Indexed: 11/09/2022] Open
Abstract
Recently, it was pointed out that all chiral crystals with spin-orbit coupling (SOC) can be Kramers Weyl semimetals (KWSs) which possess Weyl points pinned at time-reversal invariant momenta. In this work, we show that all achiral non-centrosymmetric materials with SOC can be a new class of topological materials, which we term Kramers nodal line metals (KNLMs). In KNLMs, there are doubly degenerate lines, which we call Kramers nodal lines (KNLs), connecting time-reversal invariant momenta. The KNLs create two types of Fermi surfaces, namely, the spindle torus type and the octdong type. Interestingly, all the electrons on octdong Fermi surfaces are described by two-dimensional massless Dirac Hamiltonians. These materials support quantized optical conductance in thin films. We further show that KNLMs can be regarded as parent states of KWSs. Therefore, we conclude that all non-centrosymmetric metals with SOC are topological, as they can be either KWSs or KNLMs.
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Affiliation(s)
- Ying-Ming Xie
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
| | - Xue-Jian Gao
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
| | - Xiao Yan Xu
- Department of Physics, University of California at San Diego, La Jolla, CA, USA
| | - Cheng-Ping Zhang
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
| | - Jin-Xin Hu
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
| | - Jason Z Gao
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
| | - K T Law
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China.
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6
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Du D, Manzo S, Zhang C, Saraswat V, Genser KT, Rabe KM, Voyles PM, Arnold MS, Kawasaki JK. Epitaxy, exfoliation, and strain-induced magnetism in rippled Heusler membranes. Nat Commun 2021; 12:2494. [PMID: 33941781 PMCID: PMC8093223 DOI: 10.1038/s41467-021-22784-y] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2020] [Accepted: 03/29/2021] [Indexed: 11/09/2022] Open
Abstract
Single-crystalline membranes of functional materials enable the tuning of properties via extreme strain states; however, conventional routes for producing membranes require the use of sacrificial layers and chemical etchants, which can both damage the membrane and limit the ability to make them ultrathin. Here we demonstrate the epitaxial growth of the cubic Heusler compound GdPtSb on graphene-terminated Al2O3 substrates. Despite the presence of the graphene interlayer, the Heusler films have epitaxial registry to the underlying sapphire, as revealed by x-ray diffraction, reflection high energy electron diffraction, and transmission electron microscopy. The weak Van der Waals interactions of graphene enable mechanical exfoliation to yield free-standing GdPtSb membranes, which form ripples when transferred to a flexible polymer handle. Whereas unstrained GdPtSb is antiferromagnetic, measurements on rippled membranes show a spontaneous magnetic moment at room temperature, with a saturation magnetization of 5.2 bohr magneton per Gd. First-principles calculations show that the coupling to homogeneous strain is too small to induce ferromagnetism, suggesting a dominant role for strain gradients. Our membranes provide a novel platform for tuning the magnetic properties of intermetallic compounds via strain (piezomagnetism and magnetostriction) and strain gradients (flexomagnetism).
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Affiliation(s)
- Dongxue Du
- Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI, USA
| | - Sebastian Manzo
- Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI, USA
| | - Chenyu Zhang
- Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI, USA
| | - Vivek Saraswat
- Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI, USA
| | - Konrad T Genser
- Department of Physics and Astronomy, Rutgers University, New Brunswick, NJ, USA
| | - Karin M Rabe
- Department of Physics and Astronomy, Rutgers University, New Brunswick, NJ, USA
| | - Paul M Voyles
- Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI, USA
| | - Michael S Arnold
- Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI, USA
| | - Jason K Kawasaki
- Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI, USA.
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7
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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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8
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Zhou J, Qi X, Wu Y, Kou SP. Parity anomaly of lattice Maxwell fermions in two spatial dimensions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:405503. [PMID: 32480389 DOI: 10.1088/1361-648x/ab985a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2020] [Accepted: 06/01/2020] [Indexed: 06/11/2023]
Abstract
Unconventional lattice fermions with high degeneracies that are not Weyl or Dirac fermions have attracted increased attention in recent years. In this paper, we consider pseudospin-1 Maxwell fermions and the (2 + 1)-dimensional parity anomaly, which are not constrained by the fermion doubling theorem. We derive the Hall conductivity of a single Maxwell fermion and explain how each Maxwell fermion has a quantized Hall conductance ofe2/h. Parity is spontaneously broken in the effective theory of lattice Maxwell fermions interacting with an (auxiliary) U(1) gauge field, leading to an effective anomaly-induced Chern-Simons theory. An interesting observation about the parity anomaly is that the lattice Maxwell fermions are not constrained by the fermion doubling theorem, so a single Maxwell fermion can exist in a lattice. In addition, our work considers the quantum anomaly in odd-dimensional spinor space.
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Affiliation(s)
- Jiang Zhou
- Department of Physics, Guizhou University, Guiyang 550025, People's Republic of China
| | - Xiaosi Qi
- Department of Physics, Guizhou University, Guiyang 550025, People's Republic of China
| | - Yajie Wu
- School of Science, Xi'an Technological University, Xi'an 710032, People's Republic of China
| | - Su-Peng Kou
- Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
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9
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Boettcher I. Interplay of Topology and Electron-Electron Interactions in Rarita-Schwinger-Weyl semimetals. PHYSICAL REVIEW LETTERS 2020; 124:127602. [PMID: 32281852 DOI: 10.1103/physrevlett.124.127602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2019] [Accepted: 03/11/2020] [Indexed: 06/11/2023]
Abstract
We study, for the first time, the effects of strong short-range electron-electron interactions in generic Rarita-Schwinger-Weyl semimetals hosting spin-3/2 electrons with linear dispersion at a fourfold band crossing point. The emergence of this novel quasiparticle, which is absent in high-energy physics, has recently been confirmed experimentally in the solid state. We combine symmetry considerations and a perturbative renormalization group analysis to discern three interacting phases that are prone to emerge in the strongly correlated regime: The chiral topological semimetal breaks a Z_{2} symmetry and features four Weyl nodes of monopole charge +1 located at vertices of a tetrahedron in momentum space. The s-wave superconducting state opens a Majorana mass gap for the fermions and is the leading superconducting instability. The Weyl semimetal phase removes the fourfold degeneracy and creates two Weyl nodes with either equal or opposite chirality depending on the anisotropy of the band structure. We find that symmetry breaking occurs at weaker coupling if the total monopole charge remains constant across the transition.
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Affiliation(s)
- Igor Boettcher
- Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
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10
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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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11
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Kobayashi S, Yamakage A, Tanaka Y, Sato M. Majorana Multipole Response of Topological Superconductors. PHYSICAL REVIEW LETTERS 2019; 123:097002. [PMID: 31524460 DOI: 10.1103/physrevlett.123.097002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2018] [Indexed: 06/10/2023]
Abstract
In contrast to elementary Majorana particles, emergent Majorana fermions (MFs) in condensed-matter systems may have electromagnetic multipoles. We developed a general theory of magnetic multipoles for helical MFs on time-reversal-invariant superconductors. The results show that the multipole response is governed by crystal symmetry, and that a one-to-one correspondence exists between the symmetry of Cooper pairs and the representation of magnetic multipoles under crystal symmetry. The latter property provides a way to identify unconventional pairing symmetry via the magnetic response of helical MFs. We also find that most helical MFs exhibit a magnetic-dipole response, but those on superconductors with spin-3/2 electrons may display a magnetic-octupole response in leading order, which uniquely characterizes high-spin superconductors. Detection of such an octupole response provides direct evidence of high-spin superconductivity, such as in half-Heusler superconductors.
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Affiliation(s)
- Shingo Kobayashi
- Institute for Advanced Research, Nagoya University, Nagoya 464-8601, Japan
- Department of Applied Physics, Nagoya University, Nagoya 464-8603, Japan
| | - Ai Yamakage
- Department of Physics, Nagoya University, Nagoya 464-8602, Japan
| | - Yukio Tanaka
- Department of Applied Physics, Nagoya University, Nagoya 464-8603, Japan
| | - Masatoshi Sato
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
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12
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Kim H, Wang K, Nakajima Y, Hu R, Ziemak S, Syers P, Wang L, Hodovanets H, Denlinger JD, Brydon PMR, Agterberg DF, Tanatar MA, Prozorov R, Paglione J. Beyond triplet: Unconventional superconductivity in a spin-3/2 topological semimetal. SCIENCE ADVANCES 2018; 4:eaao4513. [PMID: 29740606 PMCID: PMC5938259 DOI: 10.1126/sciadv.aao4513] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2017] [Accepted: 02/15/2018] [Indexed: 05/05/2023]
Abstract
In all known fermionic superfluids, Cooper pairs are composed of spin-1/2 quasi-particles that pair to form either spin-singlet or spin-triplet bound states. The "spin" of a Bloch electron, however, is fixed by the symmetries of the crystal and the atomic orbitals from which it is derived and, in some cases, can behave as if it were a spin-3/2 particle. The superconducting state of such a system allows pairing beyond spin-triplet, with higher spin quasi-particles combining to form quintet or septet pairs. We report evidence of unconventional superconductivity emerging from a spin-3/2 quasi-particle electronic structure in the half-Heusler semimetal YPtBi, a low-carrier density noncentrosymmetric cubic material with a high symmetry that preserves the p-like j = 3/2 manifold in the Bi-based Γ8 band in the presence of strong spin-orbit coupling. With a striking linear temperature dependence of the London penetration depth, the existence of line nodes in the superconducting order parameter Δ is directly explained by a mixed-parity Cooper pairing model with high total angular momentum, consistent with a high-spin fermionic superfluid state. We propose a k ⋅ p model of the j = 3/2 fermions to explain how a dominant J = 3 septet pairing state is the simplest solution that naturally produces nodes in the mixed even-odd parity gap. Together with the underlying topologically nontrivial band structure, the unconventional pairing in this system represents a truly novel form of superfluidity that has strong potential for leading the development of a new series of topological superconductors.
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Affiliation(s)
- Hyunsoo Kim
- Center for Nanophysics and Advanced Materials, University of Maryland, College Park, MD 20742, USA
- Department of Physics, University of Maryland, College Park, MD 20742, USA
- Ames Laboratory, Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA
- Corresponding author. (H.K.); (J.P.)
| | - Kefeng Wang
- Center for Nanophysics and Advanced Materials, University of Maryland, College Park, MD 20742, USA
- Department of Physics, University of Maryland, College Park, MD 20742, USA
| | - Yasuyuki Nakajima
- Center for Nanophysics and Advanced Materials, University of Maryland, College Park, MD 20742, USA
- Department of Physics, University of Maryland, College Park, MD 20742, USA
- Department of Physics, University of Central Florida, Orlando, FL 32816, USA
| | - Rongwei Hu
- Center for Nanophysics and Advanced Materials, University of Maryland, College Park, MD 20742, USA
- Department of Physics, University of Maryland, College Park, MD 20742, USA
| | - Steven Ziemak
- Center for Nanophysics and Advanced Materials, University of Maryland, College Park, MD 20742, USA
- Department of Physics, University of Maryland, College Park, MD 20742, USA
| | - Paul Syers
- Center for Nanophysics and Advanced Materials, University of Maryland, College Park, MD 20742, USA
- Department of Physics, University of Maryland, College Park, MD 20742, USA
| | - Limin Wang
- Center for Nanophysics and Advanced Materials, University of Maryland, College Park, MD 20742, USA
- Department of Physics, University of Maryland, College Park, MD 20742, USA
| | - Halyna Hodovanets
- Center for Nanophysics and Advanced Materials, University of Maryland, College Park, MD 20742, USA
- Department of Physics, University of Maryland, College Park, MD 20742, USA
| | - Jonathan D. Denlinger
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Philip M. R. Brydon
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, MD 20742, USA
- Department of Physics, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand
| | | | - Makariy A. Tanatar
- Ames Laboratory, Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA
| | - Ruslan Prozorov
- Ames Laboratory, Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA
| | - Johnpierre Paglione
- Center for Nanophysics and Advanced Materials, University of Maryland, College Park, MD 20742, USA
- Department of Physics, University of Maryland, College Park, MD 20742, USA
- Corresponding author. (H.K.); (J.P.)
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13
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Boettcher I, Herbut IF. Unconventional Superconductivity in Luttinger Semimetals: Theory of Complex Tensor Order and the Emergence of the Uniaxial Nematic State. PHYSICAL REVIEW LETTERS 2018; 120:057002. [PMID: 29481208 DOI: 10.1103/physrevlett.120.057002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2017] [Indexed: 06/08/2023]
Abstract
We investigate unconventional superconductivity in three-dimensional electronic systems with the chemical potential close to a quadratic band touching point in the band dispersion. Short-range interactions can lead to d-wave superconductivity, described by a complex tensor order parameter. We elucidate the general structure of the corresponding Ginzburg-Landau free energy and apply these concepts to the case of an isotropic band touching point. For a vanishing chemical potential, the ground state of the system is given by the superconductor analogue of the uniaxial nematic state, which features line nodes in the excitation spectrum of quasiparticles. In contrast to the theory of real tensor order in liquid crystals, however, the ground state is selected here by the sextic terms in the free energy. At a finite chemical potential, the nematic state has an additional instability at weak coupling and low temperatures. In particular, the one-loop coefficients in the free energy indicate that at weak coupling genuinely complex orders, which break time-reversal symmetry, are energetically favored. We relate our analysis to recent measurements in the half-Heusler compound YPtBi and discuss the role of cubic crystal symmetry.
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Affiliation(s)
- Igor Boettcher
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada, V5A 1S6
| | - Igor F Herbut
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada, V5A 1S6
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14
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Wang Y, Fu L. Topological Phase Transitions in Multicomponent Superconductors. PHYSICAL REVIEW LETTERS 2017; 119:187003. [PMID: 29219538 DOI: 10.1103/physrevlett.119.187003] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2017] [Indexed: 06/07/2023]
Abstract
We study the phase transition between a trivial and a time-reversal-invariant topological superconductor in a single-band system. By analyzing the interplay of symmetry, topology, and energetics, we show that for a generic normal state band structure, the phase transition occurs via extended intermediate phases in which even- and odd-parity pairing components coexist. For inversion-symmetric systems, the coexistence phase spontaneously breaks time-reversal symmetry. For noncentrosymmetric superconductors, the low-temperature intermediate phase is time-reversal breaking, while the high-temperature phase preserves time-reversal symmetry and has topologically protected line nodes. Furthermore, with approximate rotational invariance, the system has an emergent U(1)×U(1) symmetry, and novel topological defects, such as half vortex lines binding Majorana fermions, can exist. We analytically solve for the dispersion of the Majorana fermion and show that it exhibits small and large velocities at low and high energies. Relevance of our theory to superconducting pyrochlore oxide Cd_{2}Re_{2}O_{7} and half-Heusler materials is discussed.
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Affiliation(s)
- Yuxuan Wang
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080, USA
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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15
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Sato M, Ando Y. Topological superconductors: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:076501. [PMID: 28367833 DOI: 10.1088/1361-6633/aa6ac7] [Citation(s) in RCA: 253] [Impact Index Per Article: 36.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topological superconductors. The relation between topological superconductivity and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topological superconductivity are explained with an emphasis on the roles of spin-orbit coupling. Present experimental situations and possible signatures of topological superconductivity are summarized with an emphasis on intrinsic topological superconductors.
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Affiliation(s)
- Masatoshi Sato
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
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16
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Agterberg DF, Brydon PMR, Timm C. Bogoliubov Fermi Surfaces in Superconductors with Broken Time-Reversal Symmetry. PHYSICAL REVIEW LETTERS 2017; 118:127001. [PMID: 28388193 DOI: 10.1103/physrevlett.118.127001] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2016] [Indexed: 06/07/2023]
Abstract
It is commonly believed that, in the absence of disorder or an external magnetic field, there are three possible types of superconducting excitation gaps: The gap is nodeless, it has point nodes, or it has line nodes. Here, we show that, for an even-parity nodal superconducting state which spontaneously breaks time-reversal symmetry, the low-energy excitation spectrum generally does not belong to any of these categories; instead, it has extended Bogoliubov Fermi surfaces. These Fermi surfaces can be visualized as two-dimensional surfaces generated by "inflating" point or line nodes into spheroids or tori, respectively. These inflated nodes are topologically protected from being gapped by a Z_{2} invariant, which we give in terms of a Pfaffian. We also show that superconducting states possessing these Fermi surfaces can be energetically stable. A crucial ingredient in our theory is that more than one band is involved in the pairing; since all candidate materials for even-parity superconductivity with broken time-reversal symmetry are multiband systems, we expect these Z_{2}-protected Fermi surfaces to be ubiquitous.
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Affiliation(s)
- D F Agterberg
- Department of Physics, University of Wisconsin, Milwaukee, Wisconsin 53201, USA
| | - P M R Brydon
- Department of Physics, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand
| | - C Timm
- Institute of Theoretical Physics, Technische Universität Dresden, 01062 Dresden, Germany
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17
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Smidman M, Salamon MB, Yuan HQ, Agterberg DF. Superconductivity and spin-orbit coupling in non-centrosymmetric materials: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:036501. [PMID: 28072583 DOI: 10.1088/1361-6633/80/3/036501] [Citation(s) in RCA: 65] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
In non-centrosymmetric superconductors, where the crystal structure lacks a centre of inversion, parity is no longer a good quantum number and an electronic antisymmetric spin-orbit coupling (ASOC) is allowed to exist by symmetry. If this ASOC is sufficiently large, it has profound consequences on the superconducting state. For example, it generally leads to a superconducting pairing state which is a mixture of spin-singlet and spin-triplet components. The possibility of such novel pairing states, as well as the potential for observing a variety of unusual behaviors, led to intensive theoretical and experimental investigations. Here we review the experimental and theoretical results for superconducting systems lacking inversion symmetry. Firstly we give a conceptual overview of the key theoretical results. We then review the experimental properties of both strongly and weakly correlated bulk materials, as well as two dimensional systems. Here the focus is on evaluating the effects of ASOC on the superconducting properties and the extent to which there is evidence for singlet-triplet mixing. This is followed by a more detailed overview of theoretical aspects of non-centrosymmetric superconductivity. This includes the effects of the ASOC on the pairing symmetry and the superconducting magnetic response, magneto-electric effects, superconducting finite momentum pairing states, and the potential for non-centrosymmetric superconductors to display topological superconductivity.
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Affiliation(s)
- M Smidman
- Center for Correlated Matter and Department of Physics, Zhejiang University, Hangzhou 310058, People's Republic of China
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18
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Kozii V, Venderbos JWF, Fu L. Three-dimensional Majorana fermions in chiral superconductors. SCIENCE ADVANCES 2016; 2:e1601835. [PMID: 27957543 PMCID: PMC5142806 DOI: 10.1126/sciadv.1601835] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2016] [Accepted: 11/03/2016] [Indexed: 05/31/2023]
Abstract
Using a systematic symmetry and topology analysis, we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are spin-nondegenerate and realize Majorana fermions in three dimensions. By examining all types of chiral Cooper pairs with total angular momentum J formed by Bloch electrons with angular momentum j in crystals, we obtain a comprehensive classification of gapless Majorana quasiparticles in terms of energy-momentum relation and location on the Fermi surface. We show that the existence of bulk Majorana fermions in the vicinity of spin-selective point nodes is rooted in the nonunitary nature of chiral pairing in spin-orbit-coupled superconductors. We address experimental signatures of Majorana fermions and find that the nuclear magnetic resonance spin relaxation rate is significantly suppressed for nuclear spins polarized along the nodal direction as a consequence of the spin-selective Majorana nature of nodal quasiparticles. Furthermore, Majorana nodes in the bulk have nontrivial topology and imply the presence of Majorana bound states on the surface, which form arcs in momentum space. We conclude by proposing the heavy fermion superconductor PrOs4Sb12 and related materials as promising candidates for nonunitary chiral superconductors hosting three-dimensional Majorana fermions.
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Affiliation(s)
- Vladyslav Kozii
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Jörn W. F. Venderbos
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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19
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Nomoto T, Ikeda H. Exotic Multigap Structure in UPt_{3} Unveiled by a First-Principles Analysis. PHYSICAL REVIEW LETTERS 2016; 117:217002. [PMID: 27911558 DOI: 10.1103/physrevlett.117.217002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2016] [Indexed: 06/06/2023]
Abstract
A heavy-fermion superconductor UPt_{3} is a unique spin-triplet superconductor with multiple superconducting phases. Here, we provide the first report on a first-principles analysis of the microscopic superconducting gap structure. We find that the promising gap structure is an unprecedented E_{2u} state, which is completely different from the previous phenomenological E_{2u} models. Our obtained E_{2u} state has in-plane twofold vertical line nodes on small Fermi surfaces and point nodes with linear dispersion on a large Fermi surface. These peculiar features cannot be explained in the conventional spin 1/2 representation, but is described by the group-theoretical representation of the Cooper pairs in the total angular momentum j=5/2 space. Our findings shed new light on the long-standing problems in the superconductivity of UPt_{3}.
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Affiliation(s)
- Takuya Nomoto
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Hiroaki Ikeda
- Department of Physics, Ritsumeikan University, Kusatsu 525-8577, Japan
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