1
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Zatelli F, van Driel D, Xu D, Wang G, Liu CX, Bordin A, Roovers B, Mazur GP, van Loo N, Wolff JC, Bozkurt AM, Badawy G, Gazibegovic S, Bakkers EPAM, Wimmer M, Kouwenhoven LP, Dvir T. Robust poor man's Majorana zero modes using Yu-Shiba-Rusinov states. Nat Commun 2024; 15:7933. [PMID: 39256344 PMCID: PMC11387613 DOI: 10.1038/s41467-024-52066-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2024] [Accepted: 08/21/2024] [Indexed: 09/12/2024] Open
Abstract
Kitaev chains in quantum dot-superconductor arrays are a promising platform for the realization of topological superconductivity. As recently demonstrated, even a two-site chain can host Majorana zero modes known as "poor man's Majorana". Harnessing the potential of these states for quantum information processing, however, requires increasing their robustness to external perturbations. Here, we form a two-site Kitaev chain using Yu-Shiba-Rusinov states in proximitized quantum dots. By deterministically tuning the hybridization between the quantum dots and the superconductor, we observe poor man's Majorana states with a gap larger than 70 μeV. The sensitivity to charge fluctuations is also greatly reduced compared to Kitaev chains made with non-proximitized dots. The systematic control and improved energy scales of poor man's Majorana states realized with Yu-Shiba-Rusinov states will benefit the realization of longer Kitaev chains, parity qubits, and the demonstration of non-Abelian physics.
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Affiliation(s)
- Francesco Zatelli
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - David van Driel
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - Di Xu
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - Guanzhong Wang
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - Chun-Xiao Liu
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - Alberto Bordin
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - Bart Roovers
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - Grzegorz P Mazur
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - Nick van Loo
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - Jan C Wolff
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - A Mert Bozkurt
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - Ghada Badawy
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Sasa Gazibegovic
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Erik P A M Bakkers
- Department of Applied Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Michael Wimmer
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands.
| | - Tom Dvir
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, Delft, The Netherlands
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2
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Liu T, Wan CY, Yang H, Zhao Y, Xie B, Zheng W, Yi Z, Guan D, Wang S, Zheng H, Liu C, Fu L, Liu J, Li Y, Jia J. Signatures of hybridization of multiple Majorana zero modes in a vortex. Nature 2024; 633:71-76. [PMID: 39198651 DOI: 10.1038/s41586-024-07857-4] [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: 01/18/2024] [Accepted: 07/19/2024] [Indexed: 09/01/2024]
Abstract
Majorana zero modes (MZMs) are emergent zero-energy topological quasiparticles that are their own antiparticles1,2. Detected MZMs are spatially separated and electrically neutral, so producing hybridization between MZMs is extremely challenging in superconductors3,4. Here, we report the magnetic field response of vortex bound states in superconducting topological crystalline insulator SnTe (001) films. Several MZMs were predicted to coexist in a single vortex due to magnetic mirror symmetry. Using a scanning tunnelling microscope equipped with a three-axis vector magnet, we found that the zero-bias peak (ZBP) in a single vortex exhibits an apparent anisotropic response even though the magnetic field is weak. The ZBP can robustly extend a long distance of up to approximately 100 nm at the (001) surface when the magnetic field is parallel to the ( 1 1 ¯ 0 )-type mirror plane, otherwise it displays an asymmetric splitting. Our systematic simulations demonstrate that the anisotropic response cannot be reproduced with trivial ZBPs. Although the different MZMs cannot be directly distinguished due to the limited energy resolution in our experiments, our comparisons between experimental measurements and theoretical simulations strongly support the existence and hybridization of symmetry-protected multiple MZMs. Our work demonstrates a way to hybridize different MZMs by controlling the orientation of the magnetic field and expands the types of MZM available for tuning topological states.
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Affiliation(s)
- Tengteng Liu
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Chun Yu Wan
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
| | - Hao Yang
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Yujun Zhao
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
| | - Bangjin Xie
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Weiyan Zheng
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Zhaoxia Yi
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Dandan Guan
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
- Shanghai Research Center for Quantum Sciences, Shanghai, China
- Hefei National Laboratory, Hefei, China
| | - Shiyong Wang
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
- Shanghai Research Center for Quantum Sciences, Shanghai, China
- Hefei National Laboratory, Hefei, China
| | - Hao Zheng
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
- Shanghai Research Center for Quantum Sciences, Shanghai, China
- Hefei National Laboratory, Hefei, China
| | - Canhua Liu
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
- Shanghai Research Center for Quantum Sciences, Shanghai, China
- Hefei National Laboratory, Hefei, China
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Junwei Liu
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China.
| | - Yaoyi Li
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China.
- Shanghai Research Center for Quantum Sciences, Shanghai, China.
- Hefei National Laboratory, Hefei, China.
| | - Jinfeng Jia
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China.
- Shanghai Research Center for Quantum Sciences, Shanghai, China.
- Hefei National Laboratory, Hefei, China.
- Department of Physics, Southern University of Science and Technology, Shenzhen, China.
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3
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Odobesko A, Klees RL, Friedrich F, Hankiewicz EM, Bode M. Boosting spatial and energy resolution in STM with a double-functionalized probe. SCIENCE ADVANCES 2024; 10:eadq6975. [PMID: 39196925 PMCID: PMC11352829 DOI: 10.1126/sciadv.adq6975] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2024] [Accepted: 07/24/2024] [Indexed: 08/30/2024]
Abstract
The scattering of superconducting pairs by magnetic impurities on a superconducting surface leads to pairs of sharp in-gap resonances known as Yu-Shiba-Rusinov (YSR) bound states. Similar to the interference of itinerant electrons scattered by defects in normal metals, these resonances reveal a periodic texture around the magnetic impurity. The wavelength of these resonances is, however, often too short to be resolved even by methods capable of atomic resolution, i.e., scanning tunneling microscopy (STM). We combine a CO molecule with a superconducting cluster pre-attached to an STM tip to maximize both spatial and energy resolution, thus demonstrating the superior properties of such double-functionalized probes by imaging the spatial distribution of YSR states. Our approach reveals rich interference patterns of the hybridized YSR states of two Fe atoms on Nb(110), previously inaccessible with conventional STM probes. This advancement extends the capabilities of STM techniques, providing insights into superconducting phenomena at the atomic scale.
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Affiliation(s)
- Artem Odobesko
- Physikalisches Institut, Experimentelle Physik II, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Raffael L. Klees
- Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
- Institute of Physics, University of Augsburg, D-86159 Augsburg, Germany
| | - Felix Friedrich
- Physikalisches Institut, Experimentelle Physik II, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Ewelina M. Hankiewicz
- Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Matthias Bode
- Physikalisches Institut, Experimentelle Physik II, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
- Wilhelm Conrad Röntgen-Center for Complex Material Systems (RCCM), Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
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Li P, Zhang J, Zhu D, Chen CQ, Yi E, Shen B, Hou Y, Yan Z, Yao DX, Guo D, Zhong D. Observation of In-Gap States in a Two-Dimensional CrI 2/NbSe 2 Heterostructure. NANO LETTERS 2024; 24:9468-9476. [PMID: 39047142 DOI: 10.1021/acs.nanolett.4c01848] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/27/2024]
Abstract
Low-dimensional magnetic structures coupled with superconductors are promising platforms for realizing Majorana zero modes, which have potential applications in topological quantum computing. Here, we report a two-dimensional (2D) magnetic-superconducting heterostructure consisting of single-layer chromium diiodide (CrI2) on a niobium diselenide (NbSe2) superconductor. Single-layer CrI2 nanosheets, which hold antiferromagnetic (AFM) ground states by our first-principles calculations, were epitaxially grown on the layered NbSe2 substrate. Using scanning tunneling microscopy/spectroscopy, we observed robust in-gap states spatially located at the edge of the nanosheets and defect-induced zero-energy peaks inside the CrI2 nanosheets. Magnetic-flux vortices induced by an external field exhibit broken 3-fold rotational symmetry of the pristine NbSe2 superconductor, implying the efficient modulation of the interfacial superconducting states by the epitaxial CrI2 layer. A phenomenological model suggests the existence of chiral edge states in a 2D AFM-superconducting hybrid system with an even Chern number, providing a qualitatively plausible understanding for our experimental observation.
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Affiliation(s)
- Peigen Li
- School of Physics & Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, Sun Yat-sen University, 510275 Guangzhou, China
- State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, 510275 Guangzhou, China
| | - Jihai Zhang
- School of Physics & Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, Sun Yat-sen University, 510275 Guangzhou, China
- State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, 510275 Guangzhou, China
| | - Di Zhu
- School of Physics & Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, Sun Yat-sen University, 510275 Guangzhou, China
- State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, 510275 Guangzhou, China
| | - Cui-Qun Chen
- School of Physics & Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, Sun Yat-sen University, 510275 Guangzhou, China
- State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, 510275 Guangzhou, China
| | - Enkui Yi
- School of Physics & Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, Sun Yat-sen University, 510275 Guangzhou, China
- State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, 510275 Guangzhou, China
| | - Bing Shen
- School of Physics & Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, Sun Yat-sen University, 510275 Guangzhou, China
- State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, 510275 Guangzhou, China
| | - Yusheng Hou
- School of Physics & Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, Sun Yat-sen University, 510275 Guangzhou, China
- State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, 510275 Guangzhou, China
| | - Zhongbo Yan
- School of Physics & Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, Sun Yat-sen University, 510275 Guangzhou, China
- State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, 510275 Guangzhou, China
| | - Dao-Xin Yao
- School of Physics & Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, Sun Yat-sen University, 510275 Guangzhou, China
- State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, 510275 Guangzhou, China
| | - Donghui Guo
- School of Physics & Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, Sun Yat-sen University, 510275 Guangzhou, China
- State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, 510275 Guangzhou, China
| | - Dingyong Zhong
- School of Physics & Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, Sun Yat-sen University, 510275 Guangzhou, China
- State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, 510275 Guangzhou, China
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5
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Majek P, Weymann I. Spin-selective transport in a correlated double quantum dot-Majorana wire system. Sci Rep 2024; 14:17762. [PMID: 39085311 PMCID: PMC11291930 DOI: 10.1038/s41598-024-66478-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2024] [Accepted: 07/01/2024] [Indexed: 08/02/2024] Open
Abstract
In this work we investigate the spin-dependent transport through a double quantum dot embedded in a ferromagnetic tunnel junction and side attached to a topological superconducting nanowire hosting Majorana zero-energy modes. We focus on the transport regime when the Majorana mode leaks into the double quantum dot competing with the two-stage Kondo effect and the ferromagnetic-contact-induced exchange field. In particular, we determine the system's spectral properties and analyze the temperature dependence of the spin-resolved linear conductance by means of the numerical renormalization group method. Our study reveals unique signatures of the interplay between the spin-resolved tunneling, the Kondo effect and the Majorana modes, which are visible in the transport characteristics. In particular, we uncover a competing character of the coupling to topological superconductor and that to ferromagnetic leads, which can be observed already for very low spin polarization of the electrodes. This is signaled by an almost complete quenching of the conductance in one of the spin channels which is revealed through perfect conductance spin polarization. Moreover, we show that the conductance spin polarization can change sign depending on the magnitude of spin imbalance in the leads and strength of interaction with topological wire. Thus, our work demonstrates that even minuscule spin polarization of tunneling processes can have large impact on the transport properties of the system.
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Affiliation(s)
- Piotr Majek
- Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, ul. Uniwersytetu Poznańskiego 2, 61-614, Poznań, Poland.
| | - Ireneusz Weymann
- Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, ul. Uniwersytetu Poznańskiego 2, 61-614, Poznań, Poland
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6
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Farinacci L, Reecht G, von Oppen F, Franke KJ. Yu-Shiba-Rusinov bands in a self-assembled kagome lattice of magnetic molecules. Nat Commun 2024; 15:6474. [PMID: 39085259 PMCID: PMC11291492 DOI: 10.1038/s41467-024-50829-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Accepted: 07/22/2024] [Indexed: 08/02/2024] Open
Abstract
Kagome lattices constitute versatile platforms for studying paradigmatic correlated phases. While molecular self-assembly of kagome structures on metallic substrates is promising, it is challenging to realize pristine kagome properties because of hybridization with the bulk degrees of freedom and modified electron-electron interactions. We suggest that a superconducting substrate offers an compelling platform for realizing a magnetic kagome lattice. Exchange coupling induces kagome-derived bands at the interface, which are protected from the bulk by the superconducting energy gap. We realize a magnetic kagome lattice on a superconductor by depositing Fe-porphin-chloride molecules on Pb(111) and using temperature-activated de-chlorination and self-assembly. This allows us to control the formation of smaller kagome precursors and long-range ordered kagome islands. Using scanning tunneling microscopy and spectroscopy at 1.6 K, we identify Yu-Shiba-Rusinov states inside the superconducting energy gap and track their hybridization from the precursors to larger islands, where the kagome lattice induces extended YSR bands. These YSR-derived kagome bands inside the superconducting energy gap allow for long-range coupling and induced pairing correlations, motivating further studies to resolve possible spin-liquid or Kondo-lattice-type behavior.
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Affiliation(s)
- Laëtitia Farinacci
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195, Berlin, Germany.
| | - Gaël Reecht
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195, Berlin, Germany
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195, Berlin, Germany
| | - Katharina J Franke
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195, Berlin, Germany
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7
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Lee J, Park HR, Jin KH, Kim JS, Cheong SW, Yeom HW. Topological Complex Charge Conservation in Nontrivial Z 2 × Z 2 Domain Walls. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2024; 36:e2313803. [PMID: 38482920 DOI: 10.1002/adma.202313803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2023] [Revised: 02/14/2024] [Indexed: 03/22/2024]
Abstract
Localized topological modes such as solitons, Majorana Fermions, and skyrmions are attracting great interest as robust information carriers for future devices. Here, a novel conserved quantity for topological domain wall networks of a Z2 × Z2 order generated with spin-polarized current in Sr2VO3FeAs is discovered. Domain walls are mobilized by the scanning tunneling current, which also observes in atomic scale active dynamics of domain wall vertices including merge, bifurcation, pair creation, and annihilation. Within this dynamics, the product of the topological complex charges defined for domain wall vertices is conserved with a novel boundary-charge correspondence rule. These results may open an avenue toward topological electronics based on domain wall vertices in generic Z2 × Z2 systems.
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Affiliation(s)
- Jhinhwan Lee
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang, 37673, Republic of Korea
| | - Hae-Ryong Park
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang, 37673, Republic of Korea
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea
| | - Kyung-Hwan Jin
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang, 37673, Republic of Korea
| | - Jun Sung Kim
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang, 37673, Republic of Korea
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea
| | - Sang-Wook Cheong
- Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, Piscataway, NJ, 08854, USA
| | - Han-Woong Yeom
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang, 37673, Republic of Korea
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang, 37673, Republic of Korea
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Mesaros A, Gu GD, Massee F. Topologically trivial gap-filling in superconducting Fe(Se,Te) by one-dimensional defects. Nat Commun 2024; 15:3774. [PMID: 38710680 DOI: 10.1038/s41467-024-48047-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2023] [Accepted: 04/15/2024] [Indexed: 05/08/2024] Open
Abstract
Structural distortions and imperfections are a crucial aspect of materials science, on the macroscopic scale providing strength, but also enhancing corrosion and reducing electrical and thermal conductivity. At the nanometre scale, multi-atom imperfections, such as atomic chains and crystalline domain walls have conversely been proposed as a route to topological superconductivity, whose most prominent characteristic is the emergence of Majorana Fermions that can be used for error-free quantum computing. Here, we shed more light on the nature of purported domain walls in Fe(Se,Te) that may host 1D dispersing Majorana modes. We show that the displacement shift of the atomic lattice at these line-defects results from sub-surface impurities that warp the topmost layer(s). Using the electric field between the tip and sample, we manage to reposition the sub-surface impurities, directly visualizing the displacement shift and the underlying defect-free lattice. These results, combined with observations of a completely different type of 1D defect where superconductivity remains fully gapped, highlight the topologically trivial nature of 1D defects in Fe(Se,Te).
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Affiliation(s)
- A Mesaros
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France
| | - G D Gu
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - F Massee
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France.
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9
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Aceves Rodriguez UA, Guimarães F, Brinker S, Lounis S. Magnetic exchange interactions at the proximity of a superconductor. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:295801. [PMID: 38471158 DOI: 10.1088/1361-648x/ad32de] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2023] [Accepted: 03/12/2024] [Indexed: 03/14/2024]
Abstract
Interfacing magnetism with superconductivity gives rise to a wonderful playground for intertwining key degrees of freedom: Cooper pairs, spin, charge, and spin-orbit interaction, from which emerge a wealth of exciting phenomena, fundamental in the nascent field of superconducting spinorbitronics and topological quantum technologies. Magnetic exchange interactions (MEIs), being isotropic or chiral such as the Dzyaloshinskii-Moriya interactions, are vital in establishing the magnetic behavior at these interfaces as well as in dictating not only complex transport phenomena, but also the manifestation of topologically trivial or non-trivial objects. Here, we propose a methodology enabling the extraction of the tensor of MEI from electronic structure simulations accounting for superconductivity. We apply our scheme to the case of a Mn layer deposited on Nb(110) surface and explore proximity-induced impact on the MEI. The latter are weakly modified by a realistic electron-phonon coupling. However, tuning the superconducting order parameter, we unveil potential change of the magnetic order accompanied with chirality switching, as induced by the interplay of spin-orbit interaction and Cooper pairing. Owing to its simple formulation, our methodology can be readily implemented in state-of-the-art frameworks capable of tackling superconductivity and magnetism. We thus foresee implications in the simulations and prediction of topological superconducting bits as well as of cryogenic superconducting hybrid devices involving magnetic units.
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Affiliation(s)
- Uriel A Aceves Rodriguez
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, 52425 Jülich, Germany
- Faculty of Physics & CENIDE, University of Duisburg-Essen, 47053 Duisburg, Germany
| | - Filipe Guimarães
- Jülich Supercomputing Centre, Forschungszentrum Jülich & JARA, 52425 Jülich, Germany
| | - Sascha Brinker
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, 52425 Jülich, Germany
| | - Samir Lounis
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, 52425 Jülich, Germany
- Faculty of Physics & CENIDE, University of Duisburg-Essen, 47053 Duisburg, Germany
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10
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Schirmann J, Franca S, Flicker F, Grushin AG. Physical Properties of an Aperiodic Monotile with Graphene-like Features, Chirality, and Zero Modes. PHYSICAL REVIEW LETTERS 2024; 132:086402. [PMID: 38457726 DOI: 10.1103/physrevlett.132.086402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2023] [Revised: 11/07/2023] [Accepted: 01/08/2024] [Indexed: 03/10/2024]
Abstract
The discovery of the Hat, an aperiodic monotile, has revealed novel mathematical aspects of aperiodic tilings. However, the physics of particles propagating in such a setting remains unexplored. In this work we study spectral and transport properties of a tight-binding model defined on the Hat. We find that (i) the spectral function displays striking similarities to that of graphene, including sixfold symmetry and Dirac-like features; (ii) unlike graphene, the monotile spectral function is chiral, differing for its two enantiomers; (iii) the spectrum has a macroscopic number of degenerate states at zero energy; (iv) when the magnetic flux per plaquette (ϕ) is half of the flux quantum, zero modes are found localized around the reflected "anti-hats"; and (v) its Hofstadter spectrum is periodic in ϕ, unlike for other quasicrystals. Our work serves as a basis to study wave and electron propagation in possible experimental realizations of the Hat, which we suggest.
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Affiliation(s)
- Justin Schirmann
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - Selma Franca
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - Felix Flicker
- School of Physics and Astronomy, Cardiff University, The Parade, Cardiff CF24 3AA, United Kingdom
- School of Physics, H. H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - Adolfo G Grushin
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
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11
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Yu H, Yan D, Guo Z, Zhou Y, Yang X, Li P, Wang Z, Xiang X, Li J, Ma X, Zhou R, Hong F, Wuli Y, Shi Y, Wang JT, Yu X. Observation of Emergent Superconductivity in the Topological Insulator Ta 2Pd 3Te 5 via Pressure Manipulation. J Am Chem Soc 2024; 146:3890-3899. [PMID: 38294957 DOI: 10.1021/jacs.3c11364] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2024]
Abstract
Topological insulators offer significant potential to revolutionize diverse fields driven by nontrivial manifestations of their topological electronic band structures. However, the realization of superior integration between exotic topological states and superconductivity for practical applications remains a challenge, necessitating a profound understanding of intricate mechanisms. Here, we report experimental observations for a novel superconducting phase in the pressurized second-order topological insulator candidate Ta2Pd3Te5, and the high-pressure phase maintains its original ambient pressure lattice symmetry up to 45 GPa. Our in situ high-pressure synchrotron X-ray diffraction, electrical transport, infrared reflectance, and Raman spectroscopy measurements, in combination with rigorous theoretical calculations, provide compelling evidence for the association between the superconducting behavior and the densified phase. The electronic state change around 20 GPa was found to modify the topology of the Fermi surface directly, which synergistically fosters the emergence of robust superconductivity. In-depth comprehension of the fascinating properties exhibited by the compressed Ta2Pd3Te5 phase is achieved, highlighting the extraordinary potential of topological insulators for exploring and investigating high-performance electronic advanced devices under extreme conditions.
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Affiliation(s)
- Hui Yu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Dayu Yan
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Zhaopeng Guo
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yizhou Zhou
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Xue Yang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Peiling Li
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Zhijun Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Xiaojun Xiang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Junkai Li
- Center for High Pressure Science and Technology Advanced Research, Beijing 100094, P. R. China
| | - Xiaoli Ma
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Rui Zhou
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan523808, Guangdong, China
| | - Fang Hong
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yunxiao Wuli
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Youguo Shi
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan523808, Guangdong, China
| | - Jian-Tao Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan523808, Guangdong, China
| | - Xiaohui Yu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan523808, Guangdong, China
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12
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Aceves Rodriguez UA, Guimarães FSM, Lounis S. Superconductivity in Nb: Impact of Temperature, Dimensionality and Cooper-Pairing. NANOMATERIALS (BASEL, SWITZERLAND) 2024; 14:254. [PMID: 38334524 PMCID: PMC10856455 DOI: 10.3390/nano14030254] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2023] [Revised: 01/17/2024] [Accepted: 01/18/2024] [Indexed: 02/10/2024]
Abstract
The ability to realistically simulate the electronic structure of superconducting materials is important to understand and predict various properties emerging in both the superconducting topological and spintronics realms. We introduce a tight-binding implementation of the Bogoliubov-de Gennes method, parameterized from density functional theory, which we utilize to explore the bulk and thin films of Nb, known to host a significant superconducting gap. The latter is useful for various applications such as the exploration of trivial and topological in-gap states. Here, we focus on the simulation's aspects of superconductivity and study the impact of temperature, Cooper-pair coupling and dimensionality on the value of the superconducting pairing interactions and gaps.
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Affiliation(s)
- Uriel Allan Aceves Rodriguez
- Peter Grünberg Institut & Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, D-52425 Jülich, Germany;
- Faculty of Physics & CENIDE, University of Duisburg-Essen, D-47053 Duisburg, Germany
| | | | - Samir Lounis
- Peter Grünberg Institut & Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, D-52425 Jülich, Germany;
- Faculty of Physics & CENIDE, University of Duisburg-Essen, D-47053 Duisburg, Germany
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13
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Yazdani A, von Oppen F, Halperin BI, Yacoby A. Hunting for Majoranas. Science 2023; 380:eade0850. [PMID: 37347870 DOI: 10.1126/science.ade0850] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Accepted: 05/22/2023] [Indexed: 06/24/2023]
Abstract
Over the past decade, there have been considerable efforts to observe non-abelian quasiparticles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasiparticles beyond those of fermions and bosons and of establishing the underlying science for the creation of topologically protected quantum bits. In this Review, we focus on efforts to create topological superconducting phases that host Majorana zero modes. We consider the lessons learned from existing experimental efforts, which are motivating both improvements to present platforms and the exploration of new approaches. Although the experimental detection of non-abelian quasiparticles remains challenging, the knowledge gained thus far and the opportunities ahead offer high potential for discovery and advances in this exciting area of quantum physics.
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Affiliation(s)
- Ali Yazdani
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08540, USA
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | | | - Amir Yacoby
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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14
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Schneider L, Beck P, Rózsa L, Posske T, Wiebe J, Wiesendanger R. Probing the topologically trivial nature of end states in antiferromagnetic atomic chains on superconductors. Nat Commun 2023; 14:2742. [PMID: 37173332 PMCID: PMC10182033 DOI: 10.1038/s41467-023-38369-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2022] [Accepted: 04/25/2023] [Indexed: 05/15/2023] Open
Abstract
Spin chains proximitized by s-wave superconductors are predicted to enter a mini-gapped phase with topologically protected Majorana modes (MMs) localized at their ends. However, the presence of non-topological end states mimicking MM properties can hinder their unambiguous observation. Here, we report on a direct method to exclude the non-local nature of end states via scanning tunneling spectroscopy by introducing a locally perturbing defect on one of the chain's ends. We apply this method to particular end states observed in antiferromagnetic spin chains within a large minigap, thereby proving their topologically trivial character. A minimal model shows that, while wide trivial minigaps hosting end states are easily achieved in antiferromagnetic spin chains, unrealistically large spin-orbit coupling is required to drive the system into a topologically gapped phase with MMs. The methodology of perturbing candidate topological edge modes in future experiments is a powerful tool to probe their stability against local disorder.
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Affiliation(s)
- Lucas Schneider
- Department of Physics, University of Hamburg, D-20355, Hamburg, Germany
| | - Philip Beck
- Department of Physics, University of Hamburg, D-20355, Hamburg, Germany
| | - Levente Rózsa
- Department of Physics, University of Konstanz, D-78457, Konstanz, Germany
- Department of Theoretical Solid State Physics, Institute of Solid State Physics and Optics, Wigner Research Centre for Physics, H-1525, Budapest, Hungary
- Department of Theoretical Physics, Budapest University of Technology and Economics, H-1111, Budapest, Hungary
| | - Thore Posske
- I. Institute for Theoretical Physics, University of Hamburg, D-22607, Hamburg, Germany
- Centre for Ultrafast Imaging, Luruper Chaussee 149, D-22761, Hamburg, Germany
| | - Jens Wiebe
- Department of Physics, University of Hamburg, D-20355, Hamburg, Germany.
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15
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Trivini S, Ortuzar J, Vaxevani K, Li J, Bergeret FS, Cazalilla MA, Pascual JI. Cooper Pair Excitation Mediated by a Molecular Quantum Spin on a Superconducting Proximitized Gold Film. PHYSICAL REVIEW LETTERS 2023; 130:136004. [PMID: 37067302 DOI: 10.1103/physrevlett.130.136004] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2022] [Accepted: 02/17/2023] [Indexed: 06/19/2023]
Abstract
Breaking a correlated pair in a superconductor requires an even number of fermions providing at least twice the pairing energy Δ. Here, we show that a single tunneling electron can also excite a pair breaking excitation in a proximitized gold film in the presence of magnetic impurities. Combining scanning tunneling spectroscopy with theoretical modeling, we map the excitation spectrum of an Fe-porphyrin molecule on the Au/V(100) proximitized surface into a manifold of entangled Yu-Shiba-Rusinov and spin excitations. Pair excitations emerge in the tunneling spectra as peaks outside the spectral gap only in the strong coupling regime, where the presence of a bound quasiparticle in the ground state ensures the even fermion parity of the excitation. Our results unravel the quantum nature of magnetic impurities on superconductors and demonstrate that pair excitations unequivocally reveal the parity of the ground state.
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Affiliation(s)
| | - Jon Ortuzar
- CIC nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain
| | | | - Jingchen Li
- CIC nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain
- School of Physics, Sun Yat-sen University, Guangzhou 510275, China
| | - F Sebastian Bergeret
- Centro de Física de Materiales (CFM-MPC) Centro Mixto CSIC-UPV/EHU, E-20018 Donostia-San Sebastián, Spain
- Donostia International Physics Center (DIPC), 20018 Donostia-San Sebastian, Spain
| | - Miguel A Cazalilla
- Donostia International Physics Center (DIPC), 20018 Donostia-San Sebastian, Spain
- Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain
| | - Jose Ignacio Pascual
- CIC nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain
- Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain
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16
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Schulte S, Néel N, Rózsa L, Palotás K, Kröger J. Changing the Interaction of a Single-Molecule Magnetic Moment with a Superconductor. NANO LETTERS 2023; 23:1622-1628. [PMID: 36603183 DOI: 10.1021/acs.nanolett.2c03952] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
The exchange interaction of a brominated Co-porphyrin molecule with the Cooper pair condensate of Pb(111) is modified by reducing the Co-surface separation. The stepwise dehalogenation and dephenylation change the Co adsorption height by a few picometers. Only the residual Co-porphine core exhibits a Yu-Shiba-Rusinov bound state with low binding energy in the Bardeen-Cooper-Schrieffer energy gap. Accompanying density functional calculations reveal that the Co dz2 orbital carries the molecular magnetic moment and is responsible for the intragap state. The calculated spatial evolution of the Yu-Shiba-Rusinov wave function is compatible with the experimentally observed oscillatory attenuation of the electron-hole asymmetry with increasing lateral distance from the magnetic porphine center.
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Affiliation(s)
- Stefan Schulte
- Institut für Physik, Technische Universität Ilmenau, D-98693Ilmenau, Germany
- Peter Grünberg Institut, Forschungszentrum Jülich, D-52425Jülich, Germany
- II. Physikalisches Institut, Universität zu Köln, D-50923Cologne, Germany
| | - Nicolas Néel
- Institut für Physik, Technische Universität Ilmenau, D-98693Ilmenau, Germany
| | - Levente Rózsa
- Fachbereich Physik, Universität Konstanz, D-78457Konstanz, Germany
| | - Krisztián Palotás
- Department of Theoretical Solid State Physics, Institute for Solid State Physics and Optics, Wigner Research Center for Physics, H-1121Budapest, Hungary
- ELKH-SZTE Reaction Kinetics and Surface Chemistry Research Group, University of Szeged, H-6720Szeged, Hungary
- Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H-1111Budapest, Hungary
| | - Jörg Kröger
- Institut für Physik, Technische Universität Ilmenau, D-98693Ilmenau, Germany
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17
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Non-Majorana modes in diluted spin chains proximitized to a superconductor. Proc Natl Acad Sci U S A 2022; 119:e2210589119. [PMID: 36215505 PMCID: PMC9586262 DOI: 10.1073/pnas.2210589119] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Spin chains proximitized with superconducting condensates have emerged as one of the most promising platforms for the realization of Majorana modes. Here, we craft diluted spin chains atom by atom following a seminal theoretical proposal suggesting indirect coupling mechanisms as a viable route to trigger topological superconductivity. Starting from single adatoms hosting deep Shiba states, we use the highly anisotropic Fermi surface of the substrate to create spin chains characterized by different magnetic configurations along distinct crystallographic directions. By scrutinizing a large set of parameters we reveal the ubiquitous emergence of boundary modes. Although mimicking signatures of Majorana modes, the end modes are identified as topologically trivial Shiba states. Our work demonstrates that zero-energy modes in spin chains proximitized to superconductors are not necessarily a link to Majorana modes while simultaneously identifying other experimental platforms, driving mechanisms, and test protocols for the determination of topologically nontrivial superconducting phases.
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18
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Goedecke JJ, Schneider L, Ma Y, That KT, Wang D, Wiebe J, Wiesendanger R. Correlation of Magnetism and Disordered Shiba Bands in Fe Monolayer Islands on Nb(110). ACS NANO 2022; 16:14066-14074. [PMID: 36001503 PMCID: PMC9527798 DOI: 10.1021/acsnano.2c03965] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/22/2022] [Accepted: 08/02/2022] [Indexed: 06/15/2023]
Abstract
Two-dimensional (2D) magnet-superconductor hybrid systems are intensively studied due to their potential for the realization of 2D topological superconductors with Majorana edge modes. It is theoretically predicted that this quantum state is ubiquitous in spin-orbit-coupled ferromagnetic or skyrmionic 2D spin-lattices in proximity to an s-wave superconductor. However, recent examples suggest that the requirements for topological superconductivity are complicated by the multiorbital nature of the magnetic components and disorder effects. Here, we investigate Fe monolayer islands grown on a surface of the s-wave superconductor with the largest gap of all elemental superconductors, Nb, with respect to magnetism and superconductivity using spin-resolved scanning tunneling spectroscopy. We find three types of islands which differ by their reconstruction inducing disorder, the magnetism and the subgap electronic states. All three types are ferromagnetic with different coercive fields, indicating diverse exchange and anisotropy energies. On all three islands, there is finite spectral weight throughout the substrate's energy gap at the expense of the coherence peak intensity, indicating the formation of Shiba bands overlapping with the Fermi energy. A strong lateral variation of the spectral weight of the Shiba bands signifies substantial disorder on the order of the substrate's pairing energy with a length scale of the period of the three different reconstructions. There are neither signs of topological gaps within these bands nor of any kind of edge modes. Our work illustrates that a reconstructed growth mode of magnetic layers on superconducting surfaces is detrimental for the formation of 2D topological superconductivity.
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Affiliation(s)
- Julia J. Goedecke
- Department of Physics, University of Hamburg, D-20355 Hamburg, Germany
| | - Lucas Schneider
- Department of Physics, University of Hamburg, D-20355 Hamburg, Germany
| | | | - Khai Ton That
- Department of Physics, University of Hamburg, D-20355 Hamburg, Germany
| | | | - Jens Wiebe
- Department of Physics, University of Hamburg, D-20355 Hamburg, Germany
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