1
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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. [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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2
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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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3
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Cortés-Del Río E, Trivini S, Pascual JI, Cherkez V, Mallet P, Veuillen JY, Cuevas JC, Brihuega I. Shaping Graphene Superconductivity with Nanometer Precision. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2024; 20:e2308439. [PMID: 38112230 DOI: 10.1002/smll.202308439] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2023] [Revised: 11/23/2023] [Indexed: 12/21/2023]
Abstract
Graphene holds great potential for superconductivity due to its pure 2D nature, the ability to tune its carrier density through electrostatic gating, and its unique, relativistic-like electronic properties. At present, still far from controlling and understanding graphene superconductivity, mainly because the selective introduction of superconducting properties to graphene is experimentally very challenging. Here, a method is developed that enables shaping at will graphene superconductivity through a precise control of graphene-superconductor junctions. The method combines the proximity effect with scanning tunnelling microscope (STM) manipulation capabilities. Pb nano-islands are first grown that locally induce superconductivity in graphene. Using a STM, Pb nano-islands can be selectively displaced, over different types of graphene surfaces, with nanometre scale precision, in any direction, over distances of hundreds of nanometres. This opens an exciting playground where a large number of predefined graphene-superconductor hybrid structures can be investigated with atomic scale precision. To illustrate the potential, a series of experiments are performed, rationalized by the quasi-classical theory of superconductivity, going from the fundamental understanding of superconductor-graphene-superconductor heterostructures to the construction of superconductor nanocorrals, further used as "portable" experimental probes of local magnetic moments in graphene.
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Affiliation(s)
- Eva Cortés-Del Río
- Departamento Física de la Materia Condensada, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, E-28049, Spain
| | | | - José I Pascual
- CIC nanoGUNE-BRTA, Donostia-San Sebastián, 20018, Spain
- Ikerbasque, Basque Foundation for Science, Bilbao, 48013, Spain
| | - Vladimir Cherkez
- Université Grenoble Alpes, CNRS, Institut Néel, Grenoble, F-38400, France
- CNRS, Institut Neel, Grenoble, F-38042, France
| | - Pierre Mallet
- Université Grenoble Alpes, CNRS, Institut Néel, Grenoble, F-38400, France
- CNRS, Institut Neel, Grenoble, F-38042, France
| | - Jean-Yves Veuillen
- Université Grenoble Alpes, CNRS, Institut Néel, Grenoble, F-38400, France
- CNRS, Institut Neel, Grenoble, F-38042, France
| | - Juan C Cuevas
- Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Departamento Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
| | - Iván Brihuega
- Departamento Física de la Materia Condensada, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
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4
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Bolat R, Guevara JM, Leinen P, Knol M, Arefi HH, Maiworm M, Findeisen R, Temirov R, Hofmann OT, Maurer RJ, Tautz FS, Wagner C. Electrostatic potentials of atomic nanostructures at metal surfaces quantified by scanning quantum dot microscopy. Nat Commun 2024; 15:2259. [PMID: 38480707 PMCID: PMC10937982 DOI: 10.1038/s41467-024-46423-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2023] [Accepted: 02/26/2024] [Indexed: 03/17/2024] Open
Abstract
The discrete and charge-separated nature of matter - electrons and nuclei - results in local electrostatic fields that are ubiquitous in nanoscale structures and relevant in catalysis, nanoelectronics and quantum nanoscience. Surface-averaging techniques provide only limited experimental access to these potentials, which are determined by the shape, material, and environment of the nanostructure. Here, we image the potential over adatoms, chains, and clusters of Ag and Au atoms assembled on Ag(111) and quantify their surface dipole moments. By focusing on the total charge density, these data establish a benchmark for theory. Our density functional theory calculations show a very good agreement with experiment and allow a deeper analysis of the dipole formation mechanisms, their dependence on fundamental atomic properties and on the shape of the nanostructures. We formulate an intuitive picture of the basic mechanisms behind dipole formation, allowing better design choices for future nanoscale systems such as single-atom catalysts.
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Affiliation(s)
- Rustem Bolat
- Peter Grünberg Institut (PGI-3), Forschungszentrum Jülich, 52425, Jülich, Germany
- Jülich Aachen Research Alliance (JARA), Fundamentals of Future Information Technology, 52425, Jülich, Germany
- Experimentalphysik IV A, RWTH Aachen University, Otto-Blumenthal-Straße, 52074, Aachen, Germany
| | - Jose M Guevara
- Peter Grünberg Institut (PGI-3), Forschungszentrum Jülich, 52425, Jülich, Germany
| | - Philipp Leinen
- Peter Grünberg Institut (PGI-3), Forschungszentrum Jülich, 52425, Jülich, Germany
| | - Marvin Knol
- Peter Grünberg Institut (PGI-3), Forschungszentrum Jülich, 52425, Jülich, Germany
- Jülich Aachen Research Alliance (JARA), Fundamentals of Future Information Technology, 52425, Jülich, Germany
- Experimentalphysik IV A, RWTH Aachen University, Otto-Blumenthal-Straße, 52074, Aachen, Germany
| | - Hadi H Arefi
- Peter Grünberg Institut (PGI-3), Forschungszentrum Jülich, 52425, Jülich, Germany
- Jülich Aachen Research Alliance (JARA), Fundamentals of Future Information Technology, 52425, Jülich, Germany
| | - Michael Maiworm
- Control and Cyber-Physical Systems Laboratory, Technische Universität Darmstadt, 64277, Darmstadt, Germany
| | - Rolf Findeisen
- Control and Cyber-Physical Systems Laboratory, Technische Universität Darmstadt, 64277, Darmstadt, Germany
| | - Ruslan Temirov
- Peter Grünberg Institut (PGI-3), Forschungszentrum Jülich, 52425, Jülich, Germany
- Jülich Aachen Research Alliance (JARA), Fundamentals of Future Information Technology, 52425, Jülich, Germany
- II. Physikalisches Institut, Universität zu Köln, 50937, Köln, Germany
| | - Oliver T Hofmann
- Institute of Solid State Physics, NAWI Graz, Graz University of Technology, Petersgasse 16, 8010, Graz, Austria
| | - Reinhard J Maurer
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry, UK
- Department of Physics, University of Warwick, Gibbet Hill Road, Coventry, UK
| | - F Stefan Tautz
- Peter Grünberg Institut (PGI-3), Forschungszentrum Jülich, 52425, Jülich, Germany
- Jülich Aachen Research Alliance (JARA), Fundamentals of Future Information Technology, 52425, Jülich, Germany
- Experimentalphysik IV A, RWTH Aachen University, Otto-Blumenthal-Straße, 52074, Aachen, Germany
| | - Christian Wagner
- Peter Grünberg Institut (PGI-3), Forschungszentrum Jülich, 52425, Jülich, Germany.
- Jülich Aachen Research Alliance (JARA), Fundamentals of Future Information Technology, 52425, Jülich, Germany.
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5
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Li G, Li M, Zhou X, Gao HJ. Toward large-scale, ordered and tunable Majorana-zero-modes lattice on iron-based superconductors. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 87:016501. [PMID: 37963402 DOI: 10.1088/1361-6633/ad0c5c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2023] [Accepted: 11/14/2023] [Indexed: 11/16/2023]
Abstract
Majorana excitations are the quasiparticle analog of Majorana fermions in solid materials. Typical examples are the Majorana zero modes (MZMs) and the dispersing Majorana modes. When probed by scanning tunneling spectroscopy, the former manifest as a pronounced conductance peak locating precisely at zero-energy, while the latter behaves as constant or slowly varying density of states. The MZMs obey non-abelian statistics and are believed to be building blocks for topological quantum computing, which is highly immune to the environmental noise. Existing MZM platforms include hybrid structures such as topological insulator, semiconducting nanowire or 1D atomic chains on top of a conventional superconductor, and single materials such as the iron-based superconductors (IBSs) and 4Hb-TaS2. Very recently, ordered and tunable MZM lattice has also been realized in IBS LiFeAs, providing a scalable and applicable platform for future topological quantum computation. In this review, we present an overview of the recent local probe studies on MZMs. Classified by the material platforms, we start with the MZMs in the iron-chalcogenide superconductors where FeTe0.55Se0.45and (Li0.84Fe0.16)OHFeSe will be discussed. We then review the Majorana research in the iron-pnictide superconductors as well as other platforms beyond the IBSs. We further review recent works on ordered and tunable MZM lattice, showing that strain is a feasible tool to tune the topological superconductivity. Finally, we give our summary and perspective on future Majorana research.
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Affiliation(s)
- Geng Li
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- Hefei National Laboratory, Hefei 230088, People's Republic of China
| | - Meng Li
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, People's Republic of China
| | - Xingtai Zhou
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, People's Republic of China
| | - Hong-Jun Gao
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, People's Republic of China
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6
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Zhu W, Song R, Huang J, Wang QW, Cao Y, Zhai R, Bian Q, Shao Z, Jing H, Zhu L, Hou Y, Gao YH, Li S, Zheng F, Zhang P, Pan M, Liu J, Qu G, Gu Y, Zhang H, Dong Q, Huang Y, Yuan X, He J, Li G, Qian T, Chen G, Li SC, Pan M, Xue QK. Intrinsic surface p-wave superconductivity in layered AuSn 4. Nat Commun 2023; 14:7012. [PMID: 37919285 PMCID: PMC10622569 DOI: 10.1038/s41467-023-42781-7] [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: 06/05/2023] [Accepted: 10/20/2023] [Indexed: 11/04/2023] Open
Abstract
The search for topological superconductivity (TSC) is currently an exciting pursuit, since non-trivial topological superconducting phases could host exotic Majorana modes. However, the difficulty in fabricating proximity-induced TSC heterostructures, the sensitivity to disorder and stringent topological restrictions of intrinsic TSC place serious limitations and formidable challenges on the materials and related applications. Here, we report a new type of intrinsic TSC, namely intrinsic surface topological superconductivity (IS-TSC) and demonstrate it in layered AuSn4 with Tc of 2.4 K. Different in-plane and out-of-plane upper critical fields reflect a two-dimensional (2D) character of superconductivity. The two-fold symmetric angular dependences of both magneto-transport and the zero-bias conductance peak (ZBCP) in point-contact spectroscopy (PCS) in the superconducting regime indicate an unconventional pairing symmetry of AuSn4. The superconducting gap and surface multi-bands with Rashba splitting at the Fermi level (EF), in conjunction with first-principle calculations, strongly suggest that 2D unconventional SC in AuSn4 originates from the mixture of p-wave surface and s-wave bulk contributions, which leads to a two-fold symmetric superconductivity. Our results provide an exciting paradigm to realize TSC via Rashba effect on surface superconducting bands in layered materials.
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Affiliation(s)
- Wenliang Zhu
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710119, China
| | - Rui Song
- Science and Technology on Surface Physics and Chemistry Laboratory, Mianyang, 621908, China
| | - Jierui Huang
- Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Qi-Wei Wang
- National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China
| | - Yuan Cao
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710119, China
| | - Runqing Zhai
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710119, China
| | - Qi Bian
- School of Physics, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Zhibin Shao
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710119, China
| | - Hongmei Jing
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710119, China
| | - Lujun Zhu
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710119, China
| | - Yuefei Hou
- Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China
| | - Yu-Hang Gao
- National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China
| | - Shaojian Li
- School of Physics, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Fawei Zheng
- Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China
| | - Ping Zhang
- Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China.
- School of Physics and Physical Engineering, Qufu Normal University, Qufu, 273165, China.
| | - Mojun Pan
- Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Junde Liu
- Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Gexing Qu
- Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Yadong Gu
- Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Hao Zhang
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710119, China
| | - Qinxin Dong
- Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Yifei Huang
- Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Xiaoxia Yuan
- Shaanxi Applied Physics and Chemistry Research Institute, Xi'an, 710061, China
| | - Junbao He
- College of Physics and Electronic Engineering, Nanyang Normal University, Nanyang, 473061, China
| | - Gang Li
- Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong, 523808, China
| | - Tian Qian
- Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing, 100190, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China.
- Songshan Lake Materials Laboratory, Dongguan, Guangdong, 523808, China.
| | - Genfu Chen
- Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing, 100190, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China.
- Songshan Lake Materials Laboratory, Dongguan, Guangdong, 523808, China.
| | - Shao-Chun Li
- National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China.
| | - Minghu Pan
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710119, China.
- School of Physics, Huazhong University of Science and Technology, Wuhan, 430074, China.
| | - Qi-Kun Xue
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, 100084, China.
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China.
- Department of Physics, Southern University of Science and Technology, Shenzhen, 518055, China.
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7
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Bento Ribeiro RC, Correa JH, Ricco LS, Shelykh IA, Continentino MA, Seridonio AC, Minissale M, Le Lay G, Figueira MS. Spin-polarized Majorana zero modes in proximitized superconducting penta-silicene nanoribbons. Sci Rep 2023; 13:17965. [PMID: 37863891 PMCID: PMC10589331 DOI: 10.1038/s41598-023-44739-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2023] [Accepted: 10/11/2023] [Indexed: 10/22/2023] Open
Abstract
We theoretically propose penta-silicene nanoribbons (p-SiNRs) with induced p-wave superconductivity as a platform for the emergence of spin-polarized Majorana zero-modes (MZMs). The model explicitly considers the key ingredients of well-known Majorana hybrid nanowire setups: Rashba spin-orbit coupling, magnetic field perpendicular to the nanoribbon plane, and first nearest neighbor hopping with p-wave superconducting pairing. The energy spectrum of the system, as a function of chemical potential, reveals the existence of MZMs with a well-defined spin orientation localized at the opposite ends of both the top and bottom chains of the p-SiNR, associated with well-localized and nonoverlapping wave function profiles. Well-established experimental techniques enable the fabrication of highly ordered p-SiNRs, complemented by a thin lead film on top, responsible for inducing p-wave superconductivity through proximity effect. Moreover, the emergence of MZMs with explicit opposite spin orientations for some set of model parameters opens a new avenue for exploring quantum computing operations, which accounts for both MZMs and spin properties, as well as for new MZMs probe devices based on spin-polarized electronic transport mechanisms.
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Affiliation(s)
- R C Bento Ribeiro
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150, Urca, Rio de Janeiro, RJ, 22290-180, Brazil
| | - J H Correa
- Universidad Tecnológica del Perú, Nathalio Sánchez, 125, 15046, Lima, Peru
- AGH University of Krakow, Academic Centre for Materials and Nanotechnology, al. A. Mickiewicza 30, 30-059, Kraków, Poland
| | - L S Ricco
- Science Institute, University of Iceland, Dunhagi-3, 107, Reykjavik, Iceland
| | - I A Shelykh
- Science Institute, University of Iceland, Dunhagi-3, 107, Reykjavik, Iceland
- Russian Quantum Center, Skolkovo IC, Bolshoy Bulvar 30 bld. 1, Moscow, 121205, Russia
| | - Mucio A Continentino
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150, Urca, Rio de Janeiro, RJ, 22290-180, Brazil
| | - A C Seridonio
- School of Engineering, Department of Physics and Chemistry, São Paulo State University (UNESP), Ilha Solteira, SP, 15385-000, Brazil
| | - M Minissale
- Aix-Marseille Université, CNRS, PIIM UMR 7345, 13397, Marseille Cedex, France
| | - G Le Lay
- Aix-Marseille Université, CNRS, PIIM UMR 7345, 13397, Marseille Cedex, France
| | - M S Figueira
- Instituto de Física, Universidade Federal Fluminense, Av. Litorânea s/N, Niterói, RJ, CEP: 24210-340, Brazil.
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8
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Mandal M, Drucker NC, Siriviboon P, Nguyen T, Boonkird A, Lamichhane TN, Okabe R, Chotrattanapituk A, Li M. Topological Superconductors from a Materials Perspective. CHEMISTRY OF MATERIALS : A PUBLICATION OF THE AMERICAN CHEMICAL SOCIETY 2023; 35:6184-6200. [PMID: 37637011 PMCID: PMC10448998 DOI: 10.1021/acs.chemmater.3c00713] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Revised: 07/12/2023] [Indexed: 08/29/2023]
Abstract
Topological superconductors (TSCs) have garnered significant research and industry attention in the past two decades. By hosting Majorana bound states which can be used as qubits that are robust against local perturbations, TSCs offer a promising platform toward (nonuniversal) topological quantum computation. However, there has been a scarcity of TSC candidates, and the experimental signatures that identify a TSC are often elusive. In this Perspective, after a short review of the TSC basics and theories, we provide an overview of the TSC materials candidates, including natural compounds and synthetic material systems. We further introduce various experimental techniques to probe TSCs, focusing on how a system is identified as a TSC candidate and why a conclusive answer is often challenging to draw. We conclude by calling for new experimental signatures and stronger computational support to accelerate the search for new TSC candidates.
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Affiliation(s)
- Manasi Mandal
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, United States
| | - Nathan C. Drucker
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- School
of Engineering and Applied Sciences, Harvard
University, Cambridge, Massachusetts 02138, United States
| | - Phum Siriviboon
- Department
of Physics, MIT, Cambridge, Massachusetts 02139, United States
| | - Thanh Nguyen
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, United States
| | - Artittaya Boonkird
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, United States
| | - Tej Nath Lamichhane
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, United States
| | - Ryotaro Okabe
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Chemistry, MIT, Cambridge, Massachusetts 02139, United States
| | - Abhijatmedhi Chotrattanapituk
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Electrical Engineering and Computer Science, MIT, Cambridge, Massachusetts 02139, United States
| | - Mingda Li
- Quantum
Measurement Group, MIT, Cambridge, Massachusetts 02139, United States
- Department
of Nuclear Science and Engineering, MIT, Cambridge, Massachusetts 02139, United States
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9
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Ara F, Fakruddin Shahed SM, Hossain MI, Katoh K, Yamashita M, Komeda T. Control of the Magnetic Interaction between Single-Molecule Magnet TbPc 2 and Superconductor NbSe 2 Surface by an Intercalated Co Atom. NANO LETTERS 2023; 23:6900-6906. [PMID: 37505070 DOI: 10.1021/acs.nanolett.3c01298] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/29/2023]
Abstract
We demonstrate that an intercalated Co atom in superconductor NbSe2 could control the magnetic interaction between the adsorbed magnetic molecule of TbPc2 and the NbSe2 substrate. An intercalated Co atom enhances the magnetic interaction between the NbSe2 and the TbPc2 spin to cause Kondo resonance at the TbPc2 position, a spin-singlet state formed by the itinerary electron. By applying a surface-normal magnetic field, we change the molecule's spin direction from the initial one directed to the Co atom to the surface normal. The change appears as a split Kondo resonance at the TbPc2, one of which is enhanced at the Tb site, which disappears when the outer magnetic field normal to the surface is applied and never appears, even if we return B to 0 T. The phenomenon suggests that the intercalated magnetic atoms can control the magnetic interaction between a magnetic molecule and the superconductor NbSe2.
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Affiliation(s)
- Ferdous Ara
- Institute of Multidisciplinary Research for Advanced Materials (IMRAM), Tohoku University, 2-1-1 Katahira, Aoba-Ku, Sendai, Miyagi 980-8577, Japan
| | - Syed Mohammad Fakruddin Shahed
- Institute of Multidisciplinary Research for Advanced Materials (IMRAM), Tohoku University, 2-1-1 Katahira, Aoba-Ku, Sendai, Miyagi 980-8577, Japan
| | - Mohammad Ikram Hossain
- Department of Chemistry, Graduate School of Science, Tohoku University, Aramaki-Aza-Aoba, Aoba-Ku, Sendai, Miyagi 980-8578, Japan
| | - Keiichi Katoh
- Department of Chemistry, Graduate School of Science, Josai University, 1-1 Keyakidai, Sakado, Saitama 350-0295, Japan
| | - Masahiro Yamashita
- Department of Chemistry, Graduate School of Science, Tohoku University, Aramaki-Aza-Aoba, Aoba-Ku, Sendai, Miyagi 980-8578, Japan
- School of Materials Science and Engineering, Nankai University, Tianjin 300350, China
| | - Tadahiro Komeda
- Institute of Multidisciplinary Research for Advanced Materials (IMRAM), Tohoku University, 2-1-1 Katahira, Aoba-Ku, Sendai, Miyagi 980-8577, Japan
- Center for Spintronics Research Network, Tohoku University, 2-1-1 Katahira, Aoba-Ku, Sendai, Miyagi 980-8577, Japan
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10
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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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11
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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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12
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Lu S, Guo D, Cheng Z, Guo Y, Wang C, Deng J, Bai Y, Tian C, Zhou L, Shi Y, He J, Ji W, Zhang C. Controllable dimensionality conversion between 1D and 2D CrCl 3 magnetic nanostructures. Nat Commun 2023; 14:2465. [PMID: 37117203 PMCID: PMC10147715 DOI: 10.1038/s41467-023-38175-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2022] [Accepted: 04/19/2023] [Indexed: 04/30/2023] Open
Abstract
The fabrication of one-dimensional (1D) magnetic systems on solid surfaces, although of high fundamental interest, has yet to be achieved for a crossover between two-dimensional (2D) magnetic layers and their associated 1D spin chain systems. In this study, we report the fabrication of 1D single-unit-cell-width CrCl3 atomic wires and their stacked few-wire arrays on the surface of a van der Waals (vdW) superconductor NbSe2. Scanning tunneling microscopy/spectroscopy and first-principles calculations jointly revealed that the single wire shows an antiferromagnetic large-bandgap semiconducting state in an unexplored structure different from the well-known 2D CrCl3 phase. Competition among the total energies and nanostructure-substrate interfacial interactions of these two phases result in the appearance of the 1D phase. This phase was transformable to the 2D phase either prior to or after the growth for in situ or ex situ manipulations, in which the electronic interactions at the vdW interface play a nontrivial role that could regulate the dimensionality conversion and structural transformation between the 1D-2D CrCl3 phases.
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Affiliation(s)
- Shuangzan Lu
- School of Physics and Technology, Wuhan University, Wuhan, 430072, China
- Hubei Jiufengshan Laboratory, Wuhan, 430074, China
| | - Deping Guo
- Department of Physics and Beijing Key Laboratory of Optoelectronic Functional Materials and Micro-Nano Devices, Renmin University of China, Beijing, 100872, China
- Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing, 100872, China
| | - Zhengbo Cheng
- School of Physics and Technology, Wuhan University, Wuhan, 430072, China
| | - Yanping Guo
- School of Physics and Technology, Wuhan University, Wuhan, 430072, China
| | - Cong Wang
- Department of Physics and Beijing Key Laboratory of Optoelectronic Functional Materials and Micro-Nano Devices, Renmin University of China, Beijing, 100872, China
- Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing, 100872, China
| | - Jinghao Deng
- School of Physics and Technology, Wuhan University, Wuhan, 430072, China
| | - Yusong Bai
- School of Physics and Technology, Wuhan University, Wuhan, 430072, China
| | - Cheng Tian
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Linwei Zhou
- Department of Physics and Beijing Key Laboratory of Optoelectronic Functional Materials and Micro-Nano Devices, Renmin University of China, Beijing, 100872, China
- Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing, 100872, China
| | - Youguo Shi
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Jun He
- School of Physics and Technology, Wuhan University, Wuhan, 430072, China.
- Wuhan Institute of Quantum Technology, Wuhan, 430206, China.
| | - Wei Ji
- Department of Physics and Beijing Key Laboratory of Optoelectronic Functional Materials and Micro-Nano Devices, Renmin University of China, Beijing, 100872, China.
- Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing, 100872, China.
| | - Chendong Zhang
- School of Physics and Technology, Wuhan University, Wuhan, 430072, China.
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13
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Precise atom manipulation through deep reinforcement learning. Nat Commun 2022; 13:7499. [PMID: 36470857 PMCID: PMC9722711 DOI: 10.1038/s41467-022-35149-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Accepted: 11/18/2022] [Indexed: 12/12/2022] Open
Abstract
Atomic-scale manipulation in scanning tunneling microscopy has enabled the creation of quantum states of matter based on artificial structures and extreme miniaturization of computational circuitry based on individual atoms. The ability to autonomously arrange atomic structures with precision will enable the scaling up of nanoscale fabrication and expand the range of artificial structures hosting exotic quantum states. However, the a priori unknown manipulation parameters, the possibility of spontaneous tip apex changes, and the difficulty of modeling tip-atom interactions make it challenging to select manipulation parameters that can achieve atomic precision throughout extended operations. Here we use deep reinforcement learning (DRL) to control the real-world atom manipulation process. Several state-of-the-art reinforcement learning (RL) techniques are used jointly to boost data efficiency. The DRL agent learns to manipulate Ag adatoms on Ag(111) surfaces with optimal precision and is integrated with path planning algorithms to complete an autonomous atomic assembly system. The results demonstrate that state-of-the-art DRL can offer effective solutions to real-world challenges in nanofabrication and powerful approaches to increasingly complex scientific experiments at the atomic scale.
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14
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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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15
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Nagyfalusi B, Udvardi L, Szunyogh L. Magnetic ground state of supported monatomic Fe chains from first principles. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:395803. [PMID: 35853446 DOI: 10.1088/1361-648x/ac8260] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2022] [Accepted: 07/19/2022] [Indexed: 06/15/2023]
Abstract
A new computational scheme is presented based on a combination of the conjugate gradient and the Newton-Raphson method to self-consistently minimize the energy within local spin-density functional theory, thus to identify the ground state magnetic order of a finite cluster of atoms. The applicability of the newab initiooptimization method is demonstrated for Fe chains deposited on different metallic substrates. The optimized magnetic ground states of the Fe chains on Rh(111) are analyzed in details and a good comparison is found with those obtained from an extended Heisenberg model containing first principles based interaction parameters. Moreover, the effect of the different bilinear spin-spin interactions in the formation of the magnetic ground states is monitored. In case of Fe chains on Nb(110) spin-spiral configurations with opposite rotational sense are found as compared to previous spin-model results which hints on the importance of higher order chiral interactions. The wavelength of the spin-spiral states of Fe chains on Re(0001) was obtained in good agreement with scanning tunneling microscopy experiments.
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Affiliation(s)
- B Nagyfalusi
- Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, H-1525 Budapest, Hungary
- Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, Műegyetem rkp. 3, H-1111 Budapest, Hungary
| | - L Udvardi
- Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, Műegyetem rkp. 3, H-1111 Budapest, Hungary
- ELKH-BME Condensed Matter Research Group, Budapest University of Technology and Economics, Műegyetem rkp. 3, Budapest, H-1111, Hungary
| | - L Szunyogh
- Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, Műegyetem rkp. 3, H-1111 Budapest, Hungary
- ELKH-BME Condensed Matter Research Group, Budapest University of Technology and Economics, Műegyetem rkp. 3, Budapest, H-1111, Hungary
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16
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Gerken F, Posske T, Mukamel S, Thorwart M. Unique Signatures of Topological Phases in Two-Dimensional THz Spectroscopy. PHYSICAL REVIEW LETTERS 2022; 129:017401. [PMID: 35841546 DOI: 10.1103/physrevlett.129.017401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2021] [Revised: 01/12/2022] [Accepted: 06/03/2022] [Indexed: 06/15/2023]
Abstract
We develop a microscopic theory for the two-dimensional (2D) spectroscopy of one-dimensional topological superconductors. We consider a ring geometry of an archetypal topological superconductor with periodic boundary conditions, bypassing energy-specific differences caused by topologically protected or trivial boundary modes that are hard to distinguish. We show numerically and analytically that the cross-peak structure of the 2D spectra carries unique signatures of the topological phases of the chain. Our work reveals how 2D spectroscopy can identify topological phases in bulk properties.
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Affiliation(s)
- Felix Gerken
- I. Institut für Theoretische Physik, Universität Hamburg, Notkestraße 9, 22607 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Thore Posske
- I. Institut für Theoretische Physik, Universität Hamburg, Notkestraße 9, 22607 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Shaul Mukamel
- Departments of Chemistry and Physics and Astronomy, University of California, Irvine, California 92697-2025, USA
| | - Michael Thorwart
- I. Institut für Theoretische Physik, Universität Hamburg, Notkestraße 9, 22607 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
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17
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Thupakula U, Perrin V, Palacio-Morales A, Cario L, Aprili M, Simon P, Massee F. Coherent and Incoherent Tunneling into Yu-Shiba-Rusinov States Revealed by Atomic Scale Shot-Noise Spectroscopy. PHYSICAL REVIEW LETTERS 2022; 128:247001. [PMID: 35776485 DOI: 10.1103/physrevlett.128.247001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2021] [Revised: 12/27/2021] [Accepted: 05/18/2022] [Indexed: 06/15/2023]
Abstract
The pair breaking potential of individual magnetic impurities in s-wave superconductors generates localized states inside the superconducting gap commonly referred to as Yu-Shiba-Rusinov (YSR) states whose isolated nature makes them promising building blocks for artificial structures that may host Majorana fermions. One of the challenges in this endeavor is to understand their intrinsic lifetime, ℏ/Λ, which is expected to be limited by the inelastic coupling with the continuum thus leading to decoherence. Here we use shot-noise scanning tunneling microscopy to reveal that electron tunneling into superconducting 2H-NbSe_{2} mediated by YSR states is not Poissonian, but ordered as a function of time, as evidenced by a reduction of the noise. Moreover, our data show the concomitant transfer of charges e and 2e, indicating that incoherent single particle and coherent Andreev processes operate simultaneously. From the quantitative agreement between experiment and theory we obtain Λ=1 μeV≪k_{B}T demonstrating that shot noise can probe energy scales and timescales inaccessible by conventional spectroscopy whose resolution is thermally limited.
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Affiliation(s)
- U Thupakula
- Laboratoire de Physique des Solides (CNRS UMR 8502), Bâtiment 510, Université Paris-Sud/Université Paris-Saclay, 91405 Orsay, France
| | - V Perrin
- Laboratoire de Physique des Solides (CNRS UMR 8502), Bâtiment 510, Université Paris-Sud/Université Paris-Saclay, 91405 Orsay, France
| | - A Palacio-Morales
- Laboratoire de Physique des Solides (CNRS UMR 8502), Bâtiment 510, Université Paris-Sud/Université Paris-Saclay, 91405 Orsay, France
| | - L Cario
- Université de Nantes, CNRS, Institut des Matériaux Jean Rouxel, IMN, F-44000 Nantes, France
| | - M Aprili
- Laboratoire de Physique des Solides (CNRS UMR 8502), Bâtiment 510, Université Paris-Sud/Université Paris-Saclay, 91405 Orsay, France
| | - P Simon
- Laboratoire de Physique des Solides (CNRS UMR 8502), Bâtiment 510, Université Paris-Sud/Université Paris-Saclay, 91405 Orsay, France
| | - F Massee
- Laboratoire de Physique des Solides (CNRS UMR 8502), Bâtiment 510, Université Paris-Sud/Université Paris-Saclay, 91405 Orsay, France
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18
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Freeney SE, Slot MR, Gardenier TS, Swart I, Vanmaekelbergh D. Electronic Quantum Materials Simulated with Artificial Model Lattices. ACS NANOSCIENCE AU 2022; 2:198-224. [PMID: 35726276 PMCID: PMC9204828 DOI: 10.1021/acsnanoscienceau.1c00054] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/24/2021] [Revised: 01/24/2022] [Accepted: 01/28/2022] [Indexed: 11/29/2022]
Abstract
![]()
The
band structure and electronic properties of a material are
defined by the sort of elements, the atomic registry in the crystal,
the dimensions, the presence of spin–orbit coupling, and the
electronic interactions. In natural crystals, the interplay of these
factors is difficult to unravel, since it is usually not possible
to vary one of these factors in an independent way, keeping the others
constant. In other words, a complete understanding of complex electronic
materials remains challenging to date. The geometry of two- and one-dimensional
crystals can be mimicked in artificial lattices. Moreover, geometries
that do not exist in nature can be created for the sake of further
insight. Such engineered artificial lattices can be better controlled
and fine-tuned than natural crystals. This makes it easier to vary
the lattice geometry, dimensions, spin–orbit coupling, and
interactions independently from each other. Thus, engineering and
characterization of artificial lattices can provide unique insights.
In this Review, we focus on artificial lattices that are built atom-by-atom
on atomically flat metals, using atomic manipulation in a scanning
tunneling microscope. Cryogenic scanning tunneling microscopy allows
for consecutive creation, microscopic characterization, and band-structure
analysis by tunneling spectroscopy, amounting in the analogue quantum
simulation of a given lattice type. We first review the physical elements
of this method. We then discuss the creation and characterization
of artificial atoms and molecules. For the lattices, we review works
on honeycomb and Lieb lattices and lattices that result in crystalline
topological insulators, such as the Kekulé and “breathing”
kagome lattice. Geometric but nonperiodic structures such as electronic
quasi-crystals and fractals are discussed as well. Finally, we consider
the option to transfer the knowledge gained back to real materials,
engineered by geometric patterning of semiconductor quantum wells.
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Affiliation(s)
- Saoirsé E. Freeney
- Condensed Matter and Interfaces, Debye Institute of Nanomaterial Science, University of Utrecht, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Marlou R. Slot
- Condensed Matter and Interfaces, Debye Institute of Nanomaterial Science, University of Utrecht, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Thomas S. Gardenier
- Condensed Matter and Interfaces, Debye Institute of Nanomaterial Science, University of Utrecht, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Ingmar Swart
- Condensed Matter and Interfaces, Debye Institute of Nanomaterial Science, University of Utrecht, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - Daniel Vanmaekelbergh
- Condensed Matter and Interfaces, Debye Institute of Nanomaterial Science, University of Utrecht, Princetonplein 5, 3584 CC Utrecht, The Netherlands
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19
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Chiu CK, Wang Z. Yu-Shiba-Rusinov States in a Superconductor with Topological Z_{2} Bands. PHYSICAL REVIEW LETTERS 2022; 128:237001. [PMID: 35749202 DOI: 10.1103/physrevlett.128.237001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2021] [Revised: 04/19/2022] [Accepted: 04/26/2022] [Indexed: 06/15/2023]
Abstract
A Yu-Shiba-Rusinov (YSR) state is a localized in-gap state induced by a magnetic impurity in a superconductor. Recent experiments used an STM tip to manipulate the exchange coupling between an Fe adatom and the FeTe_{0.55}Se_{0.45} superconductor possessing a Z_{2} nontrivial band structure with topological surface states. As the tip moves close to the single Fe adatom, the energy of the in-gap state modulates and exhibits a zero-energy crossing followed by an unusual return to zero energy, which cannot be understood by coupling the magnetic impurity to the superconducting topological surface Dirac cone. Here, we numerically and analytically study the YSR states in superconductors with nontrivial Z_{2} bands and show the emergence of the two zero-energy crossings as a function of the exchange coupling between the magnetic impurity and the bulk states. We analyze the role of the topological surface states and compare in-gap states to systems with trivial Z_{2} bands. The spin polarization of the YSR states is further studied for future experimental measurement.
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Affiliation(s)
- Ching-Kai Chiu
- RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), Wako, Saitama 351-0198, Japan
- Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Ziqiang Wang
- Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA
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20
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Role of Majorana fermions in high-harmonic generation from Kitaev chain. Sci Rep 2022; 12:6722. [PMID: 35468909 PMCID: PMC9038912 DOI: 10.1038/s41598-022-10465-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2021] [Accepted: 02/14/2022] [Indexed: 11/08/2022] Open
Abstract
The observation of Majorana fermions as collective excitations in condensed-matter systems is an ongoing quest, and several state-of-the-art experiments have been performed in the last decade. As a potential avenue in this direction, we simulate the high-harmonic spectrum of Kitaev's superconducting chain model that hosts Majorana edge modes in its topological phase. It is well-known that this system exhibits a topological-trivial superconducting phase transition. We demonstrate that high-harmonic spectroscopy is sensitive to the phase transition in presence of open boundary conditions due to the presence or absence of these edge modes. The population dynamics of the Majorana edge modes are different from the bulk modes, which is the underlying reason for the distinct harmonic profile of both the phases. On the contrary, in presence of periodic boundary conditions with only bulk modes, high-harmonic spectroscopy becomes insensitive to the phase transition with similar harmonic profiles in both phases.
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21
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Quantum spins and hybridization in artificially-constructed chains of magnetic adatoms on a superconductor. Nat Commun 2022; 13:2160. [PMID: 35443753 PMCID: PMC9021194 DOI: 10.1038/s41467-022-29879-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2021] [Accepted: 04/01/2022] [Indexed: 11/09/2022] Open
Abstract
Magnetic adatom chains on surfaces constitute fascinating quantum spin systems. Superconducting substrates suppress interactions with bulk electronic excitations but couple the adatom spins to a chain of subgap Yu-Shiba-Rusinov (YSR) quasiparticles. Using a scanning tunneling microscope, we investigate such correlated spin-fermion systems by constructing Fe chains adatom by adatom on superconducting NbSe2. The adatoms couple entirely via the substrate, retaining their quantum spin nature. In dimers, we observe that the deepest YSR state undergoes a quantum phase transition due to Ruderman-Kittel-Kasuya-Yosida interactions, a distinct signature of quantum spins. Chains exhibit coherent hybridization and band formation of the YSR excitations, indicating ferromagnetic coupling. Longer chains develop separate domains due to coexisting charge-density-wave order of NbSe2. Despite the spin-orbit-coupled substrate, we find no signatures of Majoranas, possibly because quantum spins reduce the parameter range for topological superconductivity. We suggest that adatom chains are versatile systems for investigating correlated-electron physics and its interplay with topological superconductivity. Previous studies of magnetic adatom chains on superconducting substrates have mostly focused on the regime of dense chains and classical spins. Here, using scanning tunnelling microscopy, the authors study the excitation spectra of Fe chains on a NbSe2 surface, adatom by adatom, in the regime of quantum spins.
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22
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Schneider L, Beck P, Neuhaus-Steinmetz J, Rózsa L, Posske T, Wiebe J, Wiesendanger R. Precursors of Majorana modes and their length-dependent energy oscillations probed at both ends of atomic Shiba chains. NATURE NANOTECHNOLOGY 2022; 17:384-389. [PMID: 35256768 PMCID: PMC9018407 DOI: 10.1038/s41565-022-01078-4] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 01/12/2022] [Indexed: 05/27/2023]
Abstract
Isolated Majorana modes (MMs) are highly non-local quantum states with non-Abelian exchange statistics, which localize at the two ends of finite-size 1D topological superconductors of sufficient length. Experimental evidence for MMs is so far based on the detection of several key signatures: for example, a conductance peak pinned to the Fermi energy or an oscillatory peak splitting in short 1D systems when the MMs overlap. However, most of these key signatures were probed only on one of the ends of the 1D system, and firm evidence for an MM requires the simultaneous detection of all the key signatures on both ends. Here we construct short atomic spin chains on a superconductor-also known as Shiba chains-up to a chain length of 45 atoms using tip-assisted atom manipulation in scanning tunnelling microscopy experiments. We observe zero-energy conductance peaks localized at both ends of the chain that simultaneously split off from the Fermi energy in an oscillatory fashion after altering the chain length. By fitting the parameters of a low-energy model to the data, we find that the peaks are consistent with precursors of MMs that evolve into isolated MMs protected by an estimated topological gap of 50 μeV in chains of at least 35 nm length, corresponding to 70 atoms.
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Affiliation(s)
- Lucas Schneider
- Department of Physics, Universität Hamburg, Hamburg, Germany
| | - Philip Beck
- Department of Physics, Universität Hamburg, Hamburg, Germany
| | | | - Levente Rózsa
- Department of Physics, University of Konstanz, Konstanz, Germany
| | - Thore Posske
- I. Institute for Theoretical Physics, Universität Hamburg, Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee, Hamburg, Germany
| | - Jens Wiebe
- Department of Physics, Universität Hamburg, Hamburg, Germany.
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23
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Steiner JF, Mora C, Franke KJ, von Oppen F. Quantum Magnetism and Topological Superconductivity in Yu-Shiba-Rusinov Chains. PHYSICAL REVIEW LETTERS 2022; 128:036801. [PMID: 35119905 DOI: 10.1103/physrevlett.128.036801] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2021] [Revised: 11/02/2021] [Accepted: 01/07/2022] [Indexed: 06/14/2023]
Abstract
Chains of magnetic adatoms on superconductors have been discussed as promising systems for realizing Majorana end states. Here, we show that dilute Yu-Shiba-Rusinov (YSR) chains are also a versatile platform for quantum magnetism and correlated electron dynamics, with widely adjustable spin values and couplings. Focusing on subgap excitations, we derive an extended t-J model for dilute quantum YSR chains and use it to study the phase diagram as well as tunneling spectra. We explore the implications of quantum magnetism for the formation of a topological superconducting phase, contrasting it to existing models assuming classical spin textures.
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Affiliation(s)
- Jacob F Steiner
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | - Christophe Mora
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
- Laboratoire Matériaux et Phénomènes Quantiques, CNRS, Université de Paris, 75013 Paris, France
| | | | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
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24
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Drechsel C, D’Astolfo P, Liu JC, Glatzel T, Pawlak R, Meyer E. Topographic signatures and manipulations of Fe atoms, CO molecules and NaCl islands on superconducting Pb(111). BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2022; 13:1-9. [PMID: 35059274 PMCID: PMC8744454 DOI: 10.3762/bjnano.13.1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/20/2021] [Accepted: 12/08/2021] [Indexed: 06/14/2023]
Abstract
Topological superconductivity emerging in one- or two-dimensional hybrid materials is predicted as a key ingredient for quantum computing. However, not only the design of complex heterostructures is primordial for future applications but also the characterization of their electronic and structural properties at the atomic scale using the most advanced scanning probe microscopy techniques with functionalized tips. We report on the topographic signatures observed by scanning tunneling microscopy (STM) of carbon monoxide (CO) molecules, iron (Fe) atoms and sodium chloride (NaCl) islands deposited on superconducting Pb(111). For the CO adsorption a comparison with the Pb(110) substrate is demonstrated. We show a general propensity of these adsorbates to diffuse at low temperature under gentle scanning conditions. Our findings provide new insights into high-resolution probe microscopy imaging with terminated tips, decoupling atoms and molecules by NaCl islands or tip-induced lateral manipulation of iron atoms on top of the prototypical Pb(111) superconducting surface.
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Affiliation(s)
- Carl Drechsel
- Department of Physics, Universität Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Philipp D’Astolfo
- Department of Physics, Universität Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Jung-Ching Liu
- Department of Physics, Universität Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Thilo Glatzel
- Department of Physics, Universität Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Rémy Pawlak
- Department of Physics, Universität Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Ernst Meyer
- Department of Physics, Universität Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
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25
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Affiliation(s)
- Tao Zhang
- CAS Key Laboratory of Science and Technology on Applied Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
- State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
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26
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Kamlapure A, Cornils L, Žitko R, Valentyuk M, Mozara R, Pradhan S, Fransson J, Lichtenstein AI, Wiebe J, Wiesendanger R. Correlation of Yu-Shiba-Rusinov States and Kondo Resonances in Artificial Spin Arrays on an s-Wave Superconductor. NANO LETTERS 2021; 21:6748-6755. [PMID: 34351781 PMCID: PMC8392378 DOI: 10.1021/acs.nanolett.1c00387] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/28/2021] [Revised: 07/16/2021] [Indexed: 06/13/2023]
Abstract
Mutually interacting magnetic atoms coupled to a superconductor have gained enormous interest due to their potential for the realization of topological superconductivity. Individual magnetic impurities produce states within the superconducting energy gap known as Yu-Shiba-Rusinov (YSR) states. Here, using the tip of a scanning tunneling microscope, we artificially craft spin arrays consisting of an Fe adatom interacting with an assembly of interstitial Fe atoms (IFA) on a superconducting oxygen-reconstructed Ta(100) surface and show that the magnetic interaction between the adatom and the IFA assembly can be tuned by adjusting the number of IFAs in the assembly. The YSR state experiences a characteristic crossover in its energetic position and particle-hole spectral weight asymmetry when the Kondo resonance shows spectral depletion around the Fermi energy. By the help of slave-boson mean-field theory (SBMFT) and numerical renormalization group (NRG) calculations we associate the crossover with the transition from decoupled Kondo singlets to an antiferromagnetic ground state of the Fe adatom spin and the IFA assembly effective spin.
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Affiliation(s)
- Anand Kamlapure
- Department
of Physics, University of Hamburg, Jungiusstrasse 11, D-20355 Hamburg, Germany
| | - Lasse Cornils
- Department
of Physics, University of Hamburg, Jungiusstrasse 11, D-20355 Hamburg, Germany
| | - Rok Žitko
- Jožef
Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia
- Faculty
of Mathematics and Physics, University of
Ljubljana, Jadranska
19, SI-1000 Ljubljana, Slovenia
| | - Maria Valentyuk
- Department
of Physics, University of Hamburg, Jungiusstrasse 11, D-20355 Hamburg, Germany
- Department
of Theoretical Physics and Applied Mathematics, Ural Federal University, 19 Mira Street, Yekaterinburg 620002, Russia
| | - Roberto Mozara
- Department
of Physics, University of Hamburg, Jungiusstrasse 11, D-20355 Hamburg, Germany
| | - Saurabh Pradhan
- Department
of Physics and Astronomy, Uppsala University, P.O. Box 516, Uppsala SE-751 21, Sweden
| | - Jonas Fransson
- Department
of Physics and Astronomy, Uppsala University, P.O. Box 516, Uppsala SE-751 21, Sweden
| | - Alexander I. Lichtenstein
- Department
of Physics, University of Hamburg, Jungiusstrasse 11, D-20355 Hamburg, Germany
- Department
of Theoretical Physics and Applied Mathematics, Ural Federal University, 19 Mira Street, Yekaterinburg 620002, Russia
| | - Jens Wiebe
- Department
of Physics, University of Hamburg, Jungiusstrasse 11, D-20355 Hamburg, Germany
| | - Roland Wiesendanger
- Department
of Physics, University of Hamburg, Jungiusstrasse 11, D-20355 Hamburg, Germany
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27
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Park S, Barrena V, Mañas-Valero S, Baldoví JJ, Fente A, Herrera E, Mompeán F, García-Hernández M, Rubio Á, Coronado E, Guillamón I, Yeyati AL, Suderow H. Coherent coupling between vortex bound states and magnetic impurities in 2D layered superconductors. Nat Commun 2021; 12:4668. [PMID: 34344878 PMCID: PMC8333272 DOI: 10.1038/s41467-021-24531-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2021] [Accepted: 06/23/2021] [Indexed: 12/04/2022] Open
Abstract
Bound states in superconductors are expected to exhibit a spatially resolved electron-hole asymmetry which is the hallmark of their quantum nature. This asymmetry manifests as oscillations at the Fermi wavelength, which is usually tiny and thus washed out by thermal broadening or by scattering at defects. Here we demonstrate theoretically and confirm experimentally that, when coupled to magnetic impurities, bound states in a vortex core exhibit an emergent axial electron-hole asymmetry on a much longer scale, set by the coherence length. We study vortices in 2H-NbSe2 and in 2H-NbSe1.8S0.2 with magnetic impurities, characterizing these with detailed Hubbard-corrected density functional calculations. We find that the induced electron-hole imbalance depends on the band character of the superconducting material. Our results show that coupling between quantum bound states in superconductors is remarkably robust and has a strong influence in tunneling measurements.
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Affiliation(s)
- Sunghun Park
- Departamento de Física Teórica de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, Spain
| | - Víctor Barrena
- Laboratorio de Bajas Temperaturas y Altos Campos Magnéticos, Departamento de Física de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Unidad Asociada UAM-CSIC, Universidad Autónoma de Madrid, Madrid, Spain
| | - Samuel Mañas-Valero
- Instituto de Ciencia Molecular (ICMol), Universidad de Valencia, Paterna, Spain
| | - José J Baldoví
- Instituto de Ciencia Molecular (ICMol), Universidad de Valencia, Paterna, Spain
- Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany
| | - Antón Fente
- Laboratorio de Bajas Temperaturas y Altos Campos Magnéticos, Departamento de Física de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Unidad Asociada UAM-CSIC, Universidad Autónoma de Madrid, Madrid, Spain
| | - Edwin Herrera
- Laboratorio de Bajas Temperaturas y Altos Campos Magnéticos, Departamento de Física de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Unidad Asociada UAM-CSIC, Universidad Autónoma de Madrid, Madrid, Spain
| | - Federico Mompeán
- Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas (ICMM-CSIC), Madrid, Spain
| | - Mar García-Hernández
- Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas (ICMM-CSIC), Madrid, Spain
| | - Ángel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del País Vasco CFM CSIC-UPV/EHU-MPC & DIPC, San Sebastián, Spain
| | - Eugenio Coronado
- Instituto de Ciencia Molecular (ICMol), Universidad de Valencia, Paterna, Spain
| | - Isabel Guillamón
- Laboratorio de Bajas Temperaturas y Altos Campos Magnéticos, Departamento de Física de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Unidad Asociada UAM-CSIC, Universidad Autónoma de Madrid, Madrid, Spain
| | - Alfredo Levy Yeyati
- Departamento de Física Teórica de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, Spain
| | - Hermann Suderow
- Laboratorio de Bajas Temperaturas y Altos Campos Magnéticos, Departamento de Física de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Unidad Asociada UAM-CSIC, Universidad Autónoma de Madrid, Madrid, Spain.
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28
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Lászlóffy A, Palotás K, Rózsa L, Szunyogh L. Electronic and Magnetic Properties of Building Blocks of Mn and Fe Atomic Chains on Nb(110). NANOMATERIALS 2021; 11:nano11081933. [PMID: 34443761 PMCID: PMC8401957 DOI: 10.3390/nano11081933] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Revised: 07/15/2021] [Accepted: 07/16/2021] [Indexed: 11/16/2022]
Abstract
We present results for the electronic and magnetic structure of Mn and Fe clusters on Nb(110) surface, focusing on building blocks of atomic chains as possible realizations of topological superconductivity. The magnetic ground states of the atomic dimers and most of the monatomic chains are determined by the nearest-neighbor isotropic interaction. To gain physical insight, the dependence on the crystallographic direction as well as on the atomic coordination number is analyzed via an orbital decomposition of this isotropic interaction based on the spin-cluster expansion and the difference in the local density of states between ferromagnetic and antiferromagnetic configurations. A spin-spiral ground state is obtained for Fe chains along the [11¯0] direction as a consequence of the frustration of the isotropic interactions. Here, a flat spin-spiral dispersion relation is identified, which can stabilize spin spirals with various wave vectors together with the magnetic anisotropy. This may lead to the observation of spin spirals of different wave vectors and chiralities in longer chains instead of a unique ground state.
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Affiliation(s)
- András Lászlóffy
- Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, H-1525 Budapest, Hungary;
- Department of Theoretical Physics, Budapest University of Technology and Economics, H-1111 Budapest, Hungary;
| | - Krisztián Palotás
- Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, H-1525 Budapest, Hungary;
- Department of Theoretical Physics, Budapest University of Technology and Economics, H-1111 Budapest, Hungary;
- MTA-SZTE Reaction Kinetics and Surface Chemistry Research Group, University of Szeged, H-6720 Szeged, Hungary
- Correspondence:
| | - Levente Rózsa
- Department of Physics, University of Konstanz, D-78457 Konstanz, Germany;
| | - László Szunyogh
- Department of Theoretical Physics, Budapest University of Technology and Economics, H-1111 Budapest, Hungary;
- MTA-BME Condensed Matter Research Group, Budapest University of Technology and Economics, H-1111 Budapest, Hungary
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29
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Lodge MS, Yang SA, Mukherjee S, Weber B. Atomically Thin Quantum Spin Hall Insulators. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2021; 33:e2008029. [PMID: 33893669 DOI: 10.1002/adma.202008029] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2020] [Revised: 01/12/2021] [Indexed: 06/12/2023]
Abstract
Atomically thin topological materials are attracting growing attention for their potential to radically transform classical and quantum electronic device concepts. Among them is the quantum spin Hall (QSH) insulator-a 2D state of matter that arises from interplay of topological band inversion and strong spin-orbit coupling, with large tunable bulk bandgaps up to 800 meV and gapless, 1D edge states. Reviewing recent advances in materials science and engineering alongside theoretical description, the QSH materials library is surveyed with focus on the prospects for QSH-based device applications. In particular, theoretical predictions of nontrivial superconducting pairing in the QSH state toward Majorana-based topological quantum computing are discussed, which are the next frontier in QSH materials research.
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Affiliation(s)
- Michael S Lodge
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore
| | - Shengyuan A Yang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore, 487372, Singapore
| | - Shantanu Mukherjee
- Department of Physics, Indian Institute of Technology Madras, Chennai, Tamil Nadu, 600036, India
- Quantum Centres in Diamond and Emergent Materials (QCenDiem)-Group, IIT Madras, Chennai, Tamil Nadu, 600036, India
- Computational Materials Science Group, IIT Madras, Chennai, Tamil Nadu, 600036, India
| | - Bent Weber
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore
- Australian Research Council (ARC) Centre of Excellence in Future Low-Energy Electronics Techonologies (FLEET), School of Physics, Monash University, Clayton, VIC, 3800, Australia
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30
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Cortés-Del Río E, Lado JL, Cherkez V, Mallet P, Veuillen JY, Cuevas JC, Gómez-Rodríguez JM, Fernández-Rossier J, Brihuega I. Observation of Yu-Shiba-Rusinov States in Superconducting Graphene. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2021; 33:e2008113. [PMID: 33890694 DOI: 10.1002/adma.202008113] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2020] [Revised: 02/26/2021] [Indexed: 06/12/2023]
Abstract
When magnetic atoms are inserted inside a superconductor, the superconducting order is locally depleted as a result of the antagonistic nature of magnetism and superconductivity. Thereby, distinctive spectral features, known as Yu-Shiba-Rusinov states, appear inside the superconducting gap. The search for Yu-Shiba-Rusinov states in different materials is intense, as they can be used as building blocks to promote Majorana modes suitable for topological quantum computing. Here, the first observation of Yu-Shiba-Rusinov states in graphene, a non-superconducting 2D material, and without the participation of magnetic atoms, is reported. Superconductivity in graphene is induced by proximity effect brought by adsorbing nanometer-scale superconducting Pb islands. Using scanning tunneling microscopy and spectroscopy the superconducting proximity gap is measured in graphene, and Yu-Shiba-Rusinov states are visualized in graphene grain boundaries. The results reveal the very special nature of those Yu-Shiba-Rusinov states, which extends more than 20 nm away from the grain boundaries. These observations provide the long-sought experimental confirmation that graphene grain boundaries host local magnetic moments and constitute the first observation of Yu-Shiba-Rusinov states in a chemically pure system.
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Affiliation(s)
- Eva Cortés-Del Río
- Departamento Física de la Materia Condensada, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
| | - Jose Luis Lado
- Department of Applied Physics, Aalto University, Espoo, 02150, Finland
| | - Vladimir Cherkez
- Université Grenoble Alpes, Grenoble, 38000, France
- CNRS, Institut Neel, Grenoble, F-38042, France
| | - Pierre Mallet
- Université Grenoble Alpes, Grenoble, 38000, France
- CNRS, Institut Neel, Grenoble, F-38042, France
| | - Jean-Yves Veuillen
- Université Grenoble Alpes, Grenoble, 38000, France
- CNRS, Institut Neel, Grenoble, F-38042, France
| | - Juan Carlos Cuevas
- Departamento Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, E-28049, Spain
| | - José María Gómez-Rodríguez
- Departamento Física de la Materia Condensada, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
| | - Joaquín Fernández-Rossier
- QuantaLab, International Iberian Nanotechnology Laboratory (INL), Avenida Mestre José Veiga, Braga, 4715-310, Portugal
- Departamento de Física Aplicada, Universidad de Alicante, San Vicente del Raspeig, Alicante, 03690, Spain
| | - Iván Brihuega
- Departamento Física de la Materia Condensada, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
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31
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Interaction-induced topological phase transition and Majorana edge states in low-dimensional orbital-selective Mott insulators. Nat Commun 2021; 12:2955. [PMID: 34011947 PMCID: PMC8134496 DOI: 10.1038/s41467-021-23261-2] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2020] [Accepted: 04/21/2021] [Indexed: 11/08/2022] Open
Abstract
Topological phases of matter are among the most intriguing research directions in Condensed Matter Physics. It is known that superconductivity induced on a topological insulator's surface can lead to exotic Majorana modes, the main ingredient of many proposed quantum computation schemes. In this context, the iron-based high critical temperature superconductors are a promising platform to host such an exotic phenomenon in real condensed-matter compounds. The Coulomb interaction is commonly believed to be vital for the magnetic and superconducting properties of these systems. This work bridges these two perspectives and shows that the Coulomb interaction can also drive a canonical superconductor with orbital degrees of freedom into the topological state. Namely, we show that above a critical value of the Hubbard interaction the system simultaneously develops spiral spin order, a highly unusual triplet amplitude in superconductivity, and, remarkably, Majorana fermions at the edges of the system.
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32
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Bonkhoff M, Jägering K, Eggert S, Pelster A, Thorwart M, Posske T. Bosonic Continuum Theory of One-Dimensional Lattice Anyons. PHYSICAL REVIEW LETTERS 2021; 126:163201. [PMID: 33961455 DOI: 10.1103/physrevlett.126.163201] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2020] [Revised: 12/11/2020] [Accepted: 03/22/2021] [Indexed: 06/12/2023]
Abstract
Anyons with arbitrary exchange phases exist on 1D lattices in ultracold gases. Yet, known continuum theories in 1D do not match. We derive the continuum limit of 1D lattice anyons via interacting bosons. The theory maintains the exchange phase periodicity fully analogous to 2D anyons. This provides a mapping between experiments, lattice anyons, and continuum theories, including Kundu anyons with a natural regularization as a special case. We numerically estimate the Luttinger parameter as a function of the exchange angle to characterize long-range signatures of the theory and predict different velocities for left- and right-moving collective excitations.
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Affiliation(s)
- Martin Bonkhoff
- Physics Department and Research Center Optimas, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Kevin Jägering
- Physics Department and Research Center Optimas, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Sebastian Eggert
- Physics Department and Research Center Optimas, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Axel Pelster
- Physics Department and Research Center Optimas, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Michael Thorwart
- I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstraße 9, 20355 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Thore Posske
- I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstraße 9, 20355 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
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33
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Ding H, Hu Y, Randeria MT, Hoffman S, Deb O, Klinovaja J, Loss D, Yazdani A. Tuning interactions between spins in a superconductor. Proc Natl Acad Sci U S A 2021; 118:e2024837118. [PMID: 33782131 PMCID: PMC8040815 DOI: 10.1073/pnas.2024837118] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Novel many-body and topological electronic phases can be created in assemblies of interacting spins coupled to a superconductor, such as one-dimensional topological superconductors with Majorana zero modes (MZMs) at their ends. Understanding and controlling interactions between spins and the emergent band structure of the in-gap Yu-Shiba-Rusinov (YSR) states they induce in a superconductor are fundamental for engineering such phases. Here, by precisely positioning magnetic adatoms with a scanning tunneling microscope (STM), we demonstrate both the tunability of exchange interaction between spins and precise control of the hybridization of YSR states they induce on the surface of a bismuth (Bi) thin film that is made superconducting with the proximity effect. In this platform, depending on the separation of spins, the interplay among Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, spin-orbit coupling, and surface magnetic anisotropy stabilizes different types of spin alignments. Using high-resolution STM spectroscopy at millikelvin temperatures, we probe these spin alignments through monitoring the spin-induced YSR states and their energy splitting. Such measurements also reveal a quantum phase transition between the ground states with different electron number parity for a pair of spins in a superconductor tuned by their separation. Experiments on larger assemblies show that spin-spin interactions can be mediated in a superconductor over long distances. Our results show that controlling hybridization of the YSR states in this platform provides the possibility of engineering the band structure of such states for creating topological phases.
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Affiliation(s)
- Hao Ding
- Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544
- Department of Physics, Princeton University, Princeton, NJ 08544
| | - Yuwen Hu
- Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544
- Department of Physics, Princeton University, Princeton, NJ 08544
| | - Mallika T Randeria
- Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544
- Department of Physics, Princeton University, Princeton, NJ 08544
| | - Silas Hoffman
- Department of Physics, University of Basel, CH-4056 Basel, Switzerland
- Department of Physics, University of Florida, Gainesville, FL 32611
| | - Oindrila Deb
- Department of Physics, University of Basel, CH-4056 Basel, Switzerland
| | - Jelena Klinovaja
- Department of Physics, University of Basel, CH-4056 Basel, Switzerland
| | - Daniel Loss
- Department of Physics, University of Basel, CH-4056 Basel, Switzerland
| | - Ali Yazdani
- Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544;
- Department of Physics, Princeton University, Princeton, NJ 08544
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34
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Spin-orbit coupling induced splitting of Yu-Shiba-Rusinov states in antiferromagnetic dimers. Nat Commun 2021; 12:2040. [PMID: 33795672 PMCID: PMC8016932 DOI: 10.1038/s41467-021-22261-6] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2020] [Accepted: 03/02/2021] [Indexed: 11/25/2022] Open
Abstract
Magnetic atoms coupled to the Cooper pairs of a superconductor induce Yu-Shiba-Rusinov states (in short Shiba states). In the presence of sufficiently strong spin-orbit coupling, the bands formed by hybridization of the Shiba states in ensembles of such atoms can support low-dimensional topological superconductivity with Majorana bound states localized on the ensembles’ edges. Yet, the role of spin-orbit coupling for the hybridization of Shiba states in dimers of magnetic atoms, the building blocks for such systems, is largely unexplored. Here, we reveal the evolution of hybridized multi-orbital Shiba states from a single Mn adatom to artificially constructed ferromagnetically and antiferromagnetically coupled Mn dimers placed on a Nb(110) surface. Upon dimer formation, the atomic Shiba orbitals split for both types of magnetic alignment. Our theoretical calculations attribute the unexpected splitting in antiferromagnetic dimers to spin-orbit coupling and broken inversion symmetry at the surface. Our observations point out the relevance of previously unconsidered factors on the formation of Shiba bands and their topological classification. The influence of spin-orbit coupling on the hybridization of Shiba states in dimers of magnetic atoms on superconducting surfaces remains unexplored. Here, the authors reveal a splitting of atomic Shiba orbitals due to spin-orbit coupling and broken inversion symmetry in antiferromagnetically coupled Mn dimers placed on a Nb(110) surface.
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35
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Udagawa M, Takayoshi S, Oka T. Scanning Tunneling Microscopy as a Single Majorana Detector of Kitaev's Chiral Spin Liquid. PHYSICAL REVIEW LETTERS 2021; 126:127201. [PMID: 33834823 DOI: 10.1103/physrevlett.126.127201] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2020] [Accepted: 02/17/2021] [Indexed: 06/12/2023]
Abstract
We propose a local detection scheme for the Majorana zero mode (MZM) carried by a vison in Kitaev's chiral spin liquid (CSL) using scanning tunneling microscopy (STM). The STM introduces a single Majorana into the system through hole-charge injection and the Majorana interacts with the MZM to form a stable composite object. We derive the exact analytical expression of single-hole Green's function in the Mott insulating limit of Kitaev's model, and show that the differential conductance has split peaks, as a consequence of resonant tunneling through the vison-hole composite. The peak splitting turns out comparable to the Majorana gap in CSL, well within the reach of experimental observation.
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Affiliation(s)
- Masafumi Udagawa
- Department of Physics, Gakushuin University, Mejiro, Toshima-ku, Tokyo 171-8588, Japan
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
| | - Shintaro Takayoshi
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
- Department of Physics, Konan University, Kobe, 658-8501, Japan
| | - Takashi Oka
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
- Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
- Trans-scale Quantum Science Institute, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
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36
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Wang D, Wiebe J, Zhong R, Gu G, Wiesendanger R. Spin-Polarized Yu-Shiba-Rusinov States in an Iron-Based Superconductor. PHYSICAL REVIEW LETTERS 2021; 126:076802. [PMID: 33666492 DOI: 10.1103/physrevlett.126.076802] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2020] [Accepted: 01/21/2021] [Indexed: 05/06/2023]
Abstract
Yu-Shiba-Rusinov (YSR) bound states appear when a magnetic atom interacts with a superconductor. Here, we report on spin-resolved spectroscopic studies of YSR states related with Fe atoms deposited on the surface of the topological superconductor FeTe_{0.55}Se_{0.45} using a spin-polarized scanning tunneling microscope. We clearly identify the spin signature of pairs of YSR bound states at finite energies within the superconducting gap having opposite spin polarization as theoretically predicted. In addition, we also observe zero-energy bound states for some of the adsorbed Fe atoms. In this case, a spin signature is found to be absent indicating the absence of Majorana bound states associated with Fe adatoms on FeTe_{0.55}Se_{0.45}.
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Affiliation(s)
- Dongfei Wang
- Department of Physics, University of Hamburg, Jungiusstrasse 11, 20355 Hamburg, Germany
| | - Jens Wiebe
- Department of Physics, University of Hamburg, Jungiusstrasse 11, 20355 Hamburg, Germany
| | - Ruidan Zhong
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Genda Gu
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Roland Wiesendanger
- Department of Physics, University of Hamburg, Jungiusstrasse 11, 20355 Hamburg, Germany
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37
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Correlating Josephson supercurrents and Shiba states in quantum spins unconventionally coupled to superconductors. Nat Commun 2021; 12:1108. [PMID: 33597519 PMCID: PMC7889868 DOI: 10.1038/s41467-021-21347-5] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2020] [Accepted: 01/20/2021] [Indexed: 11/22/2022] Open
Abstract
Local spins coupled to superconductors give rise to several emerging phenomena directly linked to the competition between Cooper pair formation and magnetic exchange. These effects are generally scrutinized using a spectroscopic approach which relies on detecting the in-gap bound modes arising from Cooper pair breaking, the so-called Yu-Shiba-Rusinov (YSR) states. However, the impact of local magnetic impurities on the superconducting order parameter remains largely unexplored. Here, we use scanning Josephson spectroscopy to directly visualize the effect of magnetic perturbations on Cooper pair tunneling between superconducting electrodes at the atomic scale. By increasing the magnetic impurity orbital occupation by adding one electron at a time, we reveal the existence of a direct correlation between Josephson supercurrent suppression and YSR states. Moreover, in the metallic regime, we detect zero bias anomalies which break the existing framework based on competing Kondo and Cooper pair singlet formation mechanisms. Based on first-principle calculations, these results are rationalized in terms of unconventional spin-excitations induced by the finite magnetic anisotropy energy. Our findings have far reaching implications for phenomena that rely on the interplay between quantum spins and superconductivity. The impact of local magnetic impurities on superconducting order parameter remains largely unexplored. Here, the authors visualize the effect of different magnetic perturbations on a superconductor, unveiling a rich correlation of the interplay between quantum spins and superconductivity in different spectroscopic regimes.
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38
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Schneider L, Beck P, Wiebe J, Wiesendanger R. Atomic-scale spin-polarization maps using functionalized superconducting probes. SCIENCE ADVANCES 2021; 7:7/4/eabd7302. [PMID: 33523927 PMCID: PMC7817096 DOI: 10.1126/sciadv.abd7302] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2020] [Accepted: 12/02/2020] [Indexed: 05/27/2023]
Abstract
A scanning tunneling microscope (STM) with a magnetic tip that has a sufficiently strong spin polarization can be used to map the sample's spin structure down to the atomic scale but usually lacks the possibility to absolutely determine the value of the sample's spin polarization. Magnetic impurities in superconducting materials give rise to pairs of perfectly, i.e., 100%, spin-polarized subgap resonances. In this work, we functionalize the apex of a superconducting Nb STM tip with such impurity states by attaching Fe atoms to probe the spin polarization of atom-manipulated Mn nanomagnets on a Nb(110) surface. By comparison with spin-polarized STM measurements of the same nanomagnets using Cr bulk tips, we demonstrate an extraordinary spin sensitivity and the possibility to measure the sample's spin-polarization values close to the Fermi level quantitatively with our new functionalized probes.
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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
| | - Jens Wiebe
- Department of Physics, University of Hamburg, D-20355 Hamburg, Germany.
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39
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Topological superconductivity in a van der Waals heterostructure. Nature 2020; 588:424-428. [DOI: 10.1038/s41586-020-2989-y] [Citation(s) in RCA: 106] [Impact Index Per Article: 26.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2020] [Accepted: 09/23/2020] [Indexed: 11/08/2022]
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40
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Li W, Paul S, von Bergmann K, Heinze S, Wiesendanger R. Stacking-Dependent Spin Interactions in Pd/Fe Bilayers on Re(0001). PHYSICAL REVIEW LETTERS 2020; 125:227205. [PMID: 33315450 DOI: 10.1103/physrevlett.125.227205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2020] [Accepted: 10/23/2020] [Indexed: 06/12/2023]
Abstract
Using spin-polarized scanning tunneling microscopy and density functional theory, we have studied the magnetic properties of Pd/Fe atomic bilayers on Re(0001). Two kinds of magnetic ground states are discovered due to different types of stacking of the Pd adlayer on Fe/Re(0001). For fcc stacking of Pd on Fe/Re(0001), it is a spin spiral propagating along the close-packed (ΓK[over ¯]) direction with a period of about 0.9 nm, driven by frustrated exchange and Dzyaloshinskii-Moriya interactions. For the hcp stacking, the four-site four-spin interaction stabilizes an up-up-down-down state propagating perpendicular to the close-packed direction (along ΓM[over ¯]) with a period of about 1.0 nm. Our work shows how higher-order exchange interactions can be tuned at interfaces.
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Affiliation(s)
- W Li
- Department of Physics, University of Hamburg, Jungiusstrasse 9-11, 20355 Hamburg, Germany
| | - S Paul
- Institute of Theoretical Physics and Astrophysics, University of Kiel, Leibnizstrasse 15, 24098 Kiel, Germany
| | - K von Bergmann
- Department of Physics, University of Hamburg, Jungiusstrasse 9-11, 20355 Hamburg, Germany
| | - S Heinze
- Institute of Theoretical Physics and Astrophysics, University of Kiel, Leibnizstrasse 15, 24098 Kiel, Germany
| | - R Wiesendanger
- Department of Physics, University of Hamburg, Jungiusstrasse 9-11, 20355 Hamburg, Germany
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41
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Schneider L, Brinker S, Steinbrecher M, Hermenau J, Posske T, Dos Santos Dias M, Lounis S, Wiesendanger R, Wiebe J. Controlling in-gap end states by linking nonmagnetic atoms and artificially-constructed spin chains on superconductors. Nat Commun 2020; 11:4707. [PMID: 32948776 PMCID: PMC7501864 DOI: 10.1038/s41467-020-18540-3] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2020] [Accepted: 08/25/2020] [Indexed: 11/09/2022] Open
Abstract
Chains of magnetic atoms with either strong spin-orbit coupling or spiral magnetic order which are proximity-coupled to superconducting substrates can host topologically non-trivial Majorana bound states. The experimental signature of these states consists of spectral weight at the Fermi energy which is spatially localized near the ends of the chain. However, topologically trivial Yu-Shiba-Rusinov in-gap states localized near the ends of the chain can lead to similar spectra. Here, we explore a protocol to disentangle these contributions by artificially augmenting a candidate Majorana spin chain with orbitally-compatible nonmagnetic atoms. Combining scanning tunneling spectroscopy with ab-initio and tight-binding calculations, we realize a sharp spatial transition between the proximity-coupled spiral magnetic order and the non-magnetic superconducting wire termination, with persistent zero-energy spectral weight localized at either end of the magnetic spiral. Our findings open a new path towards the control of the spatial position of in-gap end states, trivial or Majorana, via different chain terminations, and the realization of designer Majorana chain networks for demonstrating topological quantum computation.
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Affiliation(s)
- Lucas Schneider
- Department of Physics, Universität Hamburg, D-20355, Hamburg, Germany
| | - Sascha Brinker
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, D-52425, Jülich, Germany.,Department of Physics, RWTH Aachen University, 52056, Aachen, Germany
| | - Manuel Steinbrecher
- Department of Physics, Universität Hamburg, D-20355, Hamburg, Germany.,Institute for Molecules and Materials (IMM), Radboud University, Nijmegen, The Netherlands
| | - Jan Hermenau
- Department of Physics, Universität Hamburg, D-20355, Hamburg, Germany
| | - Thore Posske
- I. Institute for Theoretical Physics, Universität Hamburg, D-20355, Hamburg, Germany
| | - Manuel Dos Santos Dias
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, D-52425, Jülich, Germany
| | - Samir Lounis
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, D-52425, Jülich, Germany
| | | | - Jens Wiebe
- Department of Physics, Universität Hamburg, D-20355, Hamburg, Germany.
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42
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Kim H, Rózsa L, Schreyer D, Simon E, Wiesendanger R. Long-range focusing of magnetic bound states in superconducting lanthanum. Nat Commun 2020; 11:4573. [PMID: 32917904 PMCID: PMC7486372 DOI: 10.1038/s41467-020-18406-8] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2020] [Accepted: 08/21/2020] [Indexed: 11/08/2022] Open
Abstract
Quantum mechanical systems with long-range interactions between quasiparticles provide a promising platform for coherent quantum information technology. Superconductors are a natural choice for solid-state based quantum devices, while magnetic impurities inside superconductors give rise to quasiparticle excitations of broken Cooper pairs that provide characteristic information about the host superconductor. Here, we reveal that magnetic impurities embedded below a superconducting La(0001) surface interact via quasiparticles extending to very large distances, up to several tens of nanometers. Using low-temperature scanning probe techniques, we observe the corresponding anisotropic and giant oscillations in the LDOS. Theoretical calculations indicate that the quasi-two-dimensional surface states with their strongly anisotropic Fermi surface play a crucial role for the focusing and long-range extension of the magnetic bound states. The quasiparticle focusing mechanism should facilitate the design of versatile magnetic structures with tunable and directed magnetic interactions over large distances, thereby paving the way toward the design of low-dimensional magnet-superconductor hybrid systems exhibiting topologically non-trivial quantum states as possible elements of quantum computation schemes based on Majorana quasiparticles.
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Affiliation(s)
- Howon Kim
- Department of Physics, University of Hamburg, D-20355, Hamburg, Germany.
| | - Levente Rózsa
- Department of Physics, University of Hamburg, D-20355, Hamburg, Germany
- Department of Physics, University of Konstanz, D-78457, Konstanz, Germany
| | - Dominik Schreyer
- Department of Physics, University of Hamburg, D-20355, Hamburg, Germany
| | - Eszter Simon
- Department of Theoretical Physics, Budapest University of Technology and Economics, Budafoki út 8, H-1111, Budapest, Hungary
- Department Chemie, Physikalische Chemie, Ludwig-Maximilians-Universität München, Butenandtstr. 5-13, D-81377, München, Germany
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43
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Perrin V, Santos FLN, Ménard GC, Brun C, Cren T, Civelli M, Simon P. Unveiling Odd-Frequency Pairing around a Magnetic Impurity in a Superconductor. PHYSICAL REVIEW LETTERS 2020; 125:117003. [PMID: 32975960 DOI: 10.1103/physrevlett.125.117003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2020] [Accepted: 08/17/2020] [Indexed: 06/11/2023]
Abstract
We study the unconventional superconducting correlations caused by a single isolated magnetic impurity in a conventional s-wave superconductor. Because of the local breaking of time-reversal symmetry, the impurity induces unconventional superconductivity, which is even in both space and spin variables but odd under time inversion. We derive an exact proportionality relation between the even-frequency component of the local electron density of states and the imaginary part of the odd-frequency local pairing function. By applying this relation to scanning tunneling microscopy spectra taken on top of magnetic impurities immersed in a Pb/Si(111) monolayer, we show experimental evidence of the occurrence of the odd-frequency pairing in these systems and explicitly extract its superconducting function from the data.
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Affiliation(s)
- Vivien Perrin
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Flávio L N Santos
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
- Departamento de Fisica, Universidade Federal de Minas Gerais, Caixa Postal 702, Belo Horizonte, MG 30123-970, Brazil
| | - Gerbold C Ménard
- Institut des NanoSciences de Paris, Sorbonne Université and CNRS-UMR, 7588, 75005 Paris, France
| | - Christophe Brun
- Institut des NanoSciences de Paris, Sorbonne Université and CNRS-UMR, 7588, 75005 Paris, France
| | - Tristan Cren
- Institut des NanoSciences de Paris, Sorbonne Université and CNRS-UMR, 7588, 75005 Paris, France
| | - Marcello Civelli
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
| | - Pascal Simon
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France
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44
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Leumer N, Marganska M, Muralidharan B, Grifoni M. Exact eigenvectors and eigenvalues of the finite Kitaev chain and its topological properties. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:445502. [PMID: 32320961 DOI: 10.1088/1361-648x/ab8bf9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2020] [Accepted: 04/22/2020] [Indexed: 06/11/2023]
Abstract
We present a comprehensive, analytical treatment of the finite Kitaev chain for arbitrary chemical potential and chain length. By means of an exact analytical diagonalization in the real space, we derive the momentum quantization conditions and present exact analytical formulas for the resulting energy spectrum and eigenstate wave functions, encompassing boundary and bulk states. In accordance with an analysis based on the winding number topological invariant, and as expected from the bulk-edge correspondence, the boundary states are topological in nature. They can have zero, exponentially small or even finite energy. Further, for a fixed value of the chemical potential, their properties are ruled by the ratio of the decay length to the chain length. A numerical analysis confirms the robustness of the topological states against disorder.
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Affiliation(s)
- Nico Leumer
- Institute for Theoretical Physics, University of Regensburg, 93053 Regensburg, Germany
| | - Magdalena Marganska
- Institute for Theoretical Physics, University of Regensburg, 93053 Regensburg, Germany
| | - Bhaskaran Muralidharan
- Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India
| | - Milena Grifoni
- Institute for Theoretical Physics, University of Regensburg, 93053 Regensburg, Germany
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45
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Górski G, Kucab K, Domański T. Magnetic field effect on trivial and topological bound states of superconducting quantum dot. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:445803. [PMID: 32634785 DOI: 10.1088/1361-648x/aba38a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2020] [Accepted: 07/07/2020] [Indexed: 06/11/2023]
Abstract
We investigate the properties of a quantum dot embedded between the normal and superconducting leads which is additionally side-attached to the topological superconducting nanowire, hosting the Majorana modes. This setup enables formation of the trivial (finite-energy) bound states induced in the quantum dot through the superconducting proximity effect, coexisting/competing with the topological (zero-energy) mode transmitted from the topological superconductor. We analyze their interplay, focusing on a role played by the external magnetic field. To distinguish between these bound states we analyze the qualitative and quantitative features manifested in the subgap charge tunneling originating under nonequilibrium conditions from the Andreev (particle to hole) scattering processes.
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Affiliation(s)
- G Górski
- Institute of Physics, College of Natural Sciences, University of Rzeszów, ul. Pigonia 1, PL-35-310 Rzeszów, Poland
| | - K Kucab
- Institute of Physics, College of Natural Sciences, University of Rzeszów, ul. Pigonia 1, PL-35-310 Rzeszów, Poland
| | - T Domański
- Institute of Physics, M. Curie-Skłodowska University, ul. Radziszewskiego 10, PL-20-031 Lublin, Poland
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46
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Freeney SE, van den Broeke JJ, Harsveld van der Veen AJJ, Swart I, Morais Smith C. Edge-Dependent Topology in Kekulé Lattices. PHYSICAL REVIEW LETTERS 2020; 124:236404. [PMID: 32603178 DOI: 10.1103/physrevlett.124.236404] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2019] [Accepted: 05/11/2020] [Indexed: 05/16/2023]
Abstract
The boundary states of topological insulators are thought not to depend on the precise atomic structure of the boundary. A recent theoretical study showed that, for topological crystalline insulators with given bond strengths, topological states should only emerge for certain edge geometries. We experimentally probe this effect by creating artificial Kekulé lattices with different atomically well-defined edge geometries and hopping ratios in a scanning tunneling microscope. Topological edge modes are found to only appear for specific combinations of edge geometry and hopping ratio.
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Affiliation(s)
- S E Freeney
- Debye Institute for Nanomaterials Science, Utrecht University, Utrecht 3584 CC, Netherlands
| | - J J van den Broeke
- Institute for Theoretical Physics, Utrecht University, Utrecht 3584 CC, Netherlands
| | | | - I Swart
- Debye Institute for Nanomaterials Science, Utrecht University, Utrecht 3584 CC, Netherlands
| | - C Morais Smith
- Institute for Theoretical Physics, Utrecht University, Utrecht 3584 CC, Netherlands
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47
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Chen X, Chen M, Duan W, Yang H, Wen HH. Robust Zero Energy Modes on Superconducting Bismuth Islands Deposited on Fe(Te,Se). NANO LETTERS 2020; 20:2965-2972. [PMID: 31995387 DOI: 10.1021/acs.nanolett.9b04639] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Topological superconductivity is one of the frontier research directions in condensed matter physics. One of the unique elementary excitations in topological superconducting state is the Majorana Fermion (mode) which is its own antiparticle and obeys the non-Abelian statistics and is thus useful for constructing the fault-tolerant quantum computation. The evidence for Majorana Fermions (mode) in condensed matter is now quickly accumulated. We deposit Bi islands on the iron-based superconductors Fe(Te,Se) and find the easily achievable zero energy modes on the tunneling spectra on some Bi islands. The zero energy mode is robust and appears everywhere on the island. Temperature and magnetic field dependence of the zero energy mode are also investigated. We attribute these zero energy modes to the Majorana modes due to the proximity effect-induced topological superconductivity on the Bi islands with strong spin-orbit coupling effect.
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Affiliation(s)
- Xiaoyu Chen
- National Laboratory of Solid State Microstructures and Department of Physics, Center for Superconducting Physics and Materials, Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Mingyang Chen
- National Laboratory of Solid State Microstructures and Department of Physics, Center for Superconducting Physics and Materials, Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Wen Duan
- National Laboratory of Solid State Microstructures and Department of Physics, Center for Superconducting Physics and Materials, Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Huan Yang
- National Laboratory of Solid State Microstructures and Department of Physics, Center for Superconducting Physics and Materials, Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Hai-Hu Wen
- National Laboratory of Solid State Microstructures and Department of Physics, Center for Superconducting Physics and Materials, Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing 210093, China
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48
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Large spatial extension of the zero-energy Yu-Shiba-Rusinov state in a magnetic field. Nat Commun 2020; 11:1834. [PMID: 32286260 PMCID: PMC7156378 DOI: 10.1038/s41467-020-15322-9] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Accepted: 03/03/2020] [Indexed: 11/30/2022] Open
Abstract
Various promising qubit concepts have been put forward recently based on engineered superconductor subgap states like Andreev bound states, Majorana zero modes or the Yu-Shiba-Rusinov (Shiba) states. The coupling of these subgap states via a superconductor strongly depends on their spatial extension and is an essential next step for future quantum technologies. Here we investigate the spatial extension of a Shiba state in a semiconductor quantum dot coupled to a superconductor. With detailed transport measurements and numerical renormalization group calculations we find a remarkable more than 50 nm extension of the zero energy Shiba state, much larger than the one observed in very recent scanning tunneling microscopy measurements. Moreover, we demonstrate that its spatial extension increases substantially in a magnetic field. Local magnetic moments coupled to superconductors can form subgap Yu-Shiba-Rusinov states. Here the authors show that Shiba states made with an InAs nanowire quantum dot have large spatial extent, which is beneficial for making Shiba chains that are predicted to host Majorana zero modes.
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49
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Zienkiewicz T, Barański J, Górski G, Domański T. Leakage of Majorana mode into correlated quantum dot nearby its singlet-doublet crossover. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:025302. [PMID: 31546236 DOI: 10.1088/1361-648x/ab46d9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We study quasiparticle spectrum of the correlated quantum dot (QD) deposited on superconducting (SC) substrate which is side-coupled to the Rashba nanochain, hosting Majorana end modes. Ground state of an isolated QD proximitized to SC reservoirs is represented either by the singly occupied site or BCS-type superposition of the empty and doubly occupied configurations. Quantum phase transition between these distinct ground states is spectroscopically manifested by the in-gap Andreev states which cross each other at the Fermi level. This qualitatively affects leakage of the Majorana mode from the side-attached nanowire. We inspect the spin-selective relationship between the trivial Andreev states and the leaking Majorana mode, considering (i) perfectly polarized case, when tunneling of one spin component is completely prohibited, and (ii) another one when both spins are hybridized with the nanowire but with different couplings.
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Affiliation(s)
- T Zienkiewicz
- Polish Air Force University, ul. Dywizjonu 303 no. 35, 08-521 Deblin, Poland
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Liebhaber E, Acero González S, Baba R, Reecht G, Heinrich BW, Rohlf S, Rossnagel K, von Oppen F, Franke KJ. Yu-Shiba-Rusinov States in the Charge-Density Modulated Superconductor NbSe 2. NANO LETTERS 2020; 20:339-344. [PMID: 31842547 DOI: 10.1021/acs.nanolett.9b03988] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
NbSe2 is a remarkable superconductor in which charge-density order coexists with pairing correlations at low temperatures. Here, we study the interplay of magnetic adatoms and their Yu-Shiba-Rusinov (YSR) bound states with the charge density order. Exploiting the incommensurate nature of the charge-density wave (CDW), our measurements provide a thorough picture of how the CDW affects both the energies and the wave functions of the YSR states. Key features of the dependence of the YSR states on adsorption site relative to the CDW are explained by model calculations. Several properties make NbSe2 a promising substrate for realizing topological nanostructures. Our results will be important in designing such systems.
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Affiliation(s)
| | | | | | | | | | - Sebastian Rohlf
- Ruprecht-Haensel-Labor and Institut für Experimentelle und Angewandte Physik , Christian-Albrechts-Universität zu Kiel , 24098 Kiel , Germany
| | - Kai Rossnagel
- Ruprecht-Haensel-Labor and Institut für Experimentelle und Angewandte Physik , Christian-Albrechts-Universität zu Kiel , 24098 Kiel , Germany
- Deutsches Elektronen-Synchrotron DESY , 22607 Hamburg , Germany
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