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Odobesko A, Klees RL, Friedrich F, Hankiewicz EM, Bode M. Boosting spatial and energy resolution in STM with a double-functionalized probe. SCIENCE ADVANCES 2024; 10:eadq6975. [PMID: 39196925 PMCID: PMC11352829 DOI: 10.1126/sciadv.adq6975] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2024] [Accepted: 07/24/2024] [Indexed: 08/30/2024]
Abstract
The scattering of superconducting pairs by magnetic impurities on a superconducting surface leads to pairs of sharp in-gap resonances known as Yu-Shiba-Rusinov (YSR) bound states. Similar to the interference of itinerant electrons scattered by defects in normal metals, these resonances reveal a periodic texture around the magnetic impurity. The wavelength of these resonances is, however, often too short to be resolved even by methods capable of atomic resolution, i.e., scanning tunneling microscopy (STM). We combine a CO molecule with a superconducting cluster pre-attached to an STM tip to maximize both spatial and energy resolution, thus demonstrating the superior properties of such double-functionalized probes by imaging the spatial distribution of YSR states. Our approach reveals rich interference patterns of the hybridized YSR states of two Fe atoms on Nb(110), previously inaccessible with conventional STM probes. This advancement extends the capabilities of STM techniques, providing insights into superconducting phenomena at the atomic scale.
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Affiliation(s)
- Artem Odobesko
- Physikalisches Institut, Experimentelle Physik II, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Raffael L. Klees
- Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
- Institute of Physics, University of Augsburg, D-86159 Augsburg, Germany
| | - Felix Friedrich
- Physikalisches Institut, Experimentelle Physik II, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Ewelina M. Hankiewicz
- Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Matthias Bode
- Physikalisches Institut, Experimentelle Physik II, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
- Wilhelm Conrad Röntgen-Center for Complex Material Systems (RCCM), Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
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2
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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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3
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Rubio-Verdú C, Zaldívar J, Žitko R, Pascual JI. Coupled Yu-Shiba-Rusinov States Induced by a Many-Body Molecular Spin on a Superconductor. PHYSICAL REVIEW LETTERS 2021; 126:017001. [PMID: 33480757 DOI: 10.1103/physrevlett.126.017001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2020] [Accepted: 12/04/2020] [Indexed: 06/12/2023]
Abstract
A magnetic impurity on a superconductor induces Yu-Shiba-Rusinov (YSR) bound states, detected by tunneling spectroscopy as long-lived quasiparticle excitations inside the superconducting gap. Coupled YSR states constitute basic elements to engineer artificial superconducting states, but their substrate-mediated interactions are generally weak. In this Letter, we report that intramolecular (Hund's-like) exchange interactions produce coupled YSR states across a molecular platform. We measured YSR spectra along a magnetic iron-porphyrin on Pb(111) and found evidence of two distinct interaction channels, which invert their particle-hole asymmetry across the molecule. Numerical calculations show that the identical YSR asymmetry pattern of the two channels is caused by two spin-hosting orbitals with opposite potential scattering and coupled strongly. Both channels can be similarly excited by tunneling electrons into each orbital, depicting a new scenario for entangled superconducting bound states using molecular platforms.
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Affiliation(s)
- Carmen Rubio-Verdú
- CIC nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain
- Department of Physics, Columbia University, New York, New York 10027, United States
| | | | - 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
| | - Jose Ignacio Pascual
- CIC nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain
- Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain
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4
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Liu C, Chen C, Liu X, Wang Z, Liu Y, Ye S, Wang Z, Hu J, Wang J. Zero-energy bound states in the high-temperature superconductors at the two-dimensional limit. SCIENCE ADVANCES 2020; 6:eaax7547. [PMID: 32232145 PMCID: PMC7096174 DOI: 10.1126/sciadv.aax7547] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2019] [Accepted: 01/06/2020] [Indexed: 05/25/2023]
Abstract
Majorana zero modes (MZMs) that obey the non-Abelian statistics have been intensively investigated for potential applications in topological quantum computing. The prevailing signals in tunneling experiments "fingerprinting" the existence of MZMs are the zero-energy bound states (ZEBSs). However, nearly all of the previously reported ZEBSs showing signatures of the MZMs are observed in difficult-to-fabricate heterostructures at very low temperatures and additionally require applied magnetic field. Here, by using in situ scanning tunneling spectroscopy, we detect the ZEBSs upon the interstitial Fe adatoms deposited on two different high-temperature superconducting one-unit-cell iron chalcogenides on SrTiO3(001). The spectroscopic results resemble the phenomenological characteristics of the MZMs inside the vortex cores of topological superconductors. Our experimental findings may extend the MZM explorations in connate topological superconductors toward an applicable temperature regime and down to the two-dimensional (2D) limit.
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Affiliation(s)
- Chaofei Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Cheng Chen
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Xiaoqiang Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Ziqiao Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Yi Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Shusen Ye
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
| | - Ziqiang Wang
- Department of Physics, Boston College, Chestnut Hill, MA 02467, USA
| | - Jiangping Hu
- Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Kavli Institute of Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Jian Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
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5
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Głodzik S, Kobiałka A, Gorczyca-Goraj A, Ptok A, Górski G, Maśka MM, Domański T. Interplay between pairing and correlations in spin-polarized bound states. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2018; 9:1370-1380. [PMID: 29977671 PMCID: PMC6009651 DOI: 10.3762/bjnano.9.129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/15/2017] [Accepted: 04/09/2018] [Indexed: 06/08/2023]
Abstract
We investigate single and multiple defects embedded in a superconducting host, studying the interplay between the proximity-induced pairing and interactions. We explore the influence of the spin-orbit coupling on energies, polarization and spatial patterns of the bound (Yu-Shiba-Rusinov) states of magnetic impurities in a two-dimensional square lattice. We also address the peculiar bound states in the proximitized Rashba chain, resembling the Majorana quasiparticles, focusing on their magnetic polarization that has been recently reported by S. Jeon et al. (Science2017,358, 772). Finally, we study leakage of these polarized Majorana quasiparticles into side-attached nanoscopic regions and confront them with the subgap Kondo effect near to the singlet-doublet phase transition.
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Affiliation(s)
- Szczepan Głodzik
- Institute of Physics, M. Curie-Skłodowska University, 20-031 Lublin, Poland
| | - Aksel Kobiałka
- Institute of Physics, M. Curie-Skłodowska University, 20-031 Lublin, Poland
| | | | - Andrzej Ptok
- Institute of Nuclear Physics, Polish Academy of Sciences, 31-342 Kraków, Poland
| | - Grzegorz Górski
- Faculty of Mathematics and Natural Sciences, University of Rzeszów, 35-310 Rzeszów, Poland
| | - Maciej M Maśka
- Institute of Physics, University of Silesia, 41-500 Chorzów, Poland
| | - Tadeusz Domański
- Institute of Physics, M. Curie-Skłodowska University, 20-031 Lublin, Poland
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6
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Choi DJ, Fernández CG, Herrera E, Rubio-Verdú C, Ugeda MM, Guillamón I, Suderow H, Pascual JI, Lorente N. Influence of Magnetic Ordering between Cr Adatoms on the Yu-Shiba-Rusinov States of the β-Bi_{2}Pd Superconductor. PHYSICAL REVIEW LETTERS 2018; 120:167001. [PMID: 29756947 DOI: 10.1103/physrevlett.120.167001] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2017] [Indexed: 05/27/2023]
Abstract
We show that the magnetic ordering of coupled atomic dimers on a superconductor is revealed by their intragap spectral features. Chromium atoms on the superconductor β-Bi_{2}Pd surface display Yu-Shiba-Rusinov bound states, detected as pairs of intragap excitations in tunneling spectra. By means of atomic manipulation with a scanning tunneling microscope's tip, we form Cr dimers with different arrangements and find that their intragap features appear either shifted or split with respect to single atoms. These spectral variations are associated with the magnetic coupling, ferromagnetic or antiferromagnetic, of the dimer, as confirmed by density functional theory simulations. The striking qualitative differences between the observed tunneling spectra prove that intragap Shiba states are extremely sensitive to the magnetic ordering on the atomic scale.
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Affiliation(s)
- Deung-Jang Choi
- Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), 20018 Donostia-San Sebastián, Spain
- Donostia International Physics Center (DIPC), 20018 Donostia-San Sebastián, Spain
- CIC nanoGUNE, 20018 Donostia-San Sebastián, Spain
- Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain
| | | | - Edwin Herrera
- Laboratorio de Bajas Temperaturas, Departamento de Física de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | | | - Miguel M Ugeda
- Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), 20018 Donostia-San Sebastián, Spain
- Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain
| | - Isabel Guillamón
- Laboratorio de Bajas Temperaturas, Departamento de Física de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - Hermann Suderow
- Laboratorio de Bajas Temperaturas, Departamento de Física de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - José Ignacio Pascual
- CIC nanoGUNE, 20018 Donostia-San Sebastián, Spain
- Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain
| | - Nicolás Lorente
- Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), 20018 Donostia-San Sebastián, Spain
- Donostia International Physics Center (DIPC), 20018 Donostia-San Sebastián, Spain
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7
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Mashkoori M, Björnson K, Black-Schaffer AM. Impurity bound states in fully gapped d-wave superconductors with subdominant order parameters. Sci Rep 2017; 7:44107. [PMID: 28281570 PMCID: PMC5345048 DOI: 10.1038/srep44107] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2016] [Accepted: 02/01/2017] [Indexed: 11/09/2022] Open
Abstract
Impurities in superconductors and their induced bound states are important both for engineering novel states such as Majorana zero-energy modes and for probing bulk properties of the superconducting state. The high-temperature cuprates offer a clear advantage in a much larger superconducting order parameter, but the nodal energy spectrum of a pure d-wave superconductor only allows virtual bound states. Fully gapped d-wave superconducting states have, however, been proposed in several cuprate systems thanks to subdominant order parameters producing d + is- or d + id'-wave superconducting states. Here we study both magnetic and potential impurities in these fully gapped d-wave superconductors. Using analytical T-matrix and complementary numerical tight-binding lattice calculations, we show that magnetic and potential impurities behave fundamentally different in d + is- and d + id'-wave superconductors. In a d + is-wave superconductor, there are no bound states for potential impurities, while a magnetic impurity produces one pair of bound states, with a zero-energy level crossing at a finite scattering strength. On the other hand, a d + id'-wave symmetry always gives rise to two pairs of bound states and only produce a reachable zero-energy level crossing if the normal state has a strong particle-hole asymmetry.
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Affiliation(s)
- Mahdi Mashkoori
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden
| | - Kristofer Björnson
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden
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8
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Kaladzhyan V, Bena C, Simon P. Asymptotic behavior of impurity-induced bound states in low-dimensional topological superconductors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:485701. [PMID: 27705962 DOI: 10.1088/0953-8984/28/48/485701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We study theoretically the asymptotic behavior of the Shiba bound states associated with magnetic impurities embedded in both 2D and 1D anomalous superconductors. We calculate analytically the spatial dependence of the local density of states together with the spin polarization associated with the Shiba bound states. We show that the latter quantity exhibits drastic differences between s-wave and different types of p-wave superconductors. Such properties, which could be measured using spin-polarized STM, offer therefore a way to discriminate between singlet and triplet pairing in low-dimensional superconductors, as well as a way to estimate the amplitude of the triplet pairing in these systems.
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Affiliation(s)
- V Kaladzhyan
- Institut de Physique Théorique, CEA/Saclay, Orme des Merisiers, 91190 Gif-sur-Yvette Cedex, France. Laboratoire de Physique des Solides, CNRS, University of Paris-Sud, Université Paris-Saclay, 91405 Orsay Cedex, France
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9
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Ruby M, Peng Y, von Oppen F, Heinrich BW, Franke KJ. Orbital Picture of Yu-Shiba-Rusinov Multiplets. PHYSICAL REVIEW LETTERS 2016; 117:186801. [PMID: 27835014 DOI: 10.1103/physrevlett.117.186801] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2016] [Indexed: 05/27/2023]
Abstract
We investigate the nature of Yu-Shiba-Rusinov (YSR) subgap states induced by single manganese (Mn) atoms adsorbed on different surface orientations of superconducting lead (Pb). Depending on the adsorption site, we detect a distinct number and characteristic patterns of YSR states around the Mn atoms. We suggest that the YSR states inherit their properties from the Mn d levels, which are split by the surrounding crystal field. The periodicity of the long-range YSR oscillations allows us to identify a dominant coupling of the d states to the outer Fermi sheet of the two-band superconductor Pb.
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Affiliation(s)
- Michael Ruby
- Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | - Yang Peng
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
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10
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Magnetic anisotropy in Shiba bound states across a quantum phase transition. Nat Commun 2015; 6:8988. [PMID: 26603561 PMCID: PMC4674822 DOI: 10.1038/ncomms9988] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2015] [Accepted: 10/22/2015] [Indexed: 11/08/2022] Open
Abstract
The exchange coupling between magnetic adsorbates and a superconducting substrate leads to Shiba states inside the superconducting energy gap and a Kondo resonance outside the gap. The exchange coupling strength determines whether the quantum many-body ground state is a Kondo singlet or a singlet of the paired superconducting quasiparticles. Here we use scanning tunnelling spectroscopy to identify the different quantum ground states of manganese phthalocyanine on Pb(111). We observe Shiba states, which are split into triplets by magnetocrystalline anisotropy. Their characteristic spectral weight yields an unambiguous proof of the nature of the quantum ground state. Our results provide experimental insights into the phase diagram of a magnetic impurity on a superconducting host and shine light on the effects induced by magnetic anisotropy on many-body interactions. The exchange coupling strength between magnetic adsorbates and a superconducting surface determines the nature of the system's quantum ground state. Here, the authors use scanning tunnelling microscopy to explore the ground state and excited state properties of manganese phthalocyanine adsorbed on a Pb(111) surface.
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11
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Sau JD, Brydon PMR. Bound States of a Ferromagnetic Wire in a Superconductor. PHYSICAL REVIEW LETTERS 2015; 115:127003. [PMID: 26431011 DOI: 10.1103/physrevlett.115.127003] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2015] [Indexed: 06/05/2023]
Abstract
We consider the problem of bound states in strongly anisotropic ferromagnetic impurities in a superconductor, motivated by recent experiments that claim to observe Majorana modes at the ends of ferromagnetic wires on a superconducting substrate [S. Nadj-Perge et al., Science 346, 602 (2014)]. Generalizing the successful theory of bound states of spherically symmetric impurities, we consider a wirelike potential using both analytical and numerical approaches. We find that away from the ends of the wire the bound states form bands with pronounced van Hove singularities, giving rise to subgap peaks in the local density of states. For sufficiently strong magnetization of the wire, we show that this process generically produces a sharp peak at zero energy in the local density of states near the ends of the wire. This zero-energy peak has qualitative similarities to the claimed signature of a Majorana mode observed in the aforementioned experiment.
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Affiliation(s)
- Jay D Sau
- Condensed Matter Theory Center and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742-4111, USA
| | - P M R Brydon
- Condensed Matter Theory Center and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742-4111, USA
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