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Bahari M, Zhang SB, Li CA, Choi SJ, Rüßmann P, Timm C, Trauzettel B. Helical Topological Superconducting Pairing at Finite Excitation Energies. PHYSICAL REVIEW LETTERS 2024; 132:266201. [PMID: 38996321 DOI: 10.1103/physrevlett.132.266201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2022] [Revised: 04/19/2024] [Accepted: 05/15/2024] [Indexed: 07/14/2024]
Abstract
We propose helical topological superconductivity away from the Fermi surface in three-dimensional time-reversal-symmetric odd-parity multiband superconductors. In these systems, pairing between electrons originating from different bands is responsible for the corresponding topological phase transition. Consequently, a pair of helical topological Dirac surface states emerges at finite excitation energies. These helical Dirac surface states are tunable in energy by chemical potential and strength of band splitting. They are protected by time-reversal symmetry combined with crystalline twofold rotation symmetry. We suggest concrete materials in which this phenomenon could be observed.
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Affiliation(s)
| | | | - Chang-An Li
- Institute for Theoretical Physics and Astrophysics, University of Würzburg, D-97074 Würzburg, Germany
- Würzburg-Dresden Cluster of Excellence ct.qmat, Germany
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2
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Karan S, Huang H, Ivanovic A, Padurariu C, Kubala B, Kern K, Ankerhold J, Ast CR. Tracking a spin-polarized superconducting bound state across a quantum phase transition. Nat Commun 2024; 15:459. [PMID: 38212303 PMCID: PMC10784290 DOI: 10.1038/s41467-024-44708-2] [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: 04/17/2023] [Accepted: 01/02/2024] [Indexed: 01/13/2024] Open
Abstract
The magnetic exchange coupling between magnetic impurities and a superconductor induce so-called Yu-Shiba-Rusinov (YSR) states which undergo a quantum phase transition (QPT) upon increasing the exchange interaction beyond a critical value. While the evolution through the QPT is readily observable, in particular if the YSR state features an electron-hole asymmetry, the concomitant change in the ground state is more difficult to identify. We use ultralow temperature scanning tunneling microscopy to demonstrate how the change in the YSR ground state across the QPT can be directly observed for a spin-1/2 impurity in a magnetic field. The excitation spectrum changes from featuring two peaks in the doublet (free spin) state to four peaks in the singlet (screened spin) ground state. We also identify a transition regime, where the YSR excitation energy is smaller than the Zeeman energy. We thus demonstrate a straightforward way for unambiguously identifying the ground state of a spin-1/2 YSR state.
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Affiliation(s)
- Sujoy Karan
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569, Stuttgart, Germany.
| | - Haonan Huang
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569, Stuttgart, Germany
| | - Alexander Ivanovic
- Institute for Complex Quantum Systems and IQST, Universität Ulm, Albert-Einstein-Allee 11, 89069, Ulm, Germany
| | - Ciprian Padurariu
- Institute for Complex Quantum Systems and IQST, Universität Ulm, Albert-Einstein-Allee 11, 89069, Ulm, Germany
| | - Björn Kubala
- Institute for Complex Quantum Systems and IQST, Universität Ulm, Albert-Einstein-Allee 11, 89069, Ulm, Germany
- Institute for Quantum Technologies, German Aerospace Center (DLR), Wilhelm-Runge-Straße 10, 89081, Ulm, Germany
| | - Klaus Kern
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569, Stuttgart, Germany
- Institut de Physique, Ecole Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland
| | - Joachim Ankerhold
- Institute for Complex Quantum Systems and IQST, Universität Ulm, Albert-Einstein-Allee 11, 89069, Ulm, Germany
| | - Christian R Ast
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569, Stuttgart, Germany.
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3
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van Driel D, Wang G, Bordin A, van Loo N, Zatelli F, Mazur GP, Xu D, Gazibegovic S, Badawy G, Bakkers EPAM, Kouwenhoven LP, Dvir T. Spin-filtered measurements of Andreev bound states in semiconductor-superconductor nanowire devices. Nat Commun 2023; 14:6880. [PMID: 37898657 PMCID: PMC10613242 DOI: 10.1038/s41467-023-42026-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2023] [Accepted: 09/27/2023] [Indexed: 10/30/2023] Open
Abstract
Semiconductor nanowires coupled to superconductors can host Andreev bound states with distinct spin and parity, including a spin-zero state with an even number of electrons and a spin-1/2 state with odd-parity. Considering the difference in spin of the even and odd states, spin-filtered measurements can reveal the underlying ground state. To directly measure the spin of single-electron excitations, we probe an Andreev bound state using a spin-polarized quantum dot that acts as a bipolar spin filter, in combination with a non-polarized tunnel junction in a three-terminal circuit. We observe a spin-polarized excitation spectrum of the Andreev bound state, which can be fully spin-polarized, despite strong spin-orbit interaction in the InSb nanowires. Decoupling the hybrid from the normal lead causes a current blockade, by trapping the Andreev bound state in an excited state. Spin-polarized spectroscopy of hybrid nanowire devices, as demonstrated here, is proposed as an experimental tool to support the observation of topological superconductivity.
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Affiliation(s)
- David van Driel
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Guanzhong Wang
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Alberto Bordin
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Nick van Loo
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Francesco Zatelli
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Grzegorz P Mazur
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Di Xu
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Sasa Gazibegovic
- Department of Applied Physics, Eindhoven University of Technology, 5600, MB, Eindhoven, The Netherlands
| | - Ghada Badawy
- Department of Applied Physics, Eindhoven University of Technology, 5600, MB, Eindhoven, The Netherlands
| | - Erik P A M Bakkers
- Department of Applied Physics, Eindhoven University of Technology, 5600, MB, Eindhoven, The Netherlands
| | - Leo P Kouwenhoven
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands
| | - Tom Dvir
- QuTech and Kavli Institute of NanoScience, Delft University of Technology, 2600, GA, Delft, The Netherlands.
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4
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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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5
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Zhang T, Hu Y, Su W, Chen C, Wang X, Li D, Lu Z, Yang W, Zhang Q, Dong X, Wang R, Wang X, Feng D, Zhang T. Phase Shift and Magnetic Anisotropy Induced Field Splitting of Impurity States in (Li_{1-x}Fe_{x})OHFeSe Superconductor. PHYSICAL REVIEW LETTERS 2023; 130:206001. [PMID: 37267540 DOI: 10.1103/physrevlett.130.206001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Revised: 03/21/2023] [Accepted: 04/10/2023] [Indexed: 06/04/2023]
Abstract
Revealing the energy and spatial characteristics of impurity-induced states in superconductors is essential for understanding their mechanism and fabricating a new quantum state by manipulating impurities. Here, by using high-resolution scanning tunneling microscopy and spectroscopy, we investigate the spatial distribution and magnetic field response of the impurity states in (Li_{1-x}Fe_{x})OHFeSe. We detect two pairs of strong in-gap states on the "dumbbell-shaped" defects. They display damped oscillations with different phase shifts and a direct phase-energy correlation. These features have long been predicted for the classical Yu-Shiba-Rusinov (YSR) state and are demonstrated here with unprecedented resolution for the first time. Moreover, upon applying magnetic field, all in-gap state peaks remarkably split into two rather than shift, and the splitting strength is field orientation dependent. Via detailed numerical model calculations, we find such an anisotropic splitting behavior can be naturally induced by a high-spin impurity coupled to an anisotropic environment, highlighting how magnetic anisotropy affects the behavior of YSR states.
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Affiliation(s)
- Tianzhen Zhang
- Department of Physics, State Key Laboratory of Surface Physics and Advanced Material Laboratory, Fudan University, Shanghai 200438, China
| | - Yining Hu
- Department of Physics, State Key Laboratory of Surface Physics and Advanced Material Laboratory, Fudan University, Shanghai 200438, China
| | - Wei Su
- Beijing Computational Science Research Center, Beijing 100084, China
- College of Physics and Electronic Engineering, Center for Computational Sciences, Sichuan Normal University, Chengdu 610068, China
| | - Chen Chen
- Department of Physics, State Key Laboratory of Surface Physics and Advanced Material Laboratory, Fudan University, Shanghai 200438, China
| | - Xu Wang
- Department of Physics, State Key Laboratory of Surface Physics and Advanced Material Laboratory, Fudan University, Shanghai 200438, China
| | - Dong Li
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Zouyouwei Lu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Wentao Yang
- Department of Physics, State Key Laboratory of Surface Physics and Advanced Material Laboratory, Fudan University, Shanghai 200438, China
| | - Qingle Zhang
- Department of Physics, State Key Laboratory of Surface Physics and Advanced Material Laboratory, Fudan University, Shanghai 200438, China
| | - Xiaoli Dong
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Rui Wang
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center for Advanced Microstructures, Nanjing 210093, China
| | - Xiaoqun Wang
- School of Physics, Zhejiang University, Hangzhou 310058 Zhejiang, China
| | - Donglai Feng
- Department of Physics, State Key Laboratory of Surface Physics and Advanced Material Laboratory, Fudan University, Shanghai 200438, China
- National Synchrotron Radiation Laboratory and Department of Physics, University of Science and Technology of China, Hefei 230026, China
- Collaborative Innovation Center for Advanced Microstructures, Nanjing 210093, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Tong Zhang
- Department of Physics, State Key Laboratory of Surface Physics and Advanced Material Laboratory, Fudan University, Shanghai 200438, China
- Collaborative Innovation Center for Advanced Microstructures, Nanjing 210093, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
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6
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Zhou L, He Q, Que X, Rost AW, Takagi H. A spectroscopic-imaging scanning tunneling microscope in vector magnetic field. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2023; 94:033704. [PMID: 37012779 DOI: 10.1063/5.0131532] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2022] [Accepted: 02/15/2023] [Indexed: 06/19/2023]
Abstract
Cryogenic scanning tunneling microscopy and spectroscopy (STM/STS) performed in a high vector magnetic field provide unique possibilities for imaging surface magnetic structures and anisotropic superconductivity and exploring spin physics in quantum materials with atomic precision. Here, we describe the design, construction, and performance of a low-temperature, ultra-high-vacuum (UHV) spectroscopic-imaging STM equipped with a vector magnet capable of applying a field of up to 3 T in any direction with respect to the sample surface. The STM head is housed in a fully bakeable UHV compatible cryogenic insert and is operational over variable temperatures ranging from ∼300 down to 1.5 K. The insert can be easily upgraded using our home-designed 3He refrigerator. In addition to layered compounds, which can be cleaved at a temperature of either ∼300, ∼77, or ∼4.2 K to expose an atomically flat surface, thin films can also be studied by directly transferring using a UHV suitcase from our oxide thin-film laboratory. Samples can be treated further with a heater and a liquid helium/nitrogen cooling stage on a three-axis manipulator. The STM tips can be treated in vacuo by e-beam bombardment and ion sputtering. We demonstrate the successful operation of the STM with varying the magnetic field direction. Our facility provides a way to study materials in which magnetic anisotropy is a key factor in determining the electronic properties such as in topological semimetals and superconductors.
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Affiliation(s)
- Lihui Zhou
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, Stuttgart 70569, Germany
| | - Qingyu He
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, Stuttgart 70569, Germany
| | - Xinglu Que
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, Stuttgart 70569, Germany
| | - Andreas W Rost
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, Stuttgart 70569, Germany
| | - Hide Takagi
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, Stuttgart 70569, Germany
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7
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Schulte S, Néel N, Rózsa L, Palotás K, Kröger J. Changing the Interaction of a Single-Molecule Magnetic Moment with a Superconductor. NANO LETTERS 2023; 23:1622-1628. [PMID: 36603183 DOI: 10.1021/acs.nanolett.2c03952] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
The exchange interaction of a brominated Co-porphyrin molecule with the Cooper pair condensate of Pb(111) is modified by reducing the Co-surface separation. The stepwise dehalogenation and dephenylation change the Co adsorption height by a few picometers. Only the residual Co-porphine core exhibits a Yu-Shiba-Rusinov bound state with low binding energy in the Bardeen-Cooper-Schrieffer energy gap. Accompanying density functional calculations reveal that the Co dz2 orbital carries the molecular magnetic moment and is responsible for the intragap state. The calculated spatial evolution of the Yu-Shiba-Rusinov wave function is compatible with the experimentally observed oscillatory attenuation of the electron-hole asymmetry with increasing lateral distance from the magnetic porphine center.
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Affiliation(s)
- Stefan Schulte
- Institut für Physik, Technische Universität Ilmenau, D-98693Ilmenau, Germany
- Peter Grünberg Institut, Forschungszentrum Jülich, D-52425Jülich, Germany
- II. Physikalisches Institut, Universität zu Köln, D-50923Cologne, Germany
| | - Nicolas Néel
- Institut für Physik, Technische Universität Ilmenau, D-98693Ilmenau, Germany
| | - Levente Rózsa
- Fachbereich Physik, Universität Konstanz, D-78457Konstanz, Germany
| | - Krisztián Palotás
- Department of Theoretical Solid State Physics, Institute for Solid State Physics and Optics, Wigner Research Center for Physics, H-1121Budapest, Hungary
- ELKH-SZTE Reaction Kinetics and Surface Chemistry Research Group, University of Szeged, H-6720Szeged, Hungary
- Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H-1111Budapest, Hungary
| | - Jörg Kröger
- Institut für Physik, Technische Universität Ilmenau, D-98693Ilmenau, Germany
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8
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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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9
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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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10
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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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11
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Fan P, Yang F, Qian G, Chen H, Zhang YY, Li G, Huang Z, Xing Y, Kong L, Liu W, Jiang K, Shen C, Du S, Schneeloch J, Zhong R, Gu G, Wang Z, Ding H, Gao HJ. Observation of magnetic adatom-induced Majorana vortex and its hybridization with field-induced Majorana vortex in an iron-based superconductor. Nat Commun 2021; 12:1348. [PMID: 33649307 PMCID: PMC7921435 DOI: 10.1038/s41467-021-21646-x] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2020] [Accepted: 02/05/2021] [Indexed: 11/09/2022] Open
Abstract
Braiding Majorana zero modes is essential for fault-tolerant topological quantum computing. Iron-based superconductors with nontrivial band topology have recently emerged as a surprisingly promising platform for creating distinct Majorana zero modes in magnetic vortices in a single material and at relatively high temperatures. The magnetic field-induced Abrikosov vortex lattice makes it difficult to braid a set of Majorana zero modes or to study the coupling of a Majorana doublet due to overlapping wave functions. Here we report the observation of the proposed quantum anomalous vortex with integer quantized vortex core states and the Majorana zero mode induced by magnetic Fe adatoms deposited on the surface. We observe its hybridization with a nearby field-induced Majorana vortex in iron-based superconductor FeTe0.55Se0.45. We also observe vortex-free Yu-Shiba-Rusinov bound states at the Fe adatoms with a weaker coupling to the substrate, and discover a reversible transition between Yu-Shiba-Rusinov states and Majorana zero mode by manipulating the exchange coupling strength. The dual origin of the Majorana zero modes, from magnetic adatoms and external magnetic field, provides a new single-material platform for studying their interactions and braiding in superconductors bearing topological band structures.
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Affiliation(s)
- Peng Fan
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Fazhi Yang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Guojian Qian
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Hui Chen
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong, China
| | - Yu-Yang Zhang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, China
| | - Geng Li
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, China
| | - Zihao Huang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Yuqing Xing
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Lingyuan Kong
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Wenyao Liu
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Kun Jiang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, China
- Department of Physics, Boston College, Boston, MA, USA
| | - Chengmin Shen
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, China
| | - Shixuan Du
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, China
| | - John Schneeloch
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, USA
| | - Ruidan Zhong
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, USA
| | - Genda Gu
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, USA
| | - Ziqiang Wang
- Department of Physics, Boston College, Boston, MA, USA.
| | - Hong Ding
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, China.
- Songshan Lake Materials Laboratory, Dongguan, Guangdong, China.
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, China.
| | - Hong-Jun Gao
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China.
- Songshan Lake Materials Laboratory, Dongguan, Guangdong, China.
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, China.
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12
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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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13
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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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14
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Li Z, Wu Q, Wu C. Surface/Interface Chemistry Engineering of Correlated-Electron Materials: From Conducting Solids, Phase Transitions to External-Field Response. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2021; 8:2002807. [PMID: 33643796 PMCID: PMC7887576 DOI: 10.1002/advs.202002807] [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: 07/24/2020] [Revised: 09/25/2020] [Indexed: 06/12/2023]
Abstract
Correlated electronic materials (CEMs) with strong electron-electron interactions are often associated with exotic properties, such as metal-insulator transition (MIT), charge density wave (CDW), superconductivity, and magnetoresistance (MR), which are fundamental to next generation condensed matter research and electronic devices. When the dimension of CEMs decreases, exposing extremely high specific surface area and enhancing electronic correlation, the surface states are equally important to the bulk phase. Therefore, surface/interface chemical interactions provide an alternative route to regulate the intrinsic properties of low-dimensional CEMs. Here, recent achievements in surface/interface chemistry engineering of low-dimensional CEMs are reviewed, using surface modification, molecule-solid interaction, and interface electronic coupling, toward modulation of conducting solids, phase transitions including MIT, CDW, superconductivity, and magnetism transition, as well as external-field response. Surface/interface chemistry engineering provides a promising strategy for exploring novel properties and functional applications in low-dimensional CEMs. Finally, the current challenge and outlook of the surface/interface engineering are also pointed out for future research development.
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Affiliation(s)
- Zejun Li
- Hefei National Laboratory for Physical Sciences at the MicroscaleCAS center for Excellence in Nanoscienceand CAS Key Laboratory of Mechanical Behavior and Design of MaterialsUniversity of Science and Technology of ChinaHefeiAnhui230026PR China
| | - Qiran Wu
- Hefei National Laboratory for Physical Sciences at the MicroscaleCAS center for Excellence in Nanoscienceand CAS Key Laboratory of Mechanical Behavior and Design of MaterialsUniversity of Science and Technology of ChinaHefeiAnhui230026PR China
| | - Changzheng Wu
- Hefei National Laboratory for Physical Sciences at the MicroscaleCAS center for Excellence in Nanoscienceand CAS Key Laboratory of Mechanical Behavior and Design of MaterialsUniversity of Science and Technology of ChinaHefeiAnhui230026PR China
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15
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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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16
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Farinacci L, Ahmadi G, Ruby M, Reecht G, Heinrich BW, Czekelius C, von Oppen F, Franke KJ. Interfering Tunneling Paths through Magnetic Molecules on Superconductors: Asymmetries of Kondo and Yu-Shiba-Rusinov Resonances. PHYSICAL REVIEW LETTERS 2020; 125:256805. [PMID: 33416394 DOI: 10.1103/physrevlett.125.256805] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2020] [Revised: 10/10/2020] [Accepted: 11/19/2020] [Indexed: 06/12/2023]
Abstract
Magnetic adsorbates on superconductors induce a Kondo resonance outside and Yu-Shiba-Rusinov (YSR) bound states inside the superconducting energy gap. When probed by scanning tunneling spectroscopy, the associated differential-conductance spectra frequently exhibit characteristic bias-voltage asymmetries. Here, we observe correlated variations of Kondo and YSR asymmetries across an Fe-porphyrin molecule adsorbed on Pb(111). We show that both asymmetries originate in interfering tunneling paths via a spin-carrying orbital and the highest occupied molecular orbital (HOMO). Strong evidence for this model comes from nodal planes of the HOMO, where tunneling reveals symmetric Kondo and YSR resonances. Our results establish an important mechanism for the asymmetries of Kondo and YSR line shapes.
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Affiliation(s)
- Laëtitia Farinacci
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Gelavizh Ahmadi
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Michael Ruby
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Gaël Reecht
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Benjamin W Heinrich
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Constantin Czekelius
- Institut für Organische Chemie und Makromolekulare Chemie, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, 40225Düsseldorf, Germany
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Katharina J Franke
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
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17
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Yang X, Yuan Y, Peng Y, Minamitani E, Peng L, Xian JJ, Zhang WH, Fu YS. Observation of short-range Yu-Shiba-Rusinov states with threefold symmetry in layered superconductor 2H-NbSe 2. NANOSCALE 2020; 12:8174-8179. [PMID: 32242592 DOI: 10.1039/d0nr01383h] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Yu-Shiba-Rusinov (YSR) states arise when magnetic impurities interact with superconductivity. The intricacy of coupling and the nature of the superconductivity determine the behavior of the YSR state, whose detailed correlations are not yet fully understood. Here, we study the YSR state of a single Fe adatom on the surface of 2H-NbSe2 with combined low temperature scanning tunneling microscopy/spectroscopy, density functional theory calculations and tight-binding modeling. It is found that the Fe adatom occupies the hollow site of the Se surface layer. A prominent YSR state close to the Fermi level is observed. The YSR state exhibits a threefold symmetry along the diagonal direction of the Se lattice. The spatial decay of the YSR state follows a behavior in three-dimensional superconductivity. This behavior contrasts with a previous study of imbedded Fe impurities, whose YSR state shows a six-fold symmetry and a two-dimensional long-range decay. According to our theoretical modeling, the coupling configurations affect the adatom-substrate hopping and the interlayer coupling of the substrate. Both factors are crucial for the consequent behavior of the YSR state.
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Affiliation(s)
- Xing Yang
- School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China.
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18
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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: 6] [Impact Index Per Article: 1.5] [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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19
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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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20
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Kezilebieke S, Žitko R, Dvorak M, Ojanen T, Liljeroth P. Observation of Coexistence of Yu-Shiba-Rusinov States and Spin-Flip Excitations. NANO LETTERS 2019; 19:4614-4619. [PMID: 31251066 PMCID: PMC6628613 DOI: 10.1021/acs.nanolett.9b01583] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/16/2019] [Revised: 06/05/2019] [Indexed: 06/09/2023]
Abstract
We investigate the spectral evolution in different metal phthalocyanine molecules on NbSe2 surface using scanning tunnelling microscopy (STM) as a function of the coupling with the substrate. For manganese phthalocyanine (MnPc), we demonstrate a smooth spectral crossover from Yu-Shiba-Rusinov (YSR) bound states to spin-flip excitations. This has not been observed previously and it is in contrast to simple theoretical expectations. We corroborate the experimental findings using numerical renormalization group calculations. Our results provide fundamental new insight on the behavior of atomic scale magnetic/SC hybrid systems, which is important, for example, for engineered topological superconductors and spin logic devices.
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Affiliation(s)
| | - Rok Žitko
- Jožef
Stefan Institute, Jamova 39, SI-1001 Ljubljana, Slovenia
- Faculty
of Mathematics and Physics, University of
Ljubljana, Jadranska
19, SI-1000 Ljubljana, Slovenia
| | - Marc Dvorak
- Department
of Applied Physics, Aalto University School
of Science, 00076 Aalto, Finland
| | - Teemu Ojanen
- Department
of Applied Physics, Aalto University School
of Science, 00076 Aalto, Finland
- Computational
Physics Laboratory, Physics Unit, Faculty of Engineering and Natural
Sciences, Tampere University, P.O. Box 692, FI-33014 Tampere, Finland
| | - Peter Liljeroth
- Department
of Applied Physics, Aalto University School
of Science, 00076 Aalto, Finland
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21
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Palacio-Morales A, Mascot E, Cocklin S, Kim H, Rachel S, Morr DK, Wiesendanger R. Atomic-scale interface engineering of Majorana edge modes in a 2D magnet-superconductor hybrid system. SCIENCE ADVANCES 2019; 5:eaav6600. [PMID: 31360762 PMCID: PMC6660210 DOI: 10.1126/sciadv.aav6600] [Citation(s) in RCA: 34] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2018] [Accepted: 06/19/2019] [Indexed: 05/14/2023]
Abstract
Topological superconductors are predicted to harbor exotic boundary states-Majorana zero-energy modes-whose non-Abelian braiding statistics present a new paradigm for the realization of topological quantum computing. Using low-temperature scanning tunneling spectroscopy, here, we report on the direct real-space visualization of chiral Majorana edge states in a monolayer topological superconductor, a prototypical magnet-superconductor hybrid system composed of nanoscale Fe islands of monoatomic height on a Re(0001)-O(2 × 1) surface. In particular, we demonstrate that interface engineering by an atomically thin oxide layer is crucial for driving the hybrid system into a topologically nontrivial state as confirmed by theoretical calculations of the topological invariant, the Chern number.
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Affiliation(s)
| | - Eric Mascot
- Department of Physics, University of Illinois at Chicago, 845 W. Taylor St. M/C 273, Chicago, IL, USA
| | - Sagen Cocklin
- Department of Physics, University of Illinois at Chicago, 845 W. Taylor St. M/C 273, Chicago, IL, USA
| | - Howon Kim
- Department of Physics, University of Hamburg, D-20355 Hamburg, Germany
- Corresponding author. (R.W.); (H.K.); (D.K.M.)
| | - Stephan Rachel
- School of Physics, University of Melbourne, Parkville, VIC 3010, Australia
| | - Dirk K. Morr
- Department of Physics, University of Illinois at Chicago, 845 W. Taylor St. M/C 273, Chicago, IL, USA
- Corresponding author. (R.W.); (H.K.); (D.K.M.)
| | - Roland Wiesendanger
- Department of Physics, University of Hamburg, D-20355 Hamburg, Germany
- Corresponding author. (R.W.); (H.K.); (D.K.M.)
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22
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Stefański P. Properties of the Majorana-state tunneling Josephson junction mediated by an interacting quantum dot. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:185301. [PMID: 30731436 DOI: 10.1088/1361-648x/ab052a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We consider a model of a Josephson junction of two topological superconducting wires mediated by an interacting quantum dot. An additional normal electrode coupled to the dot from the top allows to probe its density of states. The Majorana states adjacent to the dot hybridize across the junction and from a bound state in the dot. The dot is subjected to the effective magnetic field arising from the superposition of the fields driving each wire into topological states, which, dependent on the angle between the fields, introduces variable Zeeman splitting of the dot active level. We show that electron interactions in the dot diminish the characteristic for Majoranas zero bias peak arising in the transverse conductance through the dot and introduce an overall asymmetry of the conductance. They also renormalize the hybridization between the end-state Majoranas in shorter wires. The Majorana spin polarization is determined by the effective magnetic field in the dot. Phase-biased Josephson current exhibits spin polarization in thermal equilibrium, which possesses characteristic [Formula: see text] periodicity, and its sign can be switched when an unpaired Majorana state is present in the junction. We also observe spin-dependent Majorana state 'leaking', which can be controlled by the position of the dot level in energy scale.
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Affiliation(s)
- Piotr Stefański
- Institute of Molecular Physics of the Polish Academy of Sciences, ul. Smoluchowskiego 17, 60-179 Poznań, Poland
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23
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Wang R, Su W, Zhu JX, Ting CS, Li H, Chen C, Wang B, Wang X. Kondo Signatures of a Quantum Magnetic Impurity in Topological Superconductors. PHYSICAL REVIEW LETTERS 2019; 122:087001. [PMID: 30932570 DOI: 10.1103/physrevlett.122.087001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2018] [Revised: 10/14/2018] [Indexed: 06/09/2023]
Abstract
We study the Kondo physics of a quantum magnetic impurity in two-dimensional topological superconductors (TSCs), either intrinsic or induced on the surface of a bulk topological insulator, using a numerical renormalization group technique. We show that, despite sharing the p+ip pairing symmetry, intrinsic and extrinsic TSCs host different physical processes that produce distinct Kondo signatures. Extrinsic TSCs harbor an unusual screening mechanism involving both electron and orbital degrees of freedom that produces rich and prominent Kondo phenomena, especially an intriguing pseudospin Kondo singlet state in the superconducting gap and a spatially anisotropic spin correlation. In sharp contrast, intrinsic TSCs support a robust impurity spin doublet ground state and an isotropic spin correlation. These findings advance fundamental knowledge of novel Kondo phenomena in TSCs and suggest experimental avenues for their detection and distinction.
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Affiliation(s)
- Rui Wang
- School of Physics and Astronomy, Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shanghai Jiao Tong University, Shanghai 200240, China
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center for Advanced Microstructures, Nanjing 210093, China
| | - W Su
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- College of Phyics and Electronic Engineering, Center for Computational Sciences, Sichuan Nomal University, Chengdu 610068, China
| | - Jian-Xin Zhu
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C S Ting
- Department of Physics and Texas Center for Superconductivity, University of Houston, Houston, Texas 77204, USA
| | - Hai Li
- Department of Physics and Texas Center for Superconductivity, University of Houston, Houston, Texas 77204, USA
| | - Changfeng Chen
- Department of Physics and Astronomy, University of Nevada, Las Vegas, Nevada 89154, USA
| | - Baigeng Wang
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center for Advanced Microstructures, Nanjing 210093, China
| | - Xiaoqun Wang
- School of Physics and Astronomy, Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shanghai Jiao Tong University, Shanghai 200240, China
- Collaborative Innovation Center for Advanced Microstructures, Nanjing 210093, China
- Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
- Beijing Computational Science Research Center, Beijing 100084, China
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24
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Farinacci L, Ahmadi G, Reecht G, Ruby M, Bogdanoff N, Peters O, Heinrich BW, von Oppen F, Franke KJ. Tuning the Coupling of an Individual Magnetic Impurity to a Superconductor: Quantum Phase Transition and Transport. PHYSICAL REVIEW LETTERS 2018; 121:196803. [PMID: 30468615 DOI: 10.1103/physrevlett.121.196803] [Citation(s) in RCA: 38] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2018] [Indexed: 05/12/2023]
Abstract
The exchange scattering at magnetic adsorbates on superconductors gives rise to Yu-Shiba-Rusinov (YSR) bound states. Depending on the strength of the exchange coupling, the magnetic moment perturbs the Cooper pair condensate only weakly, resulting in a free-spin ground state, or binds a quasiparticle in its vicinity, leading to a (partially) screened spin state. Here, we use the flexibility of Fe-porphin (FeP) molecules adsorbed on a Pb(111) surface to reversibly and continuously tune between these distinct ground states. We find that the FeP moment is screened in the pristine adsorption state. Approaching the tip of a scanning tunneling microscope, we exert a sufficiently strong attractive force to tune the molecule through the quantum phase transition into the free-spin state. We ascertain and characterize the transition by investigating the transport processes as function of tip-molecule distance, exciting the YSR states by single-electron tunneling as well as (multiple) Andreev reflections.
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Affiliation(s)
- Laëtitia Farinacci
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Gelavizh Ahmadi
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Gaël Reecht
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Michael Ruby
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Nils Bogdanoff
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Olof Peters
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Benjamin W Heinrich
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | - Katharina J Franke
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
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Engineering the spin couplings in atomically crafted spin chains on an elemental superconductor. Nat Commun 2018; 9:3253. [PMID: 30108221 PMCID: PMC6092363 DOI: 10.1038/s41467-018-05701-8] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2018] [Accepted: 07/18/2018] [Indexed: 11/09/2022] Open
Abstract
Magnetic atoms on a superconductor give rise to Yu-Shiba-Rusinov (YSR) states within the superconducting energy gap. A spin chain of magnetic adatoms on an s-wave superconductor may lead to topological superconductivity accompanied by the emergence of Majorana modes at the chain ends. For their usage in quantum computation, it is a prerequisite to artificially assemble the chains and control the exchange couplings between the spins in the chain and in the substrate. Here, using a scanning tunneling microscope tip, we demonstrate engineering of the energy levels of the YSR states by placing interstitial Fe atoms in close proximity to adsorbed Fe atoms on an oxidized Ta surface. Based on this prototype platform, we show that the interaction within a long chain can be strengthened by linking the adsorbed Fe atoms with the interstitial ones. Our work adds an important step towards the controlled design and manipulation of Majorana end states. Magnetic atomic chains assembled on the surface of superconductors are a potential platform for engineering topological superconducting phases. Here the authors step towards this by manipulating magnetic atoms at interstitial sites to tune interatomic interactions and control the Yu-Shiba-Rusinov states that form.
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Kezilebieke S, Dvorak M, Ojanen T, Liljeroth P. Coupled Yu-Shiba-Rusinov States in Molecular Dimers on NbSe 2. NANO LETTERS 2018; 18:2311-2315. [PMID: 29533636 PMCID: PMC6095633 DOI: 10.1021/acs.nanolett.7b05050] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2017] [Revised: 03/05/2018] [Indexed: 05/22/2023]
Abstract
Magnetic impurities have a dramatic effect on superconductivity by breaking the time-reversal symmetry and inducing so-called Yu-Shiba-Rusinov (YSR) low energy bound states within the superconducting gap. The spatial extent of YSR states is greatly enhanced in two-dimensional (2D) systems, which should facilitate the formation of coupled states. Here, we observe YSR states on single cobalt phthalocyanine (CoPC) molecules on a 2D superconductor NbSe2 using low-temperature scanning tunneling microscopy (STM) and spectroscopy. We use STM lateral manipulation to create controlled CoPc dimers and demonstrate the formation of coupled YSR states. The experimental results are corroborated by theoretical analysis of the coupled states in lattice and continuum models.
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Affiliation(s)
- Shawulienu Kezilebieke
- Department
of Applied Physics, Aalto University School
of Science, P.O. Box 15100, 00076 Aalto, Finland
| | - Marc Dvorak
- Centre
of Excellence in Computational Nanoscience (COMP) and Department of
Applied Physics, Aalto University, P.O. Box 11100, 00076 Aalto, Finland
| | - Teemu Ojanen
- Department
of Applied Physics, Aalto University School
of Science, P.O. Box 15100, 00076 Aalto, Finland
- E-mail:
| | - Peter Liljeroth
- Department
of Applied Physics, Aalto University School
of Science, P.O. Box 15100, 00076 Aalto, Finland
- E-mail:
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