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Wang SZ, Yu XQ, Wei LX, Wang L, Cheng QJ, Peng K, Cheng FJ, Liu Y, Li FS, Ma XC, Xue QK, Song CL. Quantum spin driven Yu-Shiba-Rusinov multiplets and fermion-parity-preserving phase transition in K 3C 60. Sci Bull (Beijing) 2024; 69:1392-1399. [PMID: 38594099 DOI: 10.1016/j.scib.2024.03.052] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2023] [Revised: 02/07/2024] [Accepted: 03/22/2024] [Indexed: 04/11/2024]
Abstract
Magnetic impurities in superconductors are of increasing interest due to emergent Yu-Shiba-Rusinov (YSR) states and Majorana zero modes for fault-tolerant quantum computation. However, a direct relationship between the YSR multiple states and magnetic anisotropy splitting of quantum impurity spins remains poorly characterized. By using scanning tunneling microscopy, we systematically resolve individual transition-metal (Fe, Cr, and Ni) impurities induced YSR multiplets as well as their Zeeman effects in the K3C60 superconductor. The YSR multiplets show identical d orbital-like wave functions that are symmetry-mismatched to the threefold K3C60(1 1 1) host surface, breaking point-group symmetries of the spatial distribution of YSR bound states in real space. Remarkably, we identify an unprecedented fermion-parity-preserving quantum phase transition between ground states with opposite signs of the uniaxial magnetic anisotropy that can be manipulated by an external magnetic field. These findings can be readily understood in terms of anisotropy splitting of quantum impurity spins, and thus elucidate the intricate interplay between the magnetic anisotropy and YSR multiplets.
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Affiliation(s)
- Shu-Ze Wang
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Xue-Qing Yu
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Li-Xuan Wei
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Li Wang
- Vacuum Interconnected Nanotech Workstation, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou 215123, China
| | - Qiang-Jun Cheng
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Kun Peng
- Vacuum Interconnected Nanotech Workstation, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou 215123, China
| | - Fang-Jun Cheng
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Yu Liu
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Fang-Sen Li
- Vacuum Interconnected Nanotech Workstation, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou 215123, China.
| | - Xu-Cun Ma
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China; Frontier Science Center for Quantum Information, Beijing 100084, China
| | - Qi-Kun Xue
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China; Frontier Science Center for Quantum Information, Beijing 100084, China; Beijing Academy of Quantum Information Sciences, Beijing 100193, China; Southern University of Science and Technology, Shenzhen 518055, China.
| | - Can-Li Song
- State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China; Frontier Science Center for Quantum Information, Beijing 100084, China.
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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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Liu Y, Li C, Xue FH, Su W, Wang Y, Huang H, Yang H, Chen J, Guan D, Li Y, Zheng H, Liu C, Qin M, Wang X, Wang R, Li DY, Liu PN, Wang S, Jia J. Quantum Phase Transition in Magnetic Nanographenes on a Lead Superconductor. NANO LETTERS 2023; 23:9704-9710. [PMID: 37870505 DOI: 10.1021/acs.nanolett.3c02208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2023]
Abstract
Quantum spins, also known as spin operators that preserve SU(2) symmetry, lack a specific orientation in space and are hypothesized to display unique interactions with superconductivity. However, spin-orbit coupling and crystal field typically cause a significant magnetic anisotropy in d/f shell spins on surfaces. Here, we fabricate atomically precise S = 1/2 magnetic nanographenes on Pb(111) through engineering sublattice imbalance in the graphene honeycomb lattice. Through tuning the magnetic exchange strength between the unpaired spin and Cooper pairs, a quantum phase transition from the singlet to the doublet state has been observed, consistent with the quantum spin models. From our calculations, the particle-hole asymmetry is induced by the Coulomb scattering potential and gives a transition point about kBTk ≈ 1.6Δ. Our work demonstrates that delocalized π electron magnetism hosts highly tunable magnetic bound states, which can be further developed to study the Majorana bound states and other rich quantum phases of low-dimensional quantum spins on superconductors.
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Affiliation(s)
- Yu Liu
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), TD Lee Institute, Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- Shanghai Research Center for Quantum Sciences, 99 Xiupu Road, Shanghai 201315, China
| | - Can Li
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), TD Lee Institute, Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- Shanghai Research Center for Quantum Sciences, 99 Xiupu Road, Shanghai 201315, China
| | - Fu-Hua Xue
- Key Laboratory for Advanced Materials and Feringa Nobel Prize Scientist Joint Research Center, Frontiers Science Center for Materiobiology and Dynamic Chemistry, State Key Laboratory of Chemical Engineering, School of Chemistry and Molecular Engineering, East China University of Science Technology, 130 Meilong Road, Shanghai 200237, 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
| | - Ying Wang
- Key Laboratory for Advanced Materials and Feringa Nobel Prize Scientist Joint Research Center, Frontiers Science Center for Materiobiology and Dynamic Chemistry, State Key Laboratory of Chemical Engineering, School of Chemistry and Molecular Engineering, East China University of Science Technology, 130 Meilong Road, Shanghai 200237, China
| | - Haili Huang
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), TD Lee Institute, Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- Shanghai Research Center for Quantum Sciences, 99 Xiupu Road, Shanghai 201315, China
| | - Hao Yang
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), TD Lee Institute, Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- Shanghai Research Center for Quantum Sciences, 99 Xiupu Road, Shanghai 201315, China
| | - Jiayi Chen
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), TD Lee Institute, Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- Shanghai Research Center for Quantum Sciences, 99 Xiupu Road, Shanghai 201315, China
| | - Dandan Guan
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), TD Lee Institute, Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- Shanghai Research Center for Quantum Sciences, 99 Xiupu Road, Shanghai 201315, China
| | - Yaoyi Li
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), TD Lee Institute, Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- Shanghai Research Center for Quantum Sciences, 99 Xiupu Road, Shanghai 201315, China
| | - Hao Zheng
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), TD Lee Institute, Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- Shanghai Research Center for Quantum Sciences, 99 Xiupu Road, Shanghai 201315, China
| | - Canhua Liu
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), TD Lee Institute, Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- Shanghai Research Center for Quantum Sciences, 99 Xiupu Road, Shanghai 201315, China
| | - Mingpu Qin
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), TD Lee Institute, Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
| | - Xiaoqun Wang
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), TD Lee Institute, Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, 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
| | - Deng-Yuan Li
- Key Laboratory for Advanced Materials and Feringa Nobel Prize Scientist Joint Research Center, Frontiers Science Center for Materiobiology and Dynamic Chemistry, State Key Laboratory of Chemical Engineering, School of Chemistry and Molecular Engineering, East China University of Science Technology, 130 Meilong Road, Shanghai 200237, China
| | - Pei-Nian Liu
- Key Laboratory for Advanced Materials and Feringa Nobel Prize Scientist Joint Research Center, Frontiers Science Center for Materiobiology and Dynamic Chemistry, State Key Laboratory of Chemical Engineering, School of Chemistry and Molecular Engineering, East China University of Science Technology, 130 Meilong Road, Shanghai 200237, China
| | - Shiyong Wang
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), TD Lee Institute, Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- Shanghai Research Center for Quantum Sciences, 99 Xiupu Road, Shanghai 201315, China
| | - Jinfeng Jia
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), TD Lee Institute, Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- Shanghai Research Center for Quantum Sciences, 99 Xiupu Road, Shanghai 201315, China
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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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Trivini S, Ortuzar J, Vaxevani K, Li J, Bergeret FS, Cazalilla MA, Pascual JI. Cooper Pair Excitation Mediated by a Molecular Quantum Spin on a Superconducting Proximitized Gold Film. PHYSICAL REVIEW LETTERS 2023; 130:136004. [PMID: 37067302 DOI: 10.1103/physrevlett.130.136004] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2022] [Accepted: 02/17/2023] [Indexed: 06/19/2023]
Abstract
Breaking a correlated pair in a superconductor requires an even number of fermions providing at least twice the pairing energy Δ. Here, we show that a single tunneling electron can also excite a pair breaking excitation in a proximitized gold film in the presence of magnetic impurities. Combining scanning tunneling spectroscopy with theoretical modeling, we map the excitation spectrum of an Fe-porphyrin molecule on the Au/V(100) proximitized surface into a manifold of entangled Yu-Shiba-Rusinov and spin excitations. Pair excitations emerge in the tunneling spectra as peaks outside the spectral gap only in the strong coupling regime, where the presence of a bound quasiparticle in the ground state ensures the even fermion parity of the excitation. Our results unravel the quantum nature of magnetic impurities on superconductors and demonstrate that pair excitations unequivocally reveal the parity of the ground state.
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Affiliation(s)
| | - Jon Ortuzar
- CIC nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain
| | | | - Jingchen Li
- CIC nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain
- School of Physics, Sun Yat-sen University, Guangzhou 510275, China
| | - F Sebastian Bergeret
- Centro de Física de Materiales (CFM-MPC) Centro Mixto CSIC-UPV/EHU, E-20018 Donostia-San Sebastián, Spain
- Donostia International Physics Center (DIPC), 20018 Donostia-San Sebastian, Spain
| | - Miguel A Cazalilla
- Donostia International Physics Center (DIPC), 20018 Donostia-San Sebastian, Spain
- Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain
| | - Jose Ignacio Pascual
- CIC nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain
- Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain
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7
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Briganti M, Serrano G, Poggini L, Sorrentino AL, Cortigiani B, de Camargo LC, Soares JF, Motta A, Caneschi A, Mannini M, Totti F, Sessoli R. Mixed-Sandwich Titanium(III) Qubits on Au(111): Electron Delocalization Ruled by Molecular Packing. NANO LETTERS 2022; 22:8626-8632. [PMID: 36256878 PMCID: PMC9650780 DOI: 10.1021/acs.nanolett.2c03161] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2022] [Revised: 10/07/2022] [Indexed: 06/15/2023]
Abstract
Organometallic sandwich complexes are versatile molecular systems that have been recently employed for single-molecule manipulation and spin sensing experiments. Among related organometallic compounds, the mixed-sandwich S = 1/2 complex (η8-cyclooctatetraene)(η5-cyclopentadienyl)titanium, here [CpTi(cot)], has attracted interest as a spin qubit because of the long coherence time. Here the structural and chemical properties of [CpTi(cot)] on Au(111) are investigated at the monolayer level by experimental and computational methods. Scanning tunneling microscopy suggests that adsorption occurs in two molecular orientations, lying and standing, with a 3:1 ratio. XPS data evidence that a fraction of the molecules undergo partial electron transfer to gold, while our computational analysis suggests that only the standing molecules experience charge delocalization toward the surface. Such a phenomenon depends on intermolecular interactions that stabilize the molecular packing in the monolayer. This orientation-dependent molecule-surface hybridization opens exciting perspectives for selective control of the molecule-substrate spin delocalization in hybrid interfaces.
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Affiliation(s)
- Matteo Briganti
- Department
of Chemistry “U. Schiff” (DICUS) and INSTM Research
Unit, University of Florence, Via della Lastruccia 3-13, 50019 Sesto Fiorentino (FI), Italy
- Department
of Chemistry, Federal University of Parana, Centro Politecnico, Jardim das Americas, 81530-900 Curitiba, PR Brazil
| | - Giulia Serrano
- Department
of Industrial Engineering (DIEF) and INSTM Research Unit, University of Florence, Via di Santa Marta, 3, 50139 Florence, Italy
| | - Lorenzo Poggini
- Department
of Chemistry “U. Schiff” (DICUS) and INSTM Research
Unit, University of Florence, Via della Lastruccia 3-13, 50019 Sesto Fiorentino (FI), Italy
- Institute
for Chemistry of OrganoMetallic Compounds (ICCOM-CNR), Via Madonna del Piano, 50019 Sesto Fiorentino (FI) Italy
| | - Andrea Luigi Sorrentino
- Department
of Chemistry “U. Schiff” (DICUS) and INSTM Research
Unit, University of Florence, Via della Lastruccia 3-13, 50019 Sesto Fiorentino (FI), Italy
- Department
of Industrial Engineering (DIEF) and INSTM Research Unit, University of Florence, Via di Santa Marta, 3, 50139 Florence, Italy
| | - Brunetto Cortigiani
- Department
of Chemistry “U. Schiff” (DICUS) and INSTM Research
Unit, University of Florence, Via della Lastruccia 3-13, 50019 Sesto Fiorentino (FI), Italy
| | - Luana Carol de Camargo
- Department
of Chemistry, Federal University of Parana, Centro Politecnico, Jardim das Americas, 81530-900 Curitiba, PR Brazil
| | - Jaísa Fernandes Soares
- Department
of Chemistry, Federal University of Parana, Centro Politecnico, Jardim das Americas, 81530-900 Curitiba, PR Brazil
| | - Alessandro Motta
- “La
Sapienza” and INSTM Research Unit, University of Rome, Piazzale Aldo Moro 5, 00185 Rome, Italy
| | - Andrea Caneschi
- Department
of Industrial Engineering (DIEF) and INSTM Research Unit, University of Florence, Via di Santa Marta, 3, 50139 Florence, Italy
| | - Matteo Mannini
- Department
of Chemistry “U. Schiff” (DICUS) and INSTM Research
Unit, University of Florence, Via della Lastruccia 3-13, 50019 Sesto Fiorentino (FI), Italy
| | - Federico Totti
- Department
of Chemistry “U. Schiff” (DICUS) and INSTM Research
Unit, University of Florence, Via della Lastruccia 3-13, 50019 Sesto Fiorentino (FI), Italy
| | - Roberta Sessoli
- Department
of Chemistry “U. Schiff” (DICUS) and INSTM Research
Unit, University of Florence, Via della Lastruccia 3-13, 50019 Sesto Fiorentino (FI), Italy
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8
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Spin-orbital Yu-Shiba-Rusinov states in single Kondo molecular magnet. Nat Commun 2022; 13:6388. [PMID: 36302772 PMCID: PMC9613647 DOI: 10.1038/s41467-022-34187-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2021] [Accepted: 10/13/2022] [Indexed: 11/18/2022] Open
Abstract
Studies of single-spin objects are essential for designing emergent quantum states. We investigate a molecular magnet Tb2Pc3 interacting with a superconducting Pb(111) substrate, which hosts unprecedented Yu-Shiba-Rusinov (YSR) subgap states, dubbed spin-orbital YSR states. Upon adsorption of the molecule on Pb, the degeneracy of its lowest unoccupied molecular orbitals (LUMO) is lifted, and the lower LUMO forms a radical spin via charge transfer. This leads to Kondo screening and subgap states. Intriguingly, the YSR states display two pairs of resonances with clearly distinct behavior. The energy of the inner pair exhibits prominent inter and intra molecular variation, and it strongly depends on the tip height. The outer pair, however, shifts only slightly. As is unveiled through theoretical calculations, the two pairs of YSR states originate from the ligand spin and charge-fluctuating higher LUMO, coexisting in a single molecule, but only weakly coupled presumably due to different spatial distribution. Our work paves the way for understanding complex many-body excitations and constructing molecule-based topological superconductivity. Yu-Shiba-Rusinov (YSR) states result from the exchange coupling between a localized magnetic moment and a superconductor. Traditionally, the YSR states have been studied for magnetic atoms. For molecular magnets with extended ligand spin, the entanglement of spin and ligand orbital gives rise to new forms of YSR excitations. Here, Xia et al uncovered spin-orbital YSR states in an unpaired ligand spin in the molecular magnet Tb2Pc3 on Pb.
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9
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Ayani CG, Calleja F, Ibarburu IM, Casado Aguilar P, Nazriq NKM, Yamada TK, Garnica M, Vázquez de Parga AL, Miranda R. Switchable molecular functionalization of an STM tip: from a Yu-Shiba-Rusinov Tip to a Kondo tip. NANOSCALE 2022; 14:15111-15118. [PMID: 36205255 DOI: 10.1039/d1nr08227b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
In this work we fabricate and characterize a functionalized superconducting (SC) Nb tip of a scanning tunnelling microscope (STM). The tip is functionalized with a Tetracyanoquinodimethane molecule (TCNQ) that accepts charge from the tip and develops a magnetic moment. As a consequence, in scanning tunnelling spectroscopy (STS), sharp, bias symmetric sub-gap states identified as Yu-Shiba-Rusinov (YSR) bound states appear against the featureless density of states of a metallic graphene on Ir(111) sample. Although the coupling regime of the magnetic impurity with the SC tip depends on the initial absorption configuration of the molecule, the interaction strength between the SC tip and the charged TCNQ molecule can be reversibly controlled by tuning the tip-sample distance. The controlled transition from one coupling regime to the other allows us to verify the relation between the energy scales of the two competing many-body effects for the functionalized tip. Quenching the SC state of the Nb tip with a magnetic field switches abruptly from a tip dominated by the YSR bound states to a Kondo tip.
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Affiliation(s)
- Cosme G Ayani
- Departamento de Física de la Materia Condensada, Universidad Autónoma de Madrid, Cantoblanco 28049, Madrid, Spain
- IMDEA-Nanociencia, Calle Faraday 9, Cantoblanco 28049, Madrid, Spain.
| | - Fabian Calleja
- IMDEA-Nanociencia, Calle Faraday 9, Cantoblanco 28049, Madrid, Spain.
| | - Ivan M Ibarburu
- Departamento de Física de la Materia Condensada, Universidad Autónoma de Madrid, Cantoblanco 28049, Madrid, Spain
- IMDEA-Nanociencia, Calle Faraday 9, Cantoblanco 28049, Madrid, Spain.
| | - Pablo Casado Aguilar
- Departamento de Física de la Materia Condensada, Universidad Autónoma de Madrid, Cantoblanco 28049, Madrid, Spain
- IMDEA-Nanociencia, Calle Faraday 9, Cantoblanco 28049, Madrid, Spain.
| | - Nana K M Nazriq
- Department of Materials Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
| | - Toyo K Yamada
- Department of Materials Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
- Molecular Chirality Research center, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
| | - Manuela Garnica
- IMDEA-Nanociencia, Calle Faraday 9, Cantoblanco 28049, Madrid, Spain.
- Instituto 'Nicolás Cabrera', Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - Amadeo L Vázquez de Parga
- Departamento de Física de la Materia Condensada, Universidad Autónoma de Madrid, Cantoblanco 28049, Madrid, Spain
- IMDEA-Nanociencia, Calle Faraday 9, Cantoblanco 28049, Madrid, Spain.
- Condensed Matter Physics Center (IFIMAC), Cantoblanco 28049, Madrid, Spain
- Instituto 'Nicolás Cabrera', Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - Rodolfo Miranda
- Departamento de Física de la Materia Condensada, Universidad Autónoma de Madrid, Cantoblanco 28049, Madrid, Spain
- IMDEA-Nanociencia, Calle Faraday 9, Cantoblanco 28049, Madrid, Spain.
- Condensed Matter Physics Center (IFIMAC), Cantoblanco 28049, Madrid, Spain
- Instituto 'Nicolás Cabrera', Universidad Autónoma de Madrid, 28049 Madrid, Spain
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10
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Liu M, Leveillee J, Lu S, Yu J, Kim H, Tian C, Shi Y, Lai K, Zhang C, Giustino F, Shih CK. Monolayer 1T-NbSe 2 as a 2D-correlated magnetic insulator. SCIENCE ADVANCES 2021; 7:eabi6339. [PMID: 34797708 PMCID: PMC8604411 DOI: 10.1126/sciadv.abi6339] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Accepted: 09/30/2021] [Indexed: 06/13/2023]
Abstract
Monolayer group V transition metal dichalcogenides in their 1T phase have recently emerged as a platform to investigate rich phases of matter, such as spin liquid and ferromagnetism, resulting from strong electron correlations. Newly emerging 1T-NbSe2 has inspired theoretical investigations predicting collective phenomena such as charge transfer gap and ferromagnetism in two dimensions; however, the experimental evidence is still lacking. Here, by controlling the molecular beam epitaxy growth parameters, we demonstrate the successful growth of high-quality single-phase 1T-NbSe2. By combining scanning tunneling microscopy/spectroscopy and ab initio calculations, we show that this system is a charge transfer insulator with the upper Hubbard band located above the valence band maximum. To demonstrate the electron correlation resulted magnetic property, we create a vertical 1T/2H NbSe2 heterostructure, and we find unambiguous evidence of exchange interactions between the localized magnetic moments in 1T phase and the metallic/superconducting phase exemplified by Kondo resonances and Yu-Shiba-Rusinov–like bound states.
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Affiliation(s)
- Mengke Liu
- Department of Physics, The University of Texas at Austin, Austin, TX 78712, USA
| | - Joshua Leveillee
- Department of Physics, The University of Texas at Austin, Austin, TX 78712, USA
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA
| | - Shuangzan Lu
- School of Physics and Technology and Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education, Wuhan University, Wuhan 430027, China
| | - Jia Yu
- Department of Physics, The University of Texas at Austin, Austin, TX 78712, USA
| | - Hyunsue Kim
- Department of Physics, The University of Texas at Austin, Austin, TX 78712, USA
| | - Cheng Tian
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Youguo Shi
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Keji Lai
- Department of Physics, The University of Texas at Austin, Austin, TX 78712, USA
| | - Chendong Zhang
- School of Physics and Technology and Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education, Wuhan University, Wuhan 430027, China
| | - Feliciano Giustino
- Department of Physics, The University of Texas at Austin, Austin, TX 78712, USA
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA
| | - Chih-Kang Shih
- Department of Physics, The University of Texas at Austin, Austin, TX 78712, USA
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11
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Moca CP, Weymann I, Werner MA, Zaránd G. Kondo Cloud in a Superconductor. PHYSICAL REVIEW LETTERS 2021; 127:186804. [PMID: 34767427 DOI: 10.1103/physrevlett.127.186804] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Accepted: 09/03/2021] [Indexed: 06/13/2023]
Abstract
Magnetic impurities embedded in a metal are screened by the Kondo effect, signaled by the formation of an extended correlation cloud, the so-called Kondo or screening cloud. In a superconductor, the Kondo state turns into subgap Yu-Shiba-Rusinov states, and a quantum phase transition occurs between screened and unscreened phases once the superconducting energy gap Δ exceeds sufficiently the Kondo temperature, T_{K}. Here we show that, although the Kondo state does not form in the unscreened phase, the Kondo cloud does exist in both quantum phases. However, while screening is complete in the screened phase, it is only partial in the unscreened phase. Compensation, a quantity introduced to characterize the integrity of the cloud, is universal, and shown to be related to the magnetic impurities' g factor, monitored experimentally by bias spectroscopy.
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Affiliation(s)
- Cătălin Paşcu Moca
- MTA-BME Quantum Dynamics and Correlations Research Group, Eötvös Loránd Research Network, Budapest University of Technology and Economics, Budafoki út 8., H-1111 Budapest, Hungary
- Department of Physics, University of Oradea, 410087 Oradea, Romania
| | - Ireneusz Weymann
- Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland
| | - Miklós Antal Werner
- MTA-BME Quantum Dynamics and Correlations Research Group, Eötvös Loránd Research Network, Budapest University of Technology and Economics, Budafoki út 8., H-1111 Budapest, Hungary
- Department of Theoretical Physics, Budapest University of Technology and Economics, Budafoki út 8., H-1111 Budapest, Hungary
| | - Gergely Zaránd
- MTA-BME Quantum Dynamics and Correlations Research Group, Eötvös Loránd Research Network, Budapest University of Technology and Economics, Budafoki út 8., H-1111 Budapest, Hungary
- BME-MTA Exotic Quantum Phases 'Lendület' Research Group, Institute of Physics, Budapest University of Technology and Economics, Budafoki út 8., H-1111 Budapest, Hungary
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12
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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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13
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Briganti M, Totti F. Magnetic anisotropy on demand exploiting high-pressure as remote control: an ab initio proof of concept. Dalton Trans 2021; 50:10621-10628. [PMID: 34286784 DOI: 10.1039/d1dt01719e] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
Lanthanide based single molecule magnets have recently become very promising systems for creating single molecule devices working at high temperatures (nitrogen boiling temperature). However, the variation of the direction of the anisotropy tensor as a function of the applied pressure still represents a quite unexplored field. Application of external pressure can be a promising method toward neat control of magnetic anisotropy and relaxation processes in the bulk phase. Required criteria for being eligible for such systems are as follows: the presence of first excited energy levels with significantly different orientations of its anisotropy tensor; sufficiently low energies of such levels so that they can mix with the ground state; and the possibility of tuning their energies by small geometrical perturbations. The archetype compound {Na[DyDOTA(H2O)]·4H2O} (1) (H4DOTA = 1,4,7,10-tetraazacyclododecane-1,4,7,10-N,N',N'',N'''-tetraacetic acid) fulfils all such criteria. A state-of-the-art in silico proof of concept study on the possibility of controlling the orientation of the anisotropy tensor as a function of pressure in [DyDOTA(H2O)]- by inducing different apical water molecule (AWM) orientations and/or DOTA-induced crystal field is presented.
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Affiliation(s)
- Matteo Briganti
- Department of Chemistry "U. Schiff" and INSTM UdR Firenze, University of Florence, Via della Lastruccia 3-13, 50019 Sesto Fiorentino, Italy.
| | - Federico Totti
- Department of Chemistry "U. Schiff" and INSTM UdR Firenze, University of Florence, Via della Lastruccia 3-13, 50019 Sesto Fiorentino, Italy.
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14
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Montero AM, Guimarães FSM, Lounis S. Multiple magnetic states of CoPc molecule on a two-dimensional layer of NbSe 2. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:205802. [PMID: 33704093 DOI: 10.1088/1361-648x/abed64] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/29/2020] [Accepted: 03/10/2021] [Indexed: 06/12/2023]
Abstract
Molecular spintronics hinges on the detailed understanding of electronic and magnetic properties of molecules interfaced with various materials. Here we demonstrate withab initiosimulations that the prototypical Co-phthalocyanine (CoPc) molecule can surprisingly develop multi-spin states once deposited on the two-dimensional 2H-NbSe2layer. Conventional calculations based on density functional theory (DFT) show the existence of low, regular and high spin states, which reduce to regular and high spins states once correlations are incorporated with a DFT +Uapproach. Depending onU, the ground state is either the low spin or high spin state with energy differences affected by the molecular orientation on top of the substrate. Our results are compared to recent scanning probe measurements and motivate further theoretical and experimental studies on the unveiled rich multi-magnetic behavior of CoPc molecule.
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Affiliation(s)
- Ana M Montero
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszetrum Jülich and JARA, 52425 Jülich, Germany
| | - Filipe S M Guimarães
- Jülich Supercomputing Centre, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany
| | - Samir Lounis
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszetrum Jülich and JARA, 52425 Jülich, Germany
- Faculty of Physics, University of Duisburg-Essen and CENIDE, 47053 Duisburg, Germany
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15
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Ding H, Hu Y, Randeria MT, Hoffman S, Deb O, Klinovaja J, Loss D, Yazdani A. Tuning interactions between spins in a superconductor. Proc Natl Acad Sci U S A 2021; 118:e2024837118. [PMID: 33782131 PMCID: PMC8040815 DOI: 10.1073/pnas.2024837118] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Novel many-body and topological electronic phases can be created in assemblies of interacting spins coupled to a superconductor, such as one-dimensional topological superconductors with Majorana zero modes (MZMs) at their ends. Understanding and controlling interactions between spins and the emergent band structure of the in-gap Yu-Shiba-Rusinov (YSR) states they induce in a superconductor are fundamental for engineering such phases. Here, by precisely positioning magnetic adatoms with a scanning tunneling microscope (STM), we demonstrate both the tunability of exchange interaction between spins and precise control of the hybridization of YSR states they induce on the surface of a bismuth (Bi) thin film that is made superconducting with the proximity effect. In this platform, depending on the separation of spins, the interplay among Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, spin-orbit coupling, and surface magnetic anisotropy stabilizes different types of spin alignments. Using high-resolution STM spectroscopy at millikelvin temperatures, we probe these spin alignments through monitoring the spin-induced YSR states and their energy splitting. Such measurements also reveal a quantum phase transition between the ground states with different electron number parity for a pair of spins in a superconductor tuned by their separation. Experiments on larger assemblies show that spin-spin interactions can be mediated in a superconductor over long distances. Our results show that controlling hybridization of the YSR states in this platform provides the possibility of engineering the band structure of such states for creating topological phases.
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Affiliation(s)
- Hao Ding
- Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544
- Department of Physics, Princeton University, Princeton, NJ 08544
| | - Yuwen Hu
- Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544
- Department of Physics, Princeton University, Princeton, NJ 08544
| | - Mallika T Randeria
- Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544
- Department of Physics, Princeton University, Princeton, NJ 08544
| | - Silas Hoffman
- Department of Physics, University of Basel, CH-4056 Basel, Switzerland
- Department of Physics, University of Florida, Gainesville, FL 32611
| | - Oindrila Deb
- Department of Physics, University of Basel, CH-4056 Basel, Switzerland
| | - Jelena Klinovaja
- Department of Physics, University of Basel, CH-4056 Basel, Switzerland
| | - Daniel Loss
- Department of Physics, University of Basel, CH-4056 Basel, Switzerland
| | - Ali Yazdani
- Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544;
- Department of Physics, Princeton University, Princeton, NJ 08544
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16
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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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17
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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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18
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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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19
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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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20
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Yang H, Li YY, Liu TT, Guan DD, Wang SY, Zheng H, Liu C, Fu L, Jia JF. Multiple In-Gap States Induced by Topological Surface States in the Superconducting Topological Crystalline Insulator Heterostructure Sn_{1-x}Pb_{x}Te-Pb. PHYSICAL REVIEW LETTERS 2020; 125:136802. [PMID: 33034492 DOI: 10.1103/physrevlett.125.136802] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2020] [Accepted: 08/04/2020] [Indexed: 06/11/2023]
Abstract
Superconducting topological crystalline insulators (TCIs) have been proposed to be a new type of topological superconductor where multiple Majorana zero modes may coexist under the protection of lattice symmetries. The bulk superconductivity of TCIs has been realized, but it is quite challenging to detect the superconductivity of topological surface states inside their bulk superconducting gaps. Here, we report high-resolution scanning tunneling spectroscopy measurements on lateral Sn_{1-x}Pb_{x}Te-Pb heterostructures using superconducting tips. Both the bulk superconducting gap and the multiple in-gap states with energy differences of ∼0.3 meV can be clearly resolved on TCI Sn_{1-x}Pb_{x}Te at 0.38 K. Quasiparticle interference measurements further confirm the in-gap states are gapless. Our work demonstrates that the unique topological superconductivity of a TCI can be directly distinguished in the density of states, which helps to further investigate the multiple Dirac and Majorana fermions inside the superconducting gap.
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Affiliation(s)
- Hao Yang
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Yao-Yi Li
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Teng-Teng Liu
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Dan-Dan Guan
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Shi-Yong Wang
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Hao Zheng
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Canhua Liu
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Jin-Feng Jia
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 200240, China
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21
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Zhang G, Samuely T, Iwahara N, Kačmarčík J, Wang C, May PW, Jochum JK, Onufriienko O, Szabó P, Zhou S, Samuely P, Moshchalkov VV, Chibotaru LF, Rubahn HG. Yu-Shiba-Rusinov bands in ferromagnetic superconducting diamond. SCIENCE ADVANCES 2020; 6:eaaz2536. [PMID: 32440544 PMCID: PMC7228758 DOI: 10.1126/sciadv.aaz2536] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/24/2019] [Accepted: 03/03/2020] [Indexed: 06/11/2023]
Abstract
The combination of different exotic properties in materials paves the way for the emergence of their new potential applications. An example is the recently found coexistence of the mutually antagonistic ferromagnetism and superconductivity in hydrogenated boron-doped diamond, which promises to be an attractive system with which to explore unconventional physics. Here, we show the emergence of Yu-Shiba-Rusinov (YSR) bands with a spatial extent of tens of nanometers in ferromagnetic superconducting diamond using scanning tunneling spectroscopy. We demonstrate theoretically how a two-dimensional (2D) spin lattice at the surface of a three-dimensional (3D) superconductor gives rise to the YSR bands and how their density-of-states profile correlates with the spin lattice structure. The established strategy to realize new forms of the coexistence of ferromagnetism and superconductivity opens a way to engineer the unusual electronic states and also to design better-performing superconducting devices.
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Affiliation(s)
- Gufei Zhang
- NanoSYD, Mads Clausen Institute and DIAS Danish Institute for Advanced Study, University of Southern Denmark, Alsion 2, DK-6400 Sonderborg, Denmark
| | - Tomas Samuely
- Centre of Low Temperature Physics, Institute of Experimental Physics, Slovak Academy of Sciences & Faculty of Science, P. J. Safarik University, Kosice, Slovakia
| | - Naoya Iwahara
- Theory of Nanomaterials Group, KU Leuven, Celestijnenlaan 200F, B-3001 Heverlee, Belgium
- Department of Chemistry, National University of Singapore, Block S8 Level 3, 3 Science Drive 3, Singapore 117543, Singapore
| | - Jozef Kačmarčík
- Centre of Low Temperature Physics, Institute of Experimental Physics, Slovak Academy of Sciences & Faculty of Science, P. J. Safarik University, Kosice, Slovakia
| | - Changan Wang
- Helmholtz-Zentrum Dresden-Rossendorf, Institute of Ion Beam Physics and Materials Research, Bautzner Landstr. 400, 01328 Dresden, Germany
| | - Paul W. May
- School of Chemistry, University of Bristol, Bristol BS8 1TS, UK
| | - Johanna K. Jochum
- Laboratory of Solid State Physics and Magnetism, KU Leuven, B-3001 Heverlee, Belgium
- Heinz Maier-Leibnitz Zentrum (MLZ), Technische Universität München, Lichtenbergstrasse 1, 85748 Garching, Germany
| | - Oleksandr Onufriienko
- Centre of Low Temperature Physics, Institute of Experimental Physics, Slovak Academy of Sciences & Faculty of Science, P. J. Safarik University, Kosice, Slovakia
| | - Pavol Szabó
- Centre of Low Temperature Physics, Institute of Experimental Physics, Slovak Academy of Sciences & Faculty of Science, P. J. Safarik University, Kosice, Slovakia
| | - Shengqiang Zhou
- Helmholtz-Zentrum Dresden-Rossendorf, Institute of Ion Beam Physics and Materials Research, Bautzner Landstr. 400, 01328 Dresden, Germany
| | - Peter Samuely
- Centre of Low Temperature Physics, Institute of Experimental Physics, Slovak Academy of Sciences & Faculty of Science, P. J. Safarik University, Kosice, Slovakia
| | | | - Liviu F. Chibotaru
- Theory of Nanomaterials Group, KU Leuven, Celestijnenlaan 200F, B-3001 Heverlee, Belgium
| | - Horst-Günter Rubahn
- NanoSYD, Mads Clausen Institute and DIAS Danish Institute for Advanced Study, University of Southern Denmark, Alsion 2, DK-6400 Sonderborg, Denmark
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22
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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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23
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Large spatial extension of the zero-energy Yu-Shiba-Rusinov state in a magnetic field. Nat Commun 2020; 11:1834. [PMID: 32286260 PMCID: PMC7156378 DOI: 10.1038/s41467-020-15322-9] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Accepted: 03/03/2020] [Indexed: 11/30/2022] Open
Abstract
Various promising qubit concepts have been put forward recently based on engineered superconductor subgap states like Andreev bound states, Majorana zero modes or the Yu-Shiba-Rusinov (Shiba) states. The coupling of these subgap states via a superconductor strongly depends on their spatial extension and is an essential next step for future quantum technologies. Here we investigate the spatial extension of a Shiba state in a semiconductor quantum dot coupled to a superconductor. With detailed transport measurements and numerical renormalization group calculations we find a remarkable more than 50 nm extension of the zero energy Shiba state, much larger than the one observed in very recent scanning tunneling microscopy measurements. Moreover, we demonstrate that its spatial extension increases substantially in a magnetic field. Local magnetic moments coupled to superconductors can form subgap Yu-Shiba-Rusinov states. Here the authors show that Shiba states made with an InAs nanowire quantum dot have large spatial extent, which is beneficial for making Shiba chains that are predicted to host Majorana zero modes.
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24
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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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25
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Malavolti L, Briganti M, Hänze M, Serrano G, Cimatti I, McMurtrie G, Otero E, Ohresser P, Totti F, Mannini M, Sessoli R, Loth S. Tunable Spin-Superconductor Coupling of Spin 1/2 Vanadyl Phthalocyanine Molecules. NANO LETTERS 2018; 18:7955-7961. [PMID: 30452271 DOI: 10.1021/acs.nanolett.8b03921] [Citation(s) in RCA: 46] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Atomic-scale magnetic moments in contact with superconductors host rich physics based on the emergence of Yu-Shiba-Rusinov (YSR) magnetic bound states within the superconducting condensate. Here, we focus on a magnetic bound state induced into Pb nanoislands by individual vanadyl phthalocyanine (VOPc) molecules deposited on the Pb surface. The VOPc molecule is characterized by a spin magnitude of 1/2 arising from a well-isolated singly occupied d xy-orbital and is a promising candidate for a molecular spin qubit with long coherence times. X-ray magnetic circular dichroism (XMCD) measurements show that the molecular spin remains unperturbed even for molecules directly deposited on the Pb surface. Scanning tunneling spectroscopy and density functional theory (DFT) calculations identify two adsorption geometries for this "asymmetric" molecule (i.e., absence of a horizontal symmetry plane): (a) oxygen pointing toward the vacuum with the Pc laying on the Pb, showing negligible spin-superconductor interaction, and (b) oxygen pointing toward the Pb, presenting an efficient interaction with the Pb and promoting a Yu-Shiba-Rusinov bound state. Additionally, we find that in the first case a YSR state can be induced smoothly by exerting mechanical force on the molecules with the scanning tunneling microscope (STM) tip. This allows the interaction strength to be tuned continuously from an isolated molecular spin case, through the quantum critical point (where the bound state energy is zero) and beyond. DFT indicates that a gradual bending of the VO bond relative to the Pc ligand plane promoted by the STM tip can modify the interaction in a continuously tunable manner. The ability to induce a tunable YSR state in the superconductor suggests the possibility of introducing coupled spins on superconductors with switchable interaction.
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Affiliation(s)
- Luigi Malavolti
- Institute for Functional Matter and Quantum Technologies , University of Stuttgart , 70569 Stuttgart , Germany
- Max Planck Institute for the Structure and Dynamics of Matter , 22761 Hamburg , Germany
- Max Planck Institute for Solid State Research , 70569 Stuttgart , Germany
| | - Matteo Briganti
- Dipartimento di Chimica "Ugo Schiff" & INSTM RU , Università degli Studi di Firenze , Via della Lastruccia 3-13 , 150019 Sesto Fiorentino (Firenze) , Italy
| | - Max Hänze
- Institute for Functional Matter and Quantum Technologies , University of Stuttgart , 70569 Stuttgart , Germany
- Max Planck Institute for the Structure and Dynamics of Matter , 22761 Hamburg , Germany
- Max Planck Institute for Solid State Research , 70569 Stuttgart , Germany
| | - Giulia Serrano
- Dipartimento di Chimica "Ugo Schiff" & INSTM RU , Università degli Studi di Firenze , Via della Lastruccia 3-13 , 150019 Sesto Fiorentino (Firenze) , Italy
| | - Irene Cimatti
- Dipartimento di Chimica "Ugo Schiff" & INSTM RU , Università degli Studi di Firenze , Via della Lastruccia 3-13 , 150019 Sesto Fiorentino (Firenze) , Italy
| | - Gregory McMurtrie
- Institute for Functional Matter and Quantum Technologies , University of Stuttgart , 70569 Stuttgart , Germany
- Max Planck Institute for the Structure and Dynamics of Matter , 22761 Hamburg , Germany
- Max Planck Institute for Solid State Research , 70569 Stuttgart , Germany
| | - Edwige Otero
- Synchrotron SOLEIL , 4891192 Gif-sur-Yvette , France
| | | | - Federico Totti
- Dipartimento di Chimica "Ugo Schiff" & INSTM RU , Università degli Studi di Firenze , Via della Lastruccia 3-13 , 150019 Sesto Fiorentino (Firenze) , Italy
| | - Matteo Mannini
- Dipartimento di Chimica "Ugo Schiff" & INSTM RU , Università degli Studi di Firenze , Via della Lastruccia 3-13 , 150019 Sesto Fiorentino (Firenze) , Italy
| | - Roberta Sessoli
- Dipartimento di Chimica "Ugo Schiff" & INSTM RU , Università degli Studi di Firenze , Via della Lastruccia 3-13 , 150019 Sesto Fiorentino (Firenze) , Italy
| | - Sebastian Loth
- Institute for Functional Matter and Quantum Technologies , University of Stuttgart , 70569 Stuttgart , Germany
- Max Planck Institute for the Structure and Dynamics of Matter , 22761 Hamburg , Germany
- Max Planck Institute for Solid State Research , 70569 Stuttgart , Germany
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26
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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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27
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Yu-Shiba-Rusinov screening of spins in double quantum dots. Nat Commun 2018; 9:2376. [PMID: 29915280 PMCID: PMC6006160 DOI: 10.1038/s41467-018-04683-x] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2017] [Accepted: 05/17/2018] [Indexed: 11/25/2022] Open
Abstract
A magnetic impurity coupled to a superconductor gives rise to a Yu–Shiba–Rusinov (YSR) state inside the superconducting energy gap. With increasing exchange coupling the excitation energy of this state eventually crosses zero and the system switches to a YSR ground state with bound quasiparticles screening the impurity spin by ħ/2. Here we explore indium arsenide (InAs) nanowire double quantum dots tunnel coupled to a superconductor and demonstrate YSR screening of spin-1/2 and spin-1 states. Gating the double dot through nine different charge states, we show that the honeycomb pattern of zero-bias conductance peaks, archetypal of double dots coupled to normal leads, is replaced by lines of zero-energy YSR states. These enclose regions of YSR-screened dot spins displaying distinctive spectral features, and their characteristic shape and topology change markedly with tunnel coupling strengths. We find excellent agreement with a simple zero-bandwidth approximation, and with numerical renormalization group calculations for the two-orbital Anderson model. Coupling superconductors to mesoscopic systems leads to unusual effects that could be exploited in new devices including topological quantum computers. Here the authors present a double quantum dot with a Yu–Shiba–Rusinov ground state arising from the interplay of Coulomb interactions and superconductivity.
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28
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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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29
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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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30
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Ruby M, Heinrich BW, Peng Y, von Oppen F, Franke KJ. Wave-Function Hybridization in Yu-Shiba-Rusinov Dimers. PHYSICAL REVIEW LETTERS 2018; 120:156803. [PMID: 29756863 DOI: 10.1103/physrevlett.120.156803] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2018] [Indexed: 05/12/2023]
Abstract
Magnetic adsorbates on superconductors induce local bound states within the superconducting gap. These Yu-Shiba-Rusinov (YSR) states decay slowly away from the impurity compared to atomic orbitals, even in 3D bulk crystals. Here, we use scanning tunneling spectroscopy to investigate their hybridization between two nearby magnetic Mn adatoms on a superconducting Pb(001) surface. We observe that the hybridization leads to the formation of symmetric and antisymmetric combinations of YSR states. We investigate how the structure of the dimer wave functions and the energy splitting depend on the shape of the underlying monomer orbitals and the orientation of the dimer with respect to the Pb lattice.
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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
- Institute of Quantum Information and Matter and Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
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31
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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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32
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Hatter N, Heinrich BW, Rolf D, Franke KJ. Scaling of Yu-Shiba-Rusinov energies in the weak-coupling Kondo regime. Nat Commun 2017; 8:2016. [PMID: 29222411 PMCID: PMC5722882 DOI: 10.1038/s41467-017-02277-7] [Citation(s) in RCA: 38] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2017] [Accepted: 11/16/2017] [Indexed: 11/26/2022] Open
Abstract
The competition of the free-spin state of a paramagnetic impurity on a superconductor with its screened counterpart is characterized by the energy scale of Kondo screening compared to the superconducting pairing energy Δ. When the experimental temperature suppresses Kondo screening, but preserves superconductivity, i.e., when Δ/kB > T > TK (kB is Boltzmann’s constant and TK the Kondo temperature), this description fails. Here, we explore this temperature range in a set of manganese phthalocyanine molecules decorated with ammonia on Pb(111). We show that these molecules suffice the required energy conditions by exhibiting weak-coupling Kondo resonances. We correlate the Yu-Shiba-Rusinov bound states energy inside the superconducting gap with the intensity of the Kondo resonance. The observed correlation follows the expectations for a classical spin on a superconductor. This finding is important in view of many theoretical predictions using a classical spin model, in particular for the description of Majorana bound states in magnetic nanostructures on superconducting substrates. The description of a paramagnetic impurity on a superconductor remains elusive in the weak-coupling Kondo regime. Here, Hatter et al. correlate the energy of the Yu-Shiba-Rusinov bound states with the intensity of the Kondo resonances in such a regime, revealing a behavior well described by classical spin models.
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Affiliation(s)
- Nino Hatter
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195, Berlin, Germany
| | - Benjamin W Heinrich
- Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195, Berlin, Germany.
| | - Daniela Rolf
- 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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33
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Cornils L, Kamlapure A, Zhou L, Pradhan S, Khajetoorians AA, Fransson J, Wiebe J, Wiesendanger R. Spin-Resolved Spectroscopy of the Yu-Shiba-Rusinov States of Individual Atoms. PHYSICAL REVIEW LETTERS 2017; 119:197002. [PMID: 29219531 DOI: 10.1103/physrevlett.119.197002] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2017] [Indexed: 06/07/2023]
Abstract
A magnetic atom in a superconducting host induces so-called Yu-Shiba-Rusinov (YSR) bound states inside the superconducting energy gap. By combining spin-resolved scanning tunneling spectroscopy with simulations we demonstrate that the pair of peaks associated with the YSR states of an individual Fe atom coupled to an oxygen-reconstructed Ta surface gets spin polarized in an external magnetic field. As theoretically predicted, the electron and hole parts of the YSR states have opposite signs of spin polarizations which keep their spin character when crossing the Fermi level through the quantum phase transition. The simulation of a YSR state right at the Fermi level reveals zero spin polarization which can be used to distinguish such states from Majorana zero modes in chains of YSR atoms.
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Affiliation(s)
- L Cornils
- Department of Physics, Hamburg University, D-20355 Hamburg, Germany
| | - A Kamlapure
- Department of Physics, Hamburg University, D-20355 Hamburg, Germany
| | - L Zhou
- Department of Physics, Hamburg University, D-20355 Hamburg, Germany
| | - S Pradhan
- Department of Physics and Astronomy, Uppsala University, P.O. Box 516, Uppsala SE-751 21, Sweden
| | | | - J Fransson
- Department of Physics and Astronomy, Uppsala University, P.O. Box 516, Uppsala SE-751 21, Sweden
| | - J Wiebe
- Department of Physics, Hamburg University, D-20355 Hamburg, Germany
| | - R Wiesendanger
- Department of Physics, Hamburg University, D-20355 Hamburg, Germany
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34
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Mapping the orbital structure of impurity bound states in a superconductor. Nat Commun 2017; 8:15175. [PMID: 28480879 PMCID: PMC5424157 DOI: 10.1038/ncomms15175] [Citation(s) in RCA: 64] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2016] [Accepted: 03/03/2017] [Indexed: 11/08/2022] Open
Abstract
A magnetic atom inside a superconductor locally distorts superconductivity. It scatters Cooper pairs as a potential with broken time-reversal symmetry, leading to localized bound states with subgap excitation energies, named Shiba states. Most conventional approaches regarding Shiba states treat magnetic impurities as point scatterers with isotropic exchange interaction. Here, we show that the number and the shape of Shiba states are correlated to the spin-polarized atomic orbitals of the impurity, hybridized with the superconductor. Using scanning tunnelling spectroscopy, we spatially map the five Shiba excitations found on subsurface chromium atoms in Pb(111), resolving their particle and hole components. While particle components resemble d orbitals of embedded Cr atoms, hole components differ strongly from them. Density functional theory simulations correlate the orbital shapes to the magnetic ground state of the atom, and identify scattering channels and interactions, all valuable tools for designing atomic-scale superconducting devices.
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35
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Island JO, Gaudenzi R, de Bruijckere J, Burzurí E, Franco C, Mas-Torrent M, Rovira C, Veciana J, Klapwijk TM, Aguado R, van der Zant HSJ. Proximity-Induced Shiba States in a Molecular Junction. PHYSICAL REVIEW LETTERS 2017; 118:117001. [PMID: 28368652 DOI: 10.1103/physrevlett.118.117001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2016] [Indexed: 05/12/2023]
Abstract
Superconductors containing magnetic impurities exhibit intriguing phenomena derived from the competition between Cooper pairing and Kondo screening. At the heart of this competition are the Yu-Shiba-Rusinov (Shiba) states which arise from the pair breaking effects a magnetic impurity has on a superconducting host. Hybrid superconductor-molecular junctions offer unique access to these states but the added complexity in fabricating such devices has kept their exploration to a minimum. Here, we report on the successful integration of a model spin 1/2 impurity, in the form of a neutral and stable all organic radical molecule, in proximity-induced superconducting break junctions. Our measurements reveal excitations which are characteristic of a spin-induced Shiba state due to the radical's unpaired spin strongly coupled to a superconductor. By virtue of a variable molecule-electrode coupling, we access both the singlet and doublet ground states of the hybrid system which give rise to the doublet and singlet Shiba excited states, respectively. Our results show that Shiba states are a robust feature of the interaction between a paramagnetic impurity and a proximity-induced superconductor where the excited state is mediated by correlated electron-hole (Andreev) pairs instead of Cooper pairs.
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Affiliation(s)
- Joshua O Island
- Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, Netherlands
| | - Rocco Gaudenzi
- Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, Netherlands
| | - Joeri de Bruijckere
- Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, Netherlands
| | - Enrique Burzurí
- Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, Netherlands
| | - Carlos Franco
- Institut de Ciéncia de Materials de Barcelona (ICMAB-CSIC) and CIBER-BBN, Campus de la UAB, 08193 Bellaterra, Spain
| | - Marta Mas-Torrent
- Institut de Ciéncia de Materials de Barcelona (ICMAB-CSIC) and CIBER-BBN, Campus de la UAB, 08193 Bellaterra, Spain
| | - Concepció Rovira
- Institut de Ciéncia de Materials de Barcelona (ICMAB-CSIC) and CIBER-BBN, Campus de la UAB, 08193 Bellaterra, Spain
| | - Jaume Veciana
- Institut de Ciéncia de Materials de Barcelona (ICMAB-CSIC) and CIBER-BBN, Campus de la UAB, 08193 Bellaterra, Spain
| | - Teun M Klapwijk
- Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, Netherlands
- Physics Department, Moscow State Pedagogical University, Moscow 119991, Russia
| | - Ramón Aguado
- Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas (ICMM-CSIC), Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain
| | - Herre S J van der Zant
- Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, Netherlands
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36
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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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37
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Žitko R, Fabrizio M. Non-Fermi-liquid behavior in quantum impurity models with superconducting channels. PHYSICAL REVIEW. B 2017; 95:085121. [PMID: 28503673 PMCID: PMC5424882 DOI: 10.1103/physrevb.95.085121] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
We study how the non-Fermi-liquid nature of the overscreened multi-channel Kondo impurity model affects the response to a BCS pairing term that, in the absence of the impurity, opens a gap Δ. We find that the low-energy spectrum in the limit Δ → 0 actually does not correspond to the spectrum strictly at Δ = 0. In particular, in the two-channel Kondo model the Δ → 0 ground state is an orbitally degenerate spin-singlet, while it is an orbital singlet with a residual spin degeneracy at Δ = 0. In addition, there are fractionalized spin-1/2 sub-gap excitations whose energy in units of Δ tends towards a finite and universal value when Δ → 0; as if the universality of the anomalous power-law exponents that characterise the overscreened Kondo effect turned into universal energy ratios when the scale invariance is broken by Δ ≠ 0. This intriguing phenomenon can be explained by the renormalisation flow towards the overscreened fixed point and the gap cutting off the orthogonality catastrophe singularities. We also find other non-Fermi liquid features at finite Δ: the local density of states lacks coherence peaks, the states in the continuum above the gap are unconventional, and the boundary entropy is a non-monotonic function of temperature. The persistent sub-gap excitations are characteristic of the non-Fermi-liquid fixed-point of the model, and thus depend on the impurity spin and the number of screening channels.
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Affiliation(s)
- 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
| | - Michele Fabrizio
- International School for Advanced Studies (SISSA), and CNR-IOM Democritos, Via Bonomea 265, I-34136 Trieste, Italy
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38
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Čadež T, Sacramento PD. Zero energy modes in a superconductor with ferromagnetic adatom chains and quantum phase transitions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:495703. [PMID: 27754979 DOI: 10.1088/0953-8984/28/49/495703] [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 Majorana zero energy modes (MZEM) that occur in an s-wave superconducting surface, at the ends of a ferromagnetic (FM) chain of adatoms, in the presence of Rashba spin-orbit interaction (SOI) considering both non self-consistent and self-consistent superconducting order. We find that in the self-consistent solution, the average superconducting gap function over the adatom sites has a discontinuous drop with increasing exchange interaction at the same critical value where the topological phase transition occurs. We also study the MZEM for both treatments of superconducting order and find that the decay length is a linear function of the exchange coupling strength, chemical potential and superconducting order. For wider FM chains the MZEM occur at smaller exchange couplings and the slope of the decay length as a function of exchange coupling grows with chain width. Thus we suggest experimental detection of different delocalization of MZEM in chains of varying widths. We discuss similarities and differences between the MZEM for the two treatments of the superconducting order.
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Affiliation(s)
- Tilen Čadež
- Beijing Computational Science Research Center, Zhongguancun Software Park II, No. 10 West Dongbeiwang Road, Haidian District, Beijing, 100094, People's Republic of China. CeFEMA, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal. Jožef Stefan Institute, 1000 Ljubljana, Slovenia
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39
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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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40
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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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