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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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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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Müller H, Eckstein M, Viola Kusminskiy S. Control of Yu-Shiba-Rusinov States through a Bosonic Mode. PHYSICAL REVIEW LETTERS 2023; 130:106905. [PMID: 36962057 DOI: 10.1103/physrevlett.130.106905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2022] [Revised: 12/18/2022] [Accepted: 02/03/2023] [Indexed: 06/18/2023]
Abstract
We investigate the impact of a bosonic degree of freedom on Yu-Shiba-Rusinov states emerging from a magnetic impurity in a conventional superconductor. Starting from the Anderson impurity model, we predict that an additional p-wave conduction band channel opens up if a bosonic mode is coupled to the tunneling between impurity and host, which implies an additional pair of odd-parity Yu-Shiba-Rusinov states. The bosonic mode can be a vibrational mode or the electromagnetic field in a cavity. The exchange couplings in the two channels depend sensitively on the state of the bosonic mode (ground state, few quanta, or classically driven Floquet state), which opens possibilities for phononics or photonics control of such systems, with a rich variety of ground and excited states.
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Affiliation(s)
- Helene Müller
- Department of Physics, University of Erlangen-Nuremberg, 91058 Erlangen, Germany
- Max Planck Institute for the Science of Light, Staudtstrasse 2, 91058 Erlangen, Germany
| | - Martin Eckstein
- Department of Physics, University of Erlangen-Nuremberg, 91058 Erlangen, Germany
| | - Silvia Viola Kusminskiy
- Max Planck Institute for the Science of Light, Staudtstrasse 2, 91058 Erlangen, Germany
- Institute for Theoretical Solid State Physics, RWTH Aachen University, 52074 Aachen, Germany
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8
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Trahms M, Melischek L, Steiner JF, Mahendru B, Tamir I, Bogdanoff N, Peters O, Reecht G, Winkelmann CB, von Oppen F, Franke KJ. Diode effect in Josephson junctions with a single magnetic atom. Nature 2023; 615:628-633. [PMID: 36890238 PMCID: PMC10033399 DOI: 10.1038/s41586-023-05743-z] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2022] [Accepted: 01/18/2023] [Indexed: 03/10/2023]
Abstract
Current flow in electronic devices can be asymmetric with bias direction, a phenomenon underlying the utility of diodes1 and known as non-reciprocal charge transport2. The promise of dissipationless electronics has recently stimulated the quest for superconducting diodes, and non-reciprocal superconducting devices have been realized in various non-centrosymmetric systems3-10. Here we investigate the ultimate limits of miniaturization by creating atomic-scale Pb-Pb Josephson junctions in a scanning tunnelling microscope. Pristine junctions stabilized by a single Pb atom exhibit hysteretic behaviour, confirming the high quality of the junctions, but no asymmetry between the bias directions. Non-reciprocal supercurrents emerge when inserting a single magnetic atom into the junction, with the preferred direction depending on the atomic species. Aided by theoretical modelling, we trace the non-reciprocity to quasiparticle currents flowing by means of electron-hole asymmetric Yu-Shiba-Rusinov states inside the superconducting energy gap and identify a new mechanism for diode behaviour in Josephson junctions. Our results open new avenues for creating atomic-scale Josephson diodes and tuning their properties through single-atom manipulation.
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Affiliation(s)
- Martina Trahms
- Fachbereich Physik, Freie Universität Berlin, Berlin, Germany
| | - Larissa Melischek
- Dahlem Center for Complex Quantum Systems, Fachbereich Physik, Freie Universität Berlin, Berlin, Germany
| | - Jacob F Steiner
- Dahlem Center for Complex Quantum Systems, Fachbereich Physik, Freie Universität Berlin, Berlin, Germany
| | - Bharti Mahendru
- Fachbereich Physik, Freie Universität Berlin, Berlin, Germany
| | - Idan Tamir
- Fachbereich Physik, Freie Universität Berlin, Berlin, Germany
| | - Nils Bogdanoff
- Fachbereich Physik, Freie Universität Berlin, Berlin, Germany
| | - Olof Peters
- Fachbereich Physik, Freie Universität Berlin, Berlin, Germany
| | - Gaël Reecht
- Fachbereich Physik, Freie Universität Berlin, Berlin, Germany
| | | | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems, Fachbereich Physik, Freie Universität Berlin, Berlin, Germany
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9
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Schulte S, Néel N, Rózsa L, Palotás K, Kröger J. Changing the Interaction of a Single-Molecule Magnetic Moment with a Superconductor. NANO LETTERS 2023; 23:1622-1628. [PMID: 36603183 DOI: 10.1021/acs.nanolett.2c03952] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
The exchange interaction of a brominated Co-porphyrin molecule with the Cooper pair condensate of Pb(111) is modified by reducing the Co-surface separation. The stepwise dehalogenation and dephenylation change the Co adsorption height by a few picometers. Only the residual Co-porphine core exhibits a Yu-Shiba-Rusinov bound state with low binding energy in the Bardeen-Cooper-Schrieffer energy gap. Accompanying density functional calculations reveal that the Co dz2 orbital carries the molecular magnetic moment and is responsible for the intragap state. The calculated spatial evolution of the Yu-Shiba-Rusinov wave function is compatible with the experimentally observed oscillatory attenuation of the electron-hole asymmetry with increasing lateral distance from the magnetic porphine center.
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Affiliation(s)
- Stefan Schulte
- Institut für Physik, Technische Universität Ilmenau, D-98693Ilmenau, Germany
- Peter Grünberg Institut, Forschungszentrum Jülich, D-52425Jülich, Germany
- II. Physikalisches Institut, Universität zu Köln, D-50923Cologne, Germany
| | - Nicolas Néel
- Institut für Physik, Technische Universität Ilmenau, D-98693Ilmenau, Germany
| | - Levente Rózsa
- Fachbereich Physik, Universität Konstanz, D-78457Konstanz, Germany
| | - Krisztián Palotás
- Department of Theoretical Solid State Physics, Institute for Solid State Physics and Optics, Wigner Research Center for Physics, H-1121Budapest, Hungary
- ELKH-SZTE Reaction Kinetics and Surface Chemistry Research Group, University of Szeged, H-6720Szeged, Hungary
- Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, H-1111Budapest, Hungary
| | - Jörg Kröger
- Institut für Physik, Technische Universität Ilmenau, D-98693Ilmenau, Germany
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10
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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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11
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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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12
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Homberg J, Weismann A, Markussen T, Berndt R. Resonance-Enhanced Vibrational Spectroscopy of Molecules on a Superconductor. PHYSICAL REVIEW LETTERS 2022; 129:116801. [PMID: 36154405 DOI: 10.1103/physrevlett.129.116801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Revised: 04/13/2022] [Accepted: 07/13/2022] [Indexed: 06/16/2023]
Abstract
Molecular vibrational spectroscopy with the scanning tunneling microscope is feasible but usually detects few vibrational modes. We harness sharp Yu-Shiba-Rusinov states observed from molecules on a superconductor to significantly enhance the vibrational signal. From a lead phthalocyanine molecule 46 vibrational peaks are resolved enabling a comparison with calculated modes. The energy resolution is improved beyond the thermal broadening limit and shifts induced by neighbor molecules or the position of the microscope tip are determined. Vice versa, spectra of vibrational modes are used to measure the effect of an electrical field on the energy of Yu-Shiba-Rusinov states. The method may help to further probe the interaction of molecules with their environment and to better understand selection rules for vibrational excitations.
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Affiliation(s)
- Jan Homberg
- Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität zu Kiel, 24098 Kiel, Germany
| | - Alexander Weismann
- Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität zu Kiel, 24098 Kiel, Germany
| | - Troels Markussen
- Synopsys Denmark, Fruebjergvej 3, Postbox 4, DK-2100 Copenhagen, Denmark
| | - Richard Berndt
- Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität zu Kiel, 24098 Kiel, Germany
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13
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Vaxevani K, Li J, Trivini S, Ortuzar J, Longo D, Wang D, Pascual JI. Extending the Spin Excitation Lifetime of a Magnetic Molecule on a Proximitized Superconductor. NANO LETTERS 2022; 22:6075-6082. [PMID: 35895892 DOI: 10.1021/acs.nanolett.2c00924] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Molecular spins on surfaces potentially used in quantum information processing and data storage require long spin excitation lifetimes. Normally, coupling of the molecular spin with the conduction electrons of metallic surfaces causes fast relaxation of spin excitations. However, the presence of superconducting pairing effects in the substrate can protect the excited spin from decaying. In this work, we show that a proximity-induced superconducting gold film can sustain spin excitations of a FeTPP-Cl molecule for more than 80 ns. This long value was determined by studying inelastic spin excitations of the S = 5/2 multiplet of FeTPP-Cl on Au films over V(100) using scanning tunneling spectroscopy. The spin lifetime decreases with increasing film thickness, along with the decrease of the effective superconducting gap. Our results elucidate the use of proximitized gold electrodes for addressing quantum spins on surfaces, envisioning new routes for tuning the value of their spin lifetime.
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Affiliation(s)
| | - Jingcheng Li
- CIC nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain
- School of Physics, Sun Yat-sen University, Guangzhou 510275, China
| | | | - Jon Ortuzar
- CIC nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain
| | - Danilo Longo
- CIC nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain
| | - Dongfei Wang
- CIC nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain
| | - Jose Ignacio Pascual
- CIC nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain
- Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain
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14
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Chiu CK, Wang Z. Yu-Shiba-Rusinov States in a Superconductor with Topological Z_{2} Bands. PHYSICAL REVIEW LETTERS 2022; 128:237001. [PMID: 35749202 DOI: 10.1103/physrevlett.128.237001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2021] [Revised: 04/19/2022] [Accepted: 04/26/2022] [Indexed: 06/15/2023]
Abstract
A Yu-Shiba-Rusinov (YSR) state is a localized in-gap state induced by a magnetic impurity in a superconductor. Recent experiments used an STM tip to manipulate the exchange coupling between an Fe adatom and the FeTe_{0.55}Se_{0.45} superconductor possessing a Z_{2} nontrivial band structure with topological surface states. As the tip moves close to the single Fe adatom, the energy of the in-gap state modulates and exhibits a zero-energy crossing followed by an unusual return to zero energy, which cannot be understood by coupling the magnetic impurity to the superconducting topological surface Dirac cone. Here, we numerically and analytically study the YSR states in superconductors with nontrivial Z_{2} bands and show the emergence of the two zero-energy crossings as a function of the exchange coupling between the magnetic impurity and the bulk states. We analyze the role of the topological surface states and compare in-gap states to systems with trivial Z_{2} bands. The spin polarization of the YSR states is further studied for future experimental measurement.
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Affiliation(s)
- Ching-Kai Chiu
- RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), Wako, Saitama 351-0198, Japan
- Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Ziqiang Wang
- Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA
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15
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Shahed SM, Ara F, Hossain MI, Katoh K, Yamashita M, Komeda T. Observation of Yu-Shiba-Rusinov States and Inelastic Tunneling Spectroscopy for Intramolecule Magnetic Exchange Interaction Energy of Terbium Phthalocyanine (TbPc) Species Adsorbed on Superconductor NbSe 2. ACS NANO 2022; 16:7651-7661. [PMID: 35467334 PMCID: PMC9134493 DOI: 10.1021/acsnano.1c11221] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Accepted: 04/21/2022] [Indexed: 06/14/2023]
Abstract
We investigated the spin properties of the terbium phthalocyanine (TbPc) species adsorbed on the superconductor NbSe2 surface using scanning tunneling microscopy and spectroscopy. TbPc2 is a molecule in a class of single-molecule magnets (SMMs), and the use of superconductor electrodes attracts attention for the application to the devices using the spin degree of freedom. TbPc is a building block of TbPc2 and can reveal the spin component's behavior. In the experiment, TbPc species were placed on the surface of the superconductor NbSe2. We measured Yu-Shiba-Rusinov (YSR) states caused by the interaction between the superconducting state and magnetic impurity and inelastic tunneling spectroscopy (IETS) for the spin excitation, below 1 K. We also measured the Kondo state formed by the magnetic singlet formation. We detected the radical spin at the ligand position of the TbPc by the presence of the Kondo peak and demonstrated that the radical spin forms the YSR feature. In addition, the exchange interaction energy (Eex) between the spins of the radical ligand (Pc) and the center 4f metal atom (Tb3+) is determined by using the IETS technique. Eex is a critical parameter that determines the blocking temperature, below which the sample behaves as an SMM. IETS results show that the statistical distribution of Eex has peaked at 1.3, 1.6, and 1.9 meV. The energy range is comparable to the recent theoretical calculation result. In addition, we show that the energy variation is correlated with the bonding configuration of TbPc.
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Affiliation(s)
- Syed Mohammad
Fakruddin Shahed
- Institute
of Multidisciplinary Research for Advanced Materials (IMRAM, Tagen), Tohoku University, 2-1-1, Katahira, Aoba-Ku, Sendai 9800877, Japan
| | - Ferdous Ara
- Institute
of Multidisciplinary Research for Advanced Materials (IMRAM, Tagen), Tohoku University, 2-1-1, Katahira, Aoba-Ku, Sendai 9800877, Japan
| | - Mohammad Ikram Hossain
- Institute
of Multidisciplinary Research for Advanced Materials (IMRAM, Tagen), Tohoku University, 2-1-1, Katahira, Aoba-Ku, Sendai 9800877, 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 980-8578, Japan
- School
of Materials Science and Engineering, Nankai
University, Tianjin 300350, China
| | - Tadahiro Komeda
- Institute
of Multidisciplinary Research for Advanced Materials (IMRAM, Tagen), Tohoku University, 2-1-1, Katahira, Aoba-Ku, Sendai 9800877, Japan
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16
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Quantum spins and hybridization in artificially-constructed chains of magnetic adatoms on a superconductor. Nat Commun 2022; 13:2160. [PMID: 35443753 PMCID: PMC9021194 DOI: 10.1038/s41467-022-29879-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2021] [Accepted: 04/01/2022] [Indexed: 11/09/2022] Open
Abstract
Magnetic adatom chains on surfaces constitute fascinating quantum spin systems. Superconducting substrates suppress interactions with bulk electronic excitations but couple the adatom spins to a chain of subgap Yu-Shiba-Rusinov (YSR) quasiparticles. Using a scanning tunneling microscope, we investigate such correlated spin-fermion systems by constructing Fe chains adatom by adatom on superconducting NbSe2. The adatoms couple entirely via the substrate, retaining their quantum spin nature. In dimers, we observe that the deepest YSR state undergoes a quantum phase transition due to Ruderman-Kittel-Kasuya-Yosida interactions, a distinct signature of quantum spins. Chains exhibit coherent hybridization and band formation of the YSR excitations, indicating ferromagnetic coupling. Longer chains develop separate domains due to coexisting charge-density-wave order of NbSe2. Despite the spin-orbit-coupled substrate, we find no signatures of Majoranas, possibly because quantum spins reduce the parameter range for topological superconductivity. We suggest that adatom chains are versatile systems for investigating correlated-electron physics and its interplay with topological superconductivity. Previous studies of magnetic adatom chains on superconducting substrates have mostly focused on the regime of dense chains and classical spins. Here, using scanning tunnelling microscopy, the authors study the excitation spectra of Fe chains on a NbSe2 surface, adatom by adatom, in the regime of quantum spins.
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17
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Steiner JF, Mora C, Franke KJ, von Oppen F. Quantum Magnetism and Topological Superconductivity in Yu-Shiba-Rusinov Chains. PHYSICAL REVIEW LETTERS 2022; 128:036801. [PMID: 35119905 DOI: 10.1103/physrevlett.128.036801] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2021] [Revised: 11/02/2021] [Accepted: 01/07/2022] [Indexed: 06/14/2023]
Abstract
Chains of magnetic adatoms on superconductors have been discussed as promising systems for realizing Majorana end states. Here, we show that dilute Yu-Shiba-Rusinov (YSR) chains are also a versatile platform for quantum magnetism and correlated electron dynamics, with widely adjustable spin values and couplings. Focusing on subgap excitations, we derive an extended t-J model for dilute quantum YSR chains and use it to study the phase diagram as well as tunneling spectra. We explore the implications of quantum magnetism for the formation of a topological superconducting phase, contrasting it to existing models assuming classical spin textures.
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Affiliation(s)
- Jacob F Steiner
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | - Christophe Mora
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
- Laboratoire Matériaux et Phénomènes Quantiques, CNRS, Université de Paris, 75013 Paris, France
| | | | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
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18
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Küster F, Brinker S, Lounis S, Parkin SSP, Sessi P. Long range and highly tunable interaction between local spins coupled to a superconducting condensate. Nat Commun 2021; 12:6722. [PMID: 34795233 PMCID: PMC8602442 DOI: 10.1038/s41467-021-26802-x] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Accepted: 10/19/2021] [Indexed: 11/26/2022] Open
Abstract
Interfacing magnetism with superconducting condensates is rapidly emerging as a viable route for the development of innovative quantum technologies. In this context, the development of rational design strategies to controllably tune the interaction between magnetic moments is crucial. Here we address this problem demonstrating the possibility of tuning the interaction between local spins coupled through a superconducting condensate with atomic scale precision. By using Cr atoms coupled to superconducting Nb, we use atomic manipulation techniques to precisely control the relative distance between local spins along distinct crystallographic directions while simultaneously sensing their coupling by scanning tunneling spectroscopy. Our results reveal the existence of highly anisotropic interactions, lasting up to very long distances, demonstrating the possibility of crossing a quantum phase transition by acting on the direction and interatomic distance between spins. The high tunability provides novel opportunities for the realization of topological superconductivity and the rational design of magneto-superconducting interfaces.
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Affiliation(s)
- Felix Küster
- Max Planck Institute of Microstructure Physics, Halle, 06120, Germany
| | - Sascha Brinker
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, Jülich, D-52425, Germany
| | - Samir Lounis
- Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich & JARA, Jülich, D-52425, Germany.
- Faculty of Physics, University of Duisburg-Essen and CENIDE, Duisburg, 47053, Germany.
| | - Stuart S P Parkin
- Max Planck Institute of Microstructure Physics, Halle, 06120, Germany.
| | - Paolo Sessi
- Max Planck Institute of Microstructure Physics, Halle, 06120, Germany.
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19
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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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20
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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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21
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Cortés-Del Río E, Lado JL, Cherkez V, Mallet P, Veuillen JY, Cuevas JC, Gómez-Rodríguez JM, Fernández-Rossier J, Brihuega I. Observation of Yu-Shiba-Rusinov States in Superconducting Graphene. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2021; 33:e2008113. [PMID: 33890694 DOI: 10.1002/adma.202008113] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2020] [Revised: 02/26/2021] [Indexed: 06/12/2023]
Abstract
When magnetic atoms are inserted inside a superconductor, the superconducting order is locally depleted as a result of the antagonistic nature of magnetism and superconductivity. Thereby, distinctive spectral features, known as Yu-Shiba-Rusinov states, appear inside the superconducting gap. The search for Yu-Shiba-Rusinov states in different materials is intense, as they can be used as building blocks to promote Majorana modes suitable for topological quantum computing. Here, the first observation of Yu-Shiba-Rusinov states in graphene, a non-superconducting 2D material, and without the participation of magnetic atoms, is reported. Superconductivity in graphene is induced by proximity effect brought by adsorbing nanometer-scale superconducting Pb islands. Using scanning tunneling microscopy and spectroscopy the superconducting proximity gap is measured in graphene, and Yu-Shiba-Rusinov states are visualized in graphene grain boundaries. The results reveal the very special nature of those Yu-Shiba-Rusinov states, which extends more than 20 nm away from the grain boundaries. These observations provide the long-sought experimental confirmation that graphene grain boundaries host local magnetic moments and constitute the first observation of Yu-Shiba-Rusinov states in a chemically pure system.
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Affiliation(s)
- Eva Cortés-Del Río
- Departamento Física de la Materia Condensada, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
| | - Jose Luis Lado
- Department of Applied Physics, Aalto University, Espoo, 02150, Finland
| | - Vladimir Cherkez
- Université Grenoble Alpes, Grenoble, 38000, France
- CNRS, Institut Neel, Grenoble, F-38042, France
| | - Pierre Mallet
- Université Grenoble Alpes, Grenoble, 38000, France
- CNRS, Institut Neel, Grenoble, F-38042, France
| | - Jean-Yves Veuillen
- Université Grenoble Alpes, Grenoble, 38000, France
- CNRS, Institut Neel, Grenoble, F-38042, France
| | - Juan Carlos Cuevas
- Departamento Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, E-28049, Spain
| | - José María Gómez-Rodríguez
- Departamento Física de la Materia Condensada, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
| | - Joaquín Fernández-Rossier
- QuantaLab, International Iberian Nanotechnology Laboratory (INL), Avenida Mestre José Veiga, Braga, 4715-310, Portugal
- Departamento de Física Aplicada, Universidad de Alicante, San Vicente del Raspeig, Alicante, 03690, Spain
| | - Iván Brihuega
- Departamento Física de la Materia Condensada, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, Madrid, E-28049, Spain
- Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, Madrid, E-28049, Spain
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22
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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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23
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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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24
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Mier C, Verlhac B, Garnier L, Robles R, Limot L, Lorente N, Choi DJ. Superconducting Scanning Tunneling Microscope Tip to Reveal Sub-millielectronvolt Magnetic Energy Variations on Surfaces. J Phys Chem Lett 2021; 12:2983-2989. [PMID: 33730501 DOI: 10.1021/acs.jpclett.1c00328] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Combining the complex ordering ability of molecules with their local magnetic properties is a little-explored technique to tailor spin structures on surfaces. However, revealing the molecular geometry can be demanding. Nickelocene (Nc) molecules present a large spin-flip excitation leading to clear changes of conductance at the excitation-threshold bias. Using a superconducting tip, we have the energy resolution to detect small shifts of the Nc spin-flip excitation thresholds, permitting us to reveal the different individual environments of Nc molecules in an ordered layer. This knowledge allows us to reveal the adsorption configuration of a complex molecular structure formed by Nc molecules in different orientations and positions. As a consequence, we infer that Nc layers present a strong noncollinear magnetic-moment arrangement.
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Affiliation(s)
- Cristina Mier
- Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), 20018 Donostia-San Sebastián, Spain
| | - Benjamin Verlhac
- Université de Strasbourg CNRS, IPCMS, UMR 7504, F-67000 Strasbourg, France
| | - Léo Garnier
- Université de Strasbourg CNRS, IPCMS, UMR 7504, F-67000 Strasbourg, France
| | - Roberto Robles
- Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), 20018 Donostia-San Sebastián, Spain
| | - Laurent Limot
- Université de Strasbourg CNRS, IPCMS, UMR 7504, F-67000 Strasbourg, France
| | - 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
| | - 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
- Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain
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25
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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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26
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Wang D, Wiebe J, Zhong R, Gu G, Wiesendanger R. Spin-Polarized Yu-Shiba-Rusinov States in an Iron-Based Superconductor. PHYSICAL REVIEW LETTERS 2021; 126:076802. [PMID: 33666492 DOI: 10.1103/physrevlett.126.076802] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2020] [Accepted: 01/21/2021] [Indexed: 05/06/2023]
Abstract
Yu-Shiba-Rusinov (YSR) bound states appear when a magnetic atom interacts with a superconductor. Here, we report on spin-resolved spectroscopic studies of YSR states related with Fe atoms deposited on the surface of the topological superconductor FeTe_{0.55}Se_{0.45} using a spin-polarized scanning tunneling microscope. We clearly identify the spin signature of pairs of YSR bound states at finite energies within the superconducting gap having opposite spin polarization as theoretically predicted. In addition, we also observe zero-energy bound states for some of the adsorbed Fe atoms. In this case, a spin signature is found to be absent indicating the absence of Majorana bound states associated with Fe adatoms on FeTe_{0.55}Se_{0.45}.
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Affiliation(s)
- Dongfei Wang
- Department of Physics, University of Hamburg, Jungiusstrasse 11, 20355 Hamburg, Germany
| | - Jens Wiebe
- Department of Physics, University of Hamburg, Jungiusstrasse 11, 20355 Hamburg, Germany
| | - Ruidan Zhong
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Genda Gu
- Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
| | - Roland Wiesendanger
- Department of Physics, University of Hamburg, Jungiusstrasse 11, 20355 Hamburg, Germany
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27
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Chatzopoulos D, Cho D, Bastiaans KM, Steffensen GO, Bouwmeester D, Akbari A, Gu G, Paaske J, Andersen BM, Allan MP. Spatially dispersing Yu-Shiba-Rusinov states in the unconventional superconductor FeTe 0.55Se 0.45. Nat Commun 2021; 12:298. [PMID: 33436594 PMCID: PMC7804303 DOI: 10.1038/s41467-020-20529-x] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2020] [Accepted: 12/07/2020] [Indexed: 01/29/2023] Open
Abstract
By using scanning tunneling microscopy (STM) we find and characterize dispersive, energy-symmetric in-gap states in the iron-based superconductor FeTe0.55Se0.45, a material that exhibits signatures of topological superconductivity, and Majorana bound states at vortex cores or at impurity locations. We use a superconducting STM tip for enhanced energy resolution, which enables us to show that impurity states can be tuned through the Fermi level with varying tip-sample distance. We find that the impurity state is of the Yu-Shiba-Rusinov (YSR) type, and argue that the energy shift is caused by the low superfluid density in FeTe0.55Se0.45, which allows the electric field of the tip to slightly penetrate the sample. We model the newly introduced tip-gating scenario within the single-impurity Anderson model and find good agreement to the experimental data.
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Affiliation(s)
- Damianos Chatzopoulos
- grid.5132.50000 0001 2312 1970Leiden Institute of Physics, Leiden University, Niels Bohrweg 2, Leiden, CA 2333 The Netherlands
| | - Doohee Cho
- grid.5132.50000 0001 2312 1970Leiden Institute of Physics, Leiden University, Niels Bohrweg 2, Leiden, CA 2333 The Netherlands ,grid.15444.300000 0004 0470 5454Department of Physics, Yonsei University, Seoul, 03722 Republic of Korea
| | - Koen M. Bastiaans
- grid.5132.50000 0001 2312 1970Leiden Institute of Physics, Leiden University, Niels Bohrweg 2, Leiden, CA 2333 The Netherlands
| | - Gorm O. Steffensen
- grid.5254.60000 0001 0674 042XCenter for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, Copenhagen Ø, 2100 Denmark
| | - Damian Bouwmeester
- grid.5132.50000 0001 2312 1970Leiden Institute of Physics, Leiden University, Niels Bohrweg 2, Leiden, CA 2333 The Netherlands ,grid.5292.c0000 0001 2097 4740Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, Delft, CJ 2628 Netherlands
| | - Alireza Akbari
- grid.419507.e0000 0004 0491 351XMax Planck Institute for the Chemical Physics of Solids, Dresden, D-01187 Germany ,grid.49100.3c0000 0001 0742 4007Max Planck POSTECH Center for Complex Phase Materials, and Department of Physics, POSTECH, Pohang, Gyeongbuk 790-784 Korea
| | - Genda Gu
- grid.202665.50000 0001 2188 4229Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY 11973 USA
| | - Jens Paaske
- grid.5254.60000 0001 0674 042XCenter for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, Copenhagen Ø, 2100 Denmark
| | - Brian M. Andersen
- grid.5254.60000 0001 0674 042XCenter for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, Copenhagen Ø, 2100 Denmark
| | - Milan P. Allan
- grid.5132.50000 0001 2312 1970Leiden Institute of Physics, Leiden University, Niels Bohrweg 2, Leiden, CA 2333 The Netherlands
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28
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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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29
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Homberg J, Weismann A, Berndt R, Gruber M. Inducing and Controlling Molecular Magnetism through Supramolecular Manipulation. ACS NANO 2020; 14:17387-17395. [PMID: 33225694 DOI: 10.1021/acsnano.0c07574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Diamagnetic H2 phthalocyanine molecules are probed on superconducting Pb(100) using a low-temperature scanning tunneling micoscope (STM). In supramolecular arrays made with the STM, the molecules acquire a spin as detected via the emergence of Yu-Shiba-Rusinov resonances. The spin moments vary among the molecules and are determined by the electrostatic field that results from polar bonds in the surrounding Pc molecules. The moments are further finely tuned by repositioning the hydrogen atoms of the inner macrocycle of the surrounding molecules.
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Affiliation(s)
- Jan Homberg
- Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität, 24098 Kiel, Germany
| | - Alexander Weismann
- Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität, 24098 Kiel, Germany
| | - Richard Berndt
- Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität, 24098 Kiel, Germany
| | - Manuel Gruber
- Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität, 24098 Kiel, Germany
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30
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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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31
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Abstract
Emergent electronic phenomena in iron-based superconductors have been at the forefront of condensed matter physics for more than a decade. Much has been learned about the origins and intertwined roles of ordered phases, including nematicity, magnetism, and superconductivity, in this fascinating class of materials. In recent years, focus has been centered on the peculiar and highly unusual properties of FeSe and its close cousins. This family of materials has attracted considerable attention due to the discovery of unexpected superconducting gap structures, a wide range of superconducting critical temperatures, and evidence for nontrivial band topology, including associated spin-helical surface states and vortex-induced Majorana bound states. Here, we review superconductivity in iron chalcogenide superconductors, including bulk FeSe, doped bulk FeSe, FeTe1−xSex, intercalated FeSe materials, and monolayer FeSe and FeTe1−xSex on SrTiO3. We focus on the superconducting properties, including a survey of the relevant experimental studies, and a discussion of the different proposed theoretical pairing scenarios. In the last part of the paper, we review the growing recent evidence for nontrivial topological effects in FeSe-related materials, focusing again on interesting implications for superconductivity.
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32
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Malavolti L, McMurtrie G, Rolf-Pissarczyk S, Yan S, Burgess JAJ, Loth S. Minimally invasive spin sensing with scanning tunneling microscopy. NANOSCALE 2020; 12:11619-11626. [PMID: 32435779 DOI: 10.1039/c9nr10252c] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Minimizing the invasiveness of scanning tunneling measurements is paramount for observation of the magnetic properties of unperturbed atomic-scale objects. We show that the invasiveness of STM inspection on few-atom spin systems can be drastically reduced by means of a remote detection scheme, which makes use of a sensor spin weakly coupled to the sensed object. By comparing direct and remote measurements we identify the relevant perturbations caused by the local probe. For direct inspection we find that tunneling electrons strongly perturb the investigated object even for currents as low as 3 pA. Electrons injected into the sensor spin induce perturbations with much reduced probability. The sensing scheme uses standard differential conductance measurements, and is decoupled both by its non-local nature, and by dynamic decoupling due to the significantly different time scales at which the sensor and sensed object evolve. The latter makes it possible to effectively remove static interactions between the sensed object and the spin sensor while still allowing the spin sensing. In this way we achieve measurements with a reduction in perturbative effects of up to 100 times relative to direct scanning tunneling measurements, which enables minimally invasive measurements of a few-atom magnet's fragile spin states with STM.
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Affiliation(s)
- Luigi Malavolti
- Institute for Functional Matter and Quantum Technologies, University of Stuttgart, 70569 Stuttgart, Germany. and Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany and Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany
| | - Gregory McMurtrie
- Institute for Functional Matter and Quantum Technologies, University of Stuttgart, 70569 Stuttgart, Germany. and Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany and Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany
| | - Steffen Rolf-Pissarczyk
- Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany and Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany
| | - Shichao Yan
- Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany and Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany and School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - Jacob A J Burgess
- Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany and Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany and Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
| | - Sebastian Loth
- Institute for Functional Matter and Quantum Technologies, University of Stuttgart, 70569 Stuttgart, Germany. and Max Planck Institute for the Structure and Dynamics of Matter, 22761 Hamburg, Germany and Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany
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33
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Głodzik S, Domański T. In-gap states of magnetic impurity in quantum spin Hall insulator proximitized to a superconductor. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:235501. [PMID: 32079006 DOI: 10.1088/1361-648x/ab786d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We study in-gap states of a single magnetic impurity embedded in a honeycomb monolayer which is deposited on superconducting substrate. The intrinsic spin-orbit coupling induces the quantum spin Hall insulating (QSHI) phase gapped around the Fermi energy. Under such circumstances we consider the emergence of Shiba-like bound states driven by the superconducting proximity effect. We investigate their topography, spin-polarization and signatures of the quantum phase transition manifested by reversal of the local currents circulating around the magnetic impurity. These phenomena might be important for more exotic in-gap quasiparticles in such complex nanostructures as magnetic nanowires or islands, where the spin-orbit interaction along with the proximity induced electron pairing give rise to topological phases hosting the protected boundary modes.
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34
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Serrano G, Poggini L, Briganti M, Sorrentino AL, Cucinotta G, Malavolti L, Cortigiani B, Otero E, Sainctavit P, Loth S, Parenti F, Barra AL, Vindigni A, Cornia A, Totti F, Mannini M, Sessoli R. Quantum dynamics of a single molecule magnet on superconducting Pb(111). NATURE MATERIALS 2020; 19:546-551. [PMID: 32066930 DOI: 10.1038/s41563-020-0608-9] [Citation(s) in RCA: 35] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2019] [Accepted: 01/07/2020] [Indexed: 06/10/2023]
Abstract
Magnetic materials interfaced with superconductors may reveal new physical phenomena with potential for quantum technologies. The use of molecules as magnetic components has already shown great promise, but the diversity of properties offered by the molecular realm remains largely unexplored. Here we investigate a submonolayer of tetrairon(III) propeller-shaped single molecule magnets deposited on a superconducting lead surface. This material combination reveals a strong influence of the superconductor on the spin dynamics of the single molecule magnet. It is shown that the superconducting transition to the condensate state switches the single molecule magnet from a blocked magnetization state to a resonant quantum tunnelling regime. Our results open perspectives to control single molecule magnetism via superconductors and to use single molecule magnets as local probes of the superconducting state.
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Affiliation(s)
- Giulia Serrano
- Department of Chemistry 'Ugo Schiff' and INSTM Research Unit, University of Florence, Sesto Fiorentino, Italy.
- Department of Industrial Engineering and INSTM Research Unit, University of Florence, Florence, Italy.
| | - Lorenzo Poggini
- Department of Chemistry 'Ugo Schiff' and INSTM Research Unit, University of Florence, Sesto Fiorentino, Italy
| | - Matteo Briganti
- Department of Chemistry 'Ugo Schiff' and INSTM Research Unit, University of Florence, Sesto Fiorentino, Italy
- Departamento de Química, Universidade Federal do Paraná, Curitiba, Brazil
| | - Andrea Luigi Sorrentino
- Department of Chemistry 'Ugo Schiff' and INSTM Research Unit, University of Florence, Sesto Fiorentino, Italy
- Department of Industrial Engineering and INSTM Research Unit, University of Florence, Florence, Italy
| | - Giuseppe Cucinotta
- Department of Chemistry 'Ugo Schiff' and INSTM Research Unit, University of Florence, Sesto Fiorentino, Italy
| | - Luigi Malavolti
- Institute FMQ, University of Stuttgart & Max Planck Institute for Solid State Research, Stuttgart, Germany
| | - Brunetto Cortigiani
- Department of Chemistry 'Ugo Schiff' and INSTM Research Unit, University of Florence, Sesto Fiorentino, Italy
| | - Edwige Otero
- Synchrotron SOLEIL, L'Orme des Merisiers, Saint Aubin, France
| | - Philippe Sainctavit
- Synchrotron SOLEIL, L'Orme des Merisiers, Saint Aubin, France
- IMPMC, UMR7590 CNRS, Sorbonne Université, MNHN, Paris, France
| | - Sebastian Loth
- Institute FMQ, University of Stuttgart & Max Planck Institute for Solid State Research, Stuttgart, Germany
| | - Francesca Parenti
- Department of Chemical and Geological Sciences and INSTM Research Unit, University of Modena and Reggio Emilia, Modena, Italy
| | | | | | - Andrea Cornia
- Department of Chemical and Geological Sciences and INSTM Research Unit, University of Modena and Reggio Emilia, Modena, Italy
| | - Federico Totti
- Department of Chemistry 'Ugo Schiff' and INSTM Research Unit, University of Florence, Sesto Fiorentino, Italy
| | - Matteo Mannini
- Department of Chemistry 'Ugo Schiff' and INSTM Research Unit, University of Florence, Sesto Fiorentino, Italy
| | - Roberta Sessoli
- Department of Chemistry 'Ugo Schiff' and INSTM Research Unit, University of Florence, Sesto Fiorentino, Italy.
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35
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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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36
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Liebhaber E, Acero González S, Baba R, Reecht G, Heinrich BW, Rohlf S, Rossnagel K, von Oppen F, Franke KJ. Yu-Shiba-Rusinov States in the Charge-Density Modulated Superconductor NbSe 2. NANO LETTERS 2020; 20:339-344. [PMID: 31842547 DOI: 10.1021/acs.nanolett.9b03988] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
NbSe2 is a remarkable superconductor in which charge-density order coexists with pairing correlations at low temperatures. Here, we study the interplay of magnetic adatoms and their Yu-Shiba-Rusinov (YSR) bound states with the charge density order. Exploiting the incommensurate nature of the charge-density wave (CDW), our measurements provide a thorough picture of how the CDW affects both the energies and the wave functions of the YSR states. Key features of the dependence of the YSR states on adsorption site relative to the CDW are explained by model calculations. Several properties make NbSe2 a promising substrate for realizing topological nanostructures. Our results will be important in designing such systems.
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Affiliation(s)
| | | | | | | | | | - Sebastian Rohlf
- Ruprecht-Haensel-Labor and Institut für Experimentelle und Angewandte Physik , Christian-Albrechts-Universität zu Kiel , 24098 Kiel , Germany
| | - Kai Rossnagel
- Ruprecht-Haensel-Labor and Institut für Experimentelle und Angewandte Physik , Christian-Albrechts-Universität zu Kiel , 24098 Kiel , Germany
- Deutsches Elektronen-Synchrotron DESY , 22607 Hamburg , Germany
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37
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Liu C, Wang G, Wang J. Manipulating the particle-hole symmetry of quasiparticle bound states in geometric-size-varying Fe clusters on one-unit-cell FeSe/SrTiO 3(0 0 1). JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:285002. [PMID: 30947147 DOI: 10.1088/1361-648x/ab1630] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The particle-hole symmetry (PHS) of quasiparticle bound states, which is generally expected in theory, is present or absent experimentally in a seemingly irregular manner, with the physical origin little understood yet. Here, we report a study on the bound states induced by Fe clusters with different sizes on one-unit-cell (1-UC) FeSe/SrTiO3(0 0 1) by in situ scanning tunneling spectroscopy. Statistically, on the larger-scale cluster, a pair of bias-symmetric minipeaks are detected within the superconducting-gap energies. As increasing temperature, the minipeak states show negligible energy dispersion. The temperature-independent bias-symmetric minipeaks are identified as the quasiparticle bound states that preserve the PHS. However, on the smaller-scale cluster, the bound state appears as a single resonance instead. These results reveal a geometric-size-tuning effect of the PHS, which may help reconcile the contradiction between the superconductivity theory and the PHS-breaking experiments.
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Affiliation(s)
- Chaofei Liu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, People's Republic of China
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38
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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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39
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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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