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Wan P, Zheliuk O, Yuan NFQ, Peng X, Zhang L, Liang M, Zeitler U, Wiedmann S, Hussey NE, Palstra TTM, Ye J. Orbital Fulde-Ferrell-Larkin-Ovchinnikov state in an Ising superconductor. Nature 2023:10.1038/s41586-023-05967-z. [PMID: 37225992 DOI: 10.1038/s41586-023-05967-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2022] [Accepted: 03/17/2023] [Indexed: 05/26/2023]
Abstract
In superconductors possessing both time and inversion symmetries, the Zeeman effect of an external magnetic field can break the time-reversal symmetry, forming a conventional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state characterized by Cooper pairings with finite momentum1,2. In superconductors lacking (local) inversion symmetry, the Zeeman effect may still act as the underlying mechanism of FFLO states by interacting with spin-orbit coupling (SOC). Specifically, the interplay between the Zeeman effect and Rashba SOC can lead to the formation of more accessible Rashba FFLO states that cover broader regions in the phase diagram3-5. However, when the Zeeman effect is suppressed because of spin locking in the presence of Ising-type SOC, the conventional FFLO scenarios are no longer effective. Instead, an unconventional FFLO state is formed by coupling the orbital effect of magnetic fields with SOC, providing an alternative mechanism in superconductors with broken inversion symmetries6-8. Here we report the discovery of such an orbital FFLO state in the multilayer Ising superconductor 2H-NbSe2. Transport measurements show that the translational and rotational symmetries are broken in the orbital FFLO state, providing the hallmark signatures of finite-momentum Cooper pairings. We establish the entire orbital FFLO phase diagram, consisting of a normal metal, a uniform Ising superconducting phase and a six-fold orbital FFLO state. This study highlights an alternative route to achieving finite-momentum superconductivity and provides a universal mechanism to preparing orbital FFLO states in similar materials with broken inversion symmetries.
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Affiliation(s)
- Puhua Wan
- Device Physics of Complex Materials, Zernike Institute for Advanced Materials, University of Groningen, Groningen, The Netherlands
| | - Oleksandr Zheliuk
- Device Physics of Complex Materials, Zernike Institute for Advanced Materials, University of Groningen, Groningen, The Netherlands
- High Field Magnet Laboratory (HFML-EMFL), Radboud University, Nijmegen, The Netherlands
| | - Noah F Q Yuan
- School of Science, Harbin Institute of Technology, Shenzhen, China
| | - Xiaoli Peng
- Device Physics of Complex Materials, Zernike Institute for Advanced Materials, University of Groningen, Groningen, The Netherlands
| | - Le Zhang
- Device Physics of Complex Materials, Zernike Institute for Advanced Materials, University of Groningen, Groningen, The Netherlands
| | - Minpeng Liang
- Device Physics of Complex Materials, Zernike Institute for Advanced Materials, University of Groningen, Groningen, The Netherlands
| | - Uli Zeitler
- High Field Magnet Laboratory (HFML-EMFL), Radboud University, Nijmegen, The Netherlands
| | - Steffen Wiedmann
- High Field Magnet Laboratory (HFML-EMFL), Radboud University, Nijmegen, The Netherlands
| | - Nigel E Hussey
- High Field Magnet Laboratory (HFML-EMFL), Radboud University, Nijmegen, The Netherlands
- H. H. Wills Physics Laboratory, University of Bristol, Bristol, UK
| | - Thomas T M Palstra
- Nano Electronic Materials, University of Twente, Enschede, The Netherlands
| | - Jianting Ye
- Device Physics of Complex Materials, Zernike Institute for Advanced Materials, University of Groningen, Groningen, The Netherlands.
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Chen AQ, Park MJ, Gill ST, Xiao Y, Reig-I-Plessis D, MacDougall GJ, Gilbert MJ, Mason N. Finite momentum Cooper pairing in three-dimensional topological insulator Josephson junctions. Nat Commun 2018; 9:3478. [PMID: 30154472 PMCID: PMC6113236 DOI: 10.1038/s41467-018-05993-w] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2018] [Accepted: 08/06/2018] [Indexed: 11/09/2022] Open
Abstract
Unconventional superconductivity arising from the interplay between strong spin–orbit coupling and magnetism is an intensive area of research. One form of unconventional superconductivity arises when Cooper pairs subjected to a magnetic exchange coupling acquire a finite momentum. Here, we report on a signature of finite momentum Cooper pairing in the three-dimensional topological insulator Bi2Se3. We apply in-plane and out-of-plane magnetic fields to proximity-coupled Bi2Se3 and find that the in-plane field creates a spatially oscillating superconducting order parameter in the junction as evidenced by the emergence of an anomalous Fraunhofer pattern. We describe how the anomalous Fraunhofer patterns evolve for different device parameters, and we use this to understand the microscopic origin of the oscillating order parameter. The agreement between the experimental data and simulations shows that the finite momentum pairing originates from the coexistence of the Zeeman effect and Aharonov–Bohm flux. Unconventional superconductivity may emerge from the interplay between strong spin–orbit coupling and magnetism. Here, Chen et al. report an anomalous Fraunhofer pattern in three-dimensional topological insulator Bi2Se3 and attribute it as a signature of finite momentum Cooper pairing.
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Affiliation(s)
- Angela Q Chen
- Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, 61801, IL, United States
| | - Moon Jip Park
- Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, 61801, IL, United States
| | - Stephen T Gill
- Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, 61801, IL, United States
| | - Yiran Xiao
- Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, 61801, IL, United States
| | - Dalmau Reig-I-Plessis
- Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, 61801, IL, United States
| | - Gregory J MacDougall
- Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, 61801, IL, United States
| | - Matthew J Gilbert
- Department of Electrical and Computer Engineering, University of Illinois, Urbana, 61801, IL, USA
| | - Nadya Mason
- Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois, Urbana, 61801, IL, United States.
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Kinnunen JJ, Baarsma JE, Martikainen JP, Törmä P. The Fulde-Ferrell-Larkin-Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:046401. [PMID: 29293087 DOI: 10.1088/1361-6633/aaa4ad] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We review the concepts and the present state of theoretical studies of spin-imbalanced superfluidity, in particular the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in the context of ultracold quantum gases. The comprehensive presentation of the theoretical basis for the FFLO state that we provide is useful also for research on the interplay between magnetism and superconductivity in other physical systems. We focus on settings that have been predicted to be favourable for the FFLO state, such as optical lattices in various dimensions and spin-orbit coupled systems. These are also the most likely systems for near-future experimental observation of the FFLO state. Theoretical bounds, such as Bloch's and Luttinger's theorems, and experimentally important limitations, such as finite-size effects and trapping potentials, are considered. In addition, we provide a comprehensive review of the various ideas presented for the observation of the FFLO state. We conclude our review with an analysis of the open questions related to the FFLO state, such as its stability, superfluid density, collective modes and extending the FFLO superfluid concept to new types of lattice systems.
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Affiliation(s)
- Jami J Kinnunen
- COMP Center of Excellence, Department of Applied Physics, Aalto University, Fi-00076, Aalto, Finland
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4
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Zheng JH, Wang DW, Juzeliūnas G. Superfluidity enhanced by spin-flip tunnelling in the presence of a magnetic field. Sci Rep 2016; 6:33320. [PMID: 27633848 PMCID: PMC5025894 DOI: 10.1038/srep33320] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2016] [Accepted: 08/24/2016] [Indexed: 11/22/2022] Open
Abstract
It is well-known that when the magnetic field is stronger than a critical value, the spin imbalance can break the Cooper pairs of electrons and hence hinder the superconductivity in a spin-singlet channel. In a bilayer system of ultra-cold Fermi gases, however, we demonstrate that the critical value of the magnetic field at zero temperature can be significantly increased by including a spin-flip tunnelling, which opens a gap in the spin-triplet channel near the Fermi surface and hence reduces the influence of the effective magnetic field on the superfluidity. The phase transition also changes from first order to second order when the tunnelling exceeds a critical value. Considering a realistic experiment, this mechanism can be implemented by applying an intralayer Raman coupling between the spin states with a phase difference between the two layers.
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Affiliation(s)
- Jun-Hui Zheng
- Department of Physics, National Tsing Hua University, Hsinchu, 30013, Taiwan
| | - Daw-Wei Wang
- Department of Physics, National Tsing Hua University, Hsinchu, 30013, Taiwan.,Physics Division, National Center for Theoretical Sciences, Hsinchu, 30013, Taiwan
| | - Gediminas Juzeliūnas
- Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio Ave. 9, Vilnius, 10222, Lithuania
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Liu S, Zhou XF, Guo GC, Zhang YS. Anderson Localization in Degenerate Spin-Orbit Coupled Fermi Gas with Disorder. Sci Rep 2016; 6:22623. [PMID: 26936539 PMCID: PMC4776179 DOI: 10.1038/srep22623] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2015] [Accepted: 02/17/2016] [Indexed: 11/23/2022] Open
Abstract
Competition between superconductivity and disorder plays an essential role in understanding the metal-insulator transition. Based on the Bogoliubov-de Gennes framework, we studied an 2D s-wave fermionic optical lattice system with both spin- orbit coupling and disorder are presented. We find that, with the increase of the strength of disorder, the mean superconducting order parameter will vanish while the energy gap will persist, which indicates that the system undergoes a transition from a superconducting state to a gapped insulating state. This can be confirmed by calculating the inverse participation ratio. We also find that, if the strength of disorder is small, the superconducting order parameter and the energy gap will decrease if we increase the strength of spin-orbit coupling and Zeeman field. In the large disorder limits, the increase of the strength of spin- orbit coupling will increase the mean superconducting order parameter. This phenomenon shows that the system is more insensitive to disorder if the spin-orbit coupling is presented. Numerical computing also shows that the whole system breaks up into several superconducting islands instead of being superconductive.
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Affiliation(s)
- Sheng Liu
- Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Xiang-Fa Zhou
- Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Guang-Can Guo
- Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Yong-Sheng Zhang
- Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China.,Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China
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