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Zhang SB, Hu LH, Neupert T. Finite-momentum Cooper pairing in proximitized altermagnets. Nat Commun 2024; 15:1801. [PMID: 38413591 PMCID: PMC10899178 DOI: 10.1038/s41467-024-45951-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2023] [Accepted: 02/08/2024] [Indexed: 02/29/2024] Open
Abstract
Finite-momentum Cooper pairing is an unconventional form of superconductivity that is widely believed to require finite magnetization. Altermagnetism is an emerging magnetic phase with highly anisotropic spin-splitting of specific symmetries, but zero net magnetization. Here, we study Cooper pairing in metallic altermagnets connected to conventional s-wave superconductors. Remarkably, we find that the Cooper pairs induced in the altermagnets acquire a finite center-of-mass momentum, despite the zero net magnetization in the system. This anomalous Cooper-pair momentum strongly depends on the propagation direction and exhibits unusual symmetric patterns. Furthermore, it yields several unique features: (i) highly orientation-dependent oscillations in the order parameter, (ii) controllable 0-π transitions in the Josephson supercurrent, (iii) large-oblique-angle Cooper-pair transfer trajectories in junctions parallel with the direction where spin splitting vanishes, and (iv) distinct Fraunhofer patterns in junctions oriented along different directions. Finally, we discuss the implementation of our predictions in candidate materials such as RuO2 and KRu4O8.
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Affiliation(s)
- Song-Bo Zhang
- Hefei National Laboratory, Hefei, Anhui, 230088, China.
- International Center for Quantum Design of Functional Materials (ICQD), University of Science and Technology of China, Hefei, Anhui, 230026, China.
- Department of Physics, University of Zürich, Winterthurerstrasse 190, 8057, Zürich, Switzerland.
| | - Lun-Hui Hu
- Department of Applied Physics, Aalto University School of Science, FI-00076, Aalto, Finland.
- Center for Correlated Matter and School of Physics, Zhejiang University, Hangzhou, 310058, China.
- Department of Physics and Astronomy, The University of Tennessee, Knoxville, TN, 37996, USA.
| | - Titus Neupert
- Department of Physics, University of Zürich, Winterthurerstrasse 190, 8057, Zürich, Switzerland
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2
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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] [What about the content of this article? (0)] [Affiliation(s)] [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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Pęcak D, Sowiński T. Unconventional pairing in few-fermion systems at finite temperature. Sci Rep 2022; 12:17476. [PMID: 36261489 DOI: 10.1038/s41598-022-22411-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2022] [Accepted: 10/14/2022] [Indexed: 11/17/2022] Open
Abstract
Attractively interacting two-component mixtures of fermionic particles confined in a one-dimensional harmonic trap are investigated. Properties of balanced and imbalanced systems are systematically explored with the exact diagonalization approach, focusing on the finite-temperature effects. Using single- and two-particle density distributions, specific non-classical pairing correlations are analyzed in terms of the noise correlations—quantity directly accessible in state-of-the-art experiments with ultra-cold atoms. It is shown that along with increasing temperature, any imbalanced system hosting Fulde–Ferrel–Larkin–Ovchinnikov pairs crossovers to a standard Bardeen-Cooper-Schrieffer one characterized by zero net momentum of resulting pairs. By performing calculations for systems with different imbalances, the approximate boundary between the two phases on a phase diagram is determined.
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Imajo S, Nomura T, Kohama Y, Kindo K. Emergent anisotropy in the Fulde-Ferrell-Larkin-Ovchinnikov state. Nat Commun 2022; 13:5590. [PMID: 36192393 DOI: 10.1038/s41467-022-33354-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2022] [Accepted: 09/08/2022] [Indexed: 11/08/2022] Open
Abstract
Exotic superconductivity is formed by unconventional electron pairing and exhibits various unique properties that cannot be explained by the basic theory. The Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state is known as an exotic superconducting state in that the electron pairs have a finite center-of-mass momentum leading to a spatially modulated pattern of superconductivity. The spatial modulation endows the FFLO state with emergent anisotropy. However, the anisotropy has never been experimentally verified despite numerous efforts over the years. Here, we report detection of anisotropic acoustic responses depending on the sound propagation direction appearing above the Pauli limit. This anisotropy reveals that the two-dimensional FFLO state has a center-of-mass momentum parallel to the nesting vector on the Fermi surface. The present findings will facilitate our understanding of not only superconductivity in solids but also exotic pairings of various particles. The famous Fulde–Ferrell–Larkin– Ovchinnikov (FFLO) state is a spatially-modulated superconducting state with a predicted spatial anisotropy, but this anisotropy has never been experimentally verified. Here, the authors present ultrasound evidence for anisotropy of the sound velocity in the FFLO state of a 2D organic superconductor.
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Abstract
The superconducting phase diagram for a quasi-two-dimensional organic superconductor, κ-(BEDT-TTF)2Cu[N(CN)2]Br, was studied using pulsed magnetic field penetration depth measurements under rotating magnetic fields. At low temperatures, Hc2 was abruptly suppressed even by small tilts of the applied fields owing to the orbital pair-breaking effect. In magnetic fields parallel to the conducting plane, the temperature dependence of the upper critical field Hc2 exhibited an upturn and exceeded the Pauli limit field HP in the lower temperature region. Further analyses with the second derivative of the penetration depth showed an anomaly at 31–32 T, which roughly corresponded to HP. The origin of the anomaly should not be related to the orbital effect, but the paramagnetic effect, which is almost isotropic in organic salts, because it barely depends on the field angle. Based on these results, the observed anomaly is most likely due to the transition between the Bardeen-Cooper-Schrieffer (BCS) and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states. Additionally, we discuss the phase diagram and physical parameters of the transition by comparing them with other FFLO candidates.
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Abstract
This short review article provides the reader with a summary of the history of organic conductors. To retain a neutral and objective point of view regarding the history, background, novelty, and details of each research subject within this field, a thousand references have been cited with full titles and arranged in chronological order. Among the research conducted over ~70 years, topics from the last two decades are discussed in more detail than the rest. Unlike other papers in this issue, this review will help readers to understand the origin of each topic within the field of organic conductors and how they have evolved. Due to the advancements achieved over these 70 years, the field is nearing new horizons. As history is often a reflection of the future, this review is expected to show the future directions of this research field.
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Jiang D, Yuan T, Wu Y, Wei X, Mu G, An Z, Li W. Strong In-Plane Magnetic Field-Induced Reemergent Superconductivity in the van der Waals Heterointerface of NbSe 2 and CrCl 3. ACS Appl Mater Interfaces 2020; 12:49252-49257. [PMID: 33058667 DOI: 10.1021/acsami.0c15203] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
A magnetic field is generally considered to be incompatible with superconductivity as it tends to spin-polarize electrons and breaks apart the opposite-spin singlet superconducting Cooper pairs. Here, an experimental phenomenon is observed that an intriguing reemergent superconductivity evolves from a conventional superconductivity undergoing a hump-like intermediate phase with a finite electric resistance in the van der Waals heterointerface of layered NbSe2 and CrCl3 flakes. This phenomenon merely occurred when the applied magnetic field is parallel to the sample plane and perpendicular to the electric current direction as compared to the reference sample of a NbSe2 thin flake. The strong anisotropy of the reemergent superconducting phase is pointed to the nature of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state driven by the strong interfacial spin-orbit coupling between NbSe2 and CrCl3 layers. The theoretical picture of FFLO state nodes induced by Josephson vortices collectively pinning is presented for well understanding the experimental observation of the reemergent superconductivity. This finding sheds light on an opportunity to search for the exotic FFLO state in the van der Waals heterostructures with strong interfacial spin-orbit coupling.
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Affiliation(s)
- Da Jiang
- State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, and Center for Excellence in Superconducting Electronics, Chinese Academy of Science, Shanghai 200050, People's Republic of China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Tianzhong Yuan
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
| | - Yongzheng Wu
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
| | - Xinyuan Wei
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
| | - Gang Mu
- State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, and Center for Excellence in Superconducting Electronics, Chinese Academy of Science, Shanghai 200050, People's Republic of China
| | - Zhenghua An
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
| | - Wei Li
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
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9
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Croitoru M, Buzdin A. In Search of Unambiguous Evidence of the Fulde–Ferrell–Larkin–Ovchinnikov State in Quasi-Low Dimensional Superconductors. Condensed Matter 2017; 2:30. [DOI: 10.3390/condmat2030030] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Koutroulakis G, Kühne H, Schlueter JA, Wosnitza J, Brown SE. Microscopic Study of the Fulde-Ferrell-Larkin-Ovchinnikov State in an All-Organic Superconductor. Phys Rev Lett 2016; 116:067003. [PMID: 26919012 DOI: 10.1103/physrevlett.116.067003] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2015] [Indexed: 06/05/2023]
Abstract
Quasi-two-dimensional superconductors with a sufficiently weak interlayer coupling allow magnetic flux to penetrate in the form of Josephson vortices for in-plane applied magnetic fields. A consequence is the dominance of the Zeeman interaction over orbital effects. In the clean limit, the normal state is favored over superconductivity for fields greater than the paramagnetic limiting field, unless an intermediate, inhomogeneous state is stabilized. Presented here are nuclear magnetic resonance (NMR) studies of the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state for β''-(ET)2SF5CH2CF2SO3. The uniform superconductivity-FFLO transition is identified at an applied field value of 9.3(0.1) T at low temperature (T=130 mK), and evidence for a possible second transition between inhomogeneous states at ∼11 T is presented. The spin polarization distribution inferred from the NMR absorption spectrum compares favorably to a single-Q modulation of the superconducting order parameter.
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Affiliation(s)
- G Koutroulakis
- Department of Physics and Astronomy, UCLA, Los Angeles, California 90095, USA
| | - H Kühne
- Hochfeld-Magnetlabor Dresden (HLD-EMFL), Helmholtz-Zentrum Dresden-Rossendorf, D-01314 Dresden, Germany
| | - J A Schlueter
- Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
- Division of Materials Research, National Science Foundation, Arlington, Virginia 22230, USA
| | - J Wosnitza
- Hochfeld-Magnetlabor Dresden (HLD-EMFL), Helmholtz-Zentrum Dresden-Rossendorf, D-01314 Dresden, Germany
- Institut für Festkörperphysik, TU Dresden, D-01069 Dresden, Germany
| | - S E Brown
- Department of Physics and Astronomy, UCLA, Los Angeles, California 90095, USA
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11
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Roedersheimer M. Solving the Measurement Problem and then Steppin' Out over the Line Riding the Rarest Italian: Crossing the Streams to Retrieve Stable Bioactivity in Majorana Bound States of Dialy zed Human Platelet Lysates. Open Neurol J 2015; 9:32-44. [PMID: 26191092 PMCID: PMC4503829 DOI: 10.2174/1874205x01509010032] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2014] [Revised: 03/24/2014] [Accepted: 03/25/2014] [Indexed: 11/22/2022] Open
Abstract
Exhaustive dialysis (ED) of lysed human platelets against dilute HCl yields stable angiogenic activity. Dialysis against a constrained external volume, with subsequent relaxation of the separation upon opening the dialysis bag, produces material able to maintain phenotypes and viability of human cells in culture better than ED material. Significant graded changes in MTT viability measurement tracked with external volume. The presence of elements smaller than the MW cutoff, capable of setting up cycling currents initiated by oriented flow of HCl across the membrane, suggests that maturation of bioactivity occurred through establishment of a novel type of geometric phase. These information-rich bound states fit recent descriptions of topological order and Majorana fermions, suggesting relevance in testing Penrose and Hameroff's theory of Orchestrated Objective Reduction, under conditions more general, and on finer scales, than those dependent on tubulin protein. The Berry curvature appears to be a good tool for building a general field theory of physiologic stress dependent on the quantum Hall effect. A new form of geometric phase, and an associated "geometric" quantum Hall effect underlying memory retrieval, dependent on the rate of path traversal and reduction from more than two initial field influences is described.
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12
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Xu Y, Zhang C. Berezinskii-Kosterlitz-Thouless phase transition in 2D spin-orbit-coupled Fulde-Ferrell superfluids. Phys Rev Lett 2015; 114:110401. [PMID: 25839244 DOI: 10.1103/physrevlett.114.110401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2014] [Indexed: 06/04/2023]
Abstract
The experimental observation of traditional Zeeman-field induced Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids has been hindered by various challenges, in particular, the requirement of low dimensional systems. In 2D, finite temperature phase fluctuations lead to an extremely small Berezinskii-Kosterlitz-Thouless (BKT) transition temperature for FFLO superfluids, raising serious concerns regarding their experimental observability. Recently, it was shown that FFLO superfluids can be realized using a Rashba spin-orbit coupled Fermi gas subject to Zeeman fields, which may also support topological excitations such as Majorana fermions in 2D. Here we address the finite temperature BKT transition issue in this system, which may exhibit gapped, gapless, topological, and gapless topological FF phases. We find a large BKT transition temperature due to large effective superfluid densities, making it possible to observe 2D FF superfluids at finite temperature. In addition, we show that gapless FF superfluids can be stable due to their positive superfluid densities. These findings pave the way for the experimental observation of 2D gapped and gapless FF superfluids and their associated topological excitations at finite temperature.
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Affiliation(s)
- Yong Xu
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Chuanwei Zhang
- Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080, USA
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13
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Cao Y, Zou SH, Liu XJ, Yi S, Long GL, Hu H. Gapless topological Fulde-Ferrell superfluidity in spin-orbit coupled Fermi gases. Phys Rev Lett 2014; 113:115302. [PMID: 25259986 DOI: 10.1103/physrevlett.113.115302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2014] [Indexed: 06/03/2023]
Abstract
Topological superfluids usually refer to a superfluid state which is gapped in the bulk but metallic at the boundary. Here we report that a gapless, topologically nontrivial superfluid with an inhomogeneous Fulde-Ferrell pairing order parameter can emerge in a two-dimensional spin-orbit coupled Fermi gas, in the presence of both in-plane and out-of-plane Zeeman fields. The Fulde-Ferrell pairing-induced by the spin-orbit coupling and in-plane Zeeman field-is responsible for this gapless feature. This exotic superfluid has a significant Berezinskii-Kosterlitz-Thouless transition temperature and has robust Majorana edge modes against disorder owing to its topological nature.
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Affiliation(s)
- Ye Cao
- Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne 3122, Australia and State Key Laboratory of Low-dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China
| | - Shu-Hao Zou
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
| | - Xia-Ji Liu
- Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne 3122, Australia
| | - Su Yi
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
| | - Gui-Lu Long
- State Key Laboratory of Low-dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China and Collaborative Innovation Center of Quantum Matter, Beijing 100084, People's Republic of China and Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, People's Republic of China
| | - Hui Hu
- Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne 3122, Australia
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Aoyama K, Beaird R, Sheehy DE, Vekhter I. Inhomogeneous superconducting States of mesoscopic thin-walled cylinders in external magnetic fields. Phys Rev Lett 2013; 110:177004. [PMID: 23679762 DOI: 10.1103/physrevlett.110.177004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2012] [Indexed: 06/02/2023]
Abstract
We theoretically investigate the appearance of spatially modulated superconducting states in mesoscopic superconducting thin-wall cylinders in a magnetic field at low temperatures. Quantization of the electron motion around the circumference of the cylinder leads to a discontinuous evolution of the spatial modulation of the superconducting order parameter along the transition line T(c)(H). We show that this discontinuity leads to the nonmonotonic behavior of the specific heat jump at the onset of superconductivity as a function of temperature and field. We argue that this geometry provides an excellent opportunity to directly and unambiguously detect distinctive signatures of the Fulde-Ferrell-Larkin-Ovchinnikov modulation of the superconducting order.
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Affiliation(s)
- K Aoyama
- The Hakubi Center for Advanced Research, Kyoto University, Kyoto 606-8501, Japan
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15
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Croitoru MD, Buzdin AI. The Fulde-Ferrell-Larkin-Ovchinnikov state in layered d-wave superconductors: in-plane anisotropy and resonance effects in the angular dependence of the upper critical field. J Phys Condens Matter 2013; 25:125702. [PMID: 23448967 DOI: 10.1088/0953-8984/25/12/125702] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We study the anisotropy of the in-plane upper critical magnetic field coupled to the orbital motion and the spins of electrons in a layered d(x2-y2) organic superconductor in the spatially modulated Fulde-Ferrell-Larkin-Ovchinnikov phase. We show that the interplay between the nodal structure of the order parameter and its spatial modulation results in the very peculiar angular dependence of the onset of superconductivity in the high-field regime. The principal axis of the field-direction dependence of the onset of superconductivity is tilted by π/4 in the temperature range 0.056 < or approximately equal T < 0.56. In some cases the resonance between the modulation wavevector and the vector potential of a parallel magnetic field may lead to anomalous cusps in the temperature and in-plane angular dependences of the onset of superconductivity. The obtained results support the interpretation of the recent experiments as evidence of the FFLO state.
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Affiliation(s)
- M D Croitoru
- Université Bordeaux I, LOMA, UMR 5798, F-33400 Talence, France.
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16
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Wright JA, Green E, Kuhns P, Reyes A, Brooks J, Schlueter J, Kato R, Yamamoto H, Kobayashi M, Brown SE. Zeeman-driven phase transition within the superconducting state of κ-(BEDT-TTF)2Cu(NCS)2. Phys Rev Lett 2011; 107:087002. [PMID: 21929196 DOI: 10.1103/physrevlett.107.087002] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2011] [Indexed: 05/31/2023]
Abstract
(13)C nuclear magnetic resonance measurements were performed on κ-(BEDT-TTF)(2)Cu(NCS)(2), with the external field placed parallel to the quasi-2D conducting layers. The absorption spectrum is used to determine the electronic spin polarization M(s) as a function of external field H at a temperature T=0.35 K. A discontinuity in the derivative dM(s)/dH at an applied field of H(s)=213±3 kOe is taken as evidence for a Zeeman-driven transition within the superconducting state and stabilization of inhomogeneous superconductivity.
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Affiliation(s)
- J A Wright
- Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1547, USA
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17
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Kobayashi H, Kobayashi A, Tajima H. Studies on Molecular Conductors: From Organic Semiconductors to Molecular Metals and Superconductors. Chem Asian J 2011; 6:1688-704. [DOI: 10.1002/asia.201100061] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2011] [Indexed: 11/05/2022]
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18
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Yanase Y, Sigrist M. Magnetic structure of the antiferromagnetic Fulde-Ferrell-Larkin-Ovchinnikov state. J Phys Condens Matter 2011; 23:094219. [PMID: 21339572 DOI: 10.1088/0953-8984/23/9/094219] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The properties of incommensurate antiferromagnetic (AFM) order in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state are studied by solving the Bogoliubov-de Gennes (BdG) equations. The relationship between the electronic structure and the magnetic structure is clarified. We find that the magnetic structure in the AFM-FFLO state includes three cases. (I) In the strongly localized case, the AFM staggered moment is confined into the FFLO nodal planes where the superconducting order parameter vanishes. (II) In the weakly localized case, the AFM staggered moment appears in the whole spatial region, and its magnitude is enhanced around the FFLO nodal planes. (III) In the extended case, the AFM staggered moment is nearly homogeneous and slightly suppressed in the vicinity of the FFLO nodal planes. The structure of Bragg peaks in the momentum resolved structure factor is studied in each case. We discuss the possibility of an AFM-FFLO state in the heavy fermion superconductor CeCoIn5 by comparing these results with the neutron scattering data of CeCoIn5. Experimentally the magnetic structure and its dependence on the magnetic field orientation in the high-field superconducting phase of CeCoIn5 are consistent with case (II).
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Affiliation(s)
- Youichi Yanase
- Department of Physics, Niigata University, Niigata 950-2041, Japan. Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland
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Liao Y, Rittner ASC, Paprotta T, Li W, Partridge GB, Hulet RG, Baur SK, Mueller EJ. Spin-imbalance in a one-dimensional Fermi gas. Nature 2010; 467:567-9. [DOI: 10.1038/nature09393] [Citation(s) in RCA: 428] [Impact Index Per Article: 30.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2010] [Accepted: 08/03/2010] [Indexed: 11/08/2022]
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Brooks JS. Organic conductors: A dash of salt is superconducting. Nat Nanotechnol 2010; 5:244-245. [PMID: 20348910 DOI: 10.1038/nnano.2010.63] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
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Aizawa H, Kuroki K, Yokoyama T, Tanaka Y. Strong parity mixing in the Fulde-Ferrell-Larkin-Ovchinnikov superconductivity in systems with coexisting spin and charge fluctuations. Phys Rev Lett 2009; 102:016403. [PMID: 19257219 DOI: 10.1103/physrevlett.102.016403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2008] [Indexed: 05/27/2023]
Abstract
We study the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of spin fluctuation mediated pairing, and focus on the effect of coexisting charge fluctuations. We find that (i) consecutive transitions from singlet pairing to FFLO and further to S_{z}=1 triplet pairing can generally take place upon increasing the magnetic field when strong charge fluctuations coexist with spin fluctuations, and (ii) the enhancement of the charge fluctuations lead to a significant increase of the parity mixing in the FFLO state, where the triplet/singlet component ratio in the gap function can be close to unity. We propose that such consecutive pairing state transition and strong parity mixing in the FFLO state may take place in a quasi-one-dimensional organic superconductor (TMTSF)2X.
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Affiliation(s)
- Hirohito Aizawa
- Department of Applied Physics and Chemistry, The University of Electro-Communications, Chofu, Tokyo 182-8585, Japan
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Koutroulakis G, Mitrović VF, Horvatić M, Berthier C, Lapertot G, Flouquet J. Field dependence of the ground state in the exotic superconductor CeCoIn5: a nuclear magnetic resonance investigation. Phys Rev Lett 2008; 101:047004. [PMID: 18764359 DOI: 10.1103/physrevlett.101.047004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2008] [Indexed: 05/26/2023]
Abstract
We report 115In nuclear magnetic resonance (NMR) measurements in CeCoIn5 at low temperature (T approximately 70 mK) as a function of the magnetic field (H0) from 2 to 13.5 T applied perpendicular to the c axis. A NMR line shift reveals that below 10 T the spin susceptibility increases as sqrt[H0]. We associate this with an increase of the density of states due to the Zeeman and Doppler-shifted quasiparticles extended outside the vortex cores in a d-wave superconductor. Above 10 T a new superconducting state is stabilized, possibly the modulated phase predicted by Fulde, Ferrell, Larkin, and Ovchinnikov. This phase is clearly identified by a strong and linear increase of the NMR shift with the field, before a jump at the first order transition to the normal state.
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Affiliation(s)
- G Koutroulakis
- Department of Physics, Brown University, Providence, Rhode Island 02912, USA
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Tokumoto T, Brooks JS, Oshima Y, Choi ES, Brunel LC, Akutsu H, Kaihatsu T, Yamada J, van Tol J. Antiferromagnetic d-electron exchange via a spin-singlet pi-electron ground state in an organic conductor. Phys Rev Lett 2008; 100:147602. [PMID: 18518072 DOI: 10.1103/physrevlett.100.147602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2007] [Indexed: 05/26/2023]
Abstract
Electron spin resonance reveals the spin behavior of conduction (pi) and localized (d) electrons in beta-(BDA-TTP)2MCl4 (M=Fe, Ga). Both the Ga3+(S=0) and Fe3+(S=5/2) compounds exhibit a metal-insulator transition at 113 K with the simultaneous formation of a spin-singlet ground state in the pi electron system of the donor molecules. The behavior is consistent with charge ordering in beta-(BDA-TTP)2MCl4 at the metal-insulator transition. At 5 K, the Fe3+ compound orders antiferromagnetically, even though the pi electrons, which normally would facilitate magnetic exchange, are localized nonmagnetic singlets.
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Affiliation(s)
- T Tokumoto
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA
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Lortz R, Wang Y, Demuer A, Böttger PHM, Bergk B, Zwicknagl G, Nakazawa Y, Wosnitza J. Calorimetric evidence for a Fulde-Ferrell-Larkin-Ovchinnikov superconducting state in the layered organic superconductor kappa-(BEDT-TTF)2Cu(NCS)2. Phys Rev Lett 2007; 99:187002. [PMID: 17995428 DOI: 10.1103/physrevlett.99.187002] [Citation(s) in RCA: 61] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2007] [Indexed: 05/25/2023]
Abstract
The specific heat of the layered organic superconductor kappa-(BEDT-TTF)(2)Cu(NCS)(2), where BEDT-TTF is bisethylenedithio-tetrathiafulvalene, has been studied in magnetic fields up to 28 T applied perpendicular and parallel to the superconducting layers. In parallel fields above 21 T, the superconducting transition becomes first order, which signals that the Pauli-limiting field is reached. Instead of saturating at this field value, the upper-critical-field increases sharply and a second first-order transition line appears within the superconducting phase. Our results give strong evidence that the phase, which separates the homogeneous superconducting state from the normal state is a realization of a Fulde-Ferrell-Larkin-Ovchinnikov state.
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Affiliation(s)
- R Lortz
- Department of Condensed Matter Physics, University of Geneva, CH-1211 Geneva 4, Switzerland
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