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Zhang JL, Chen W, Liu HT, Li Y, Wang Z, Huang W. Quantum-Geometry-Induced Anomalous Hall Effect in Nonunitary Superconductors and Application to Sr_{2}RuO_{4}. PHYSICAL REVIEW LETTERS 2024; 132:136001. [PMID: 38613301 DOI: 10.1103/physrevlett.132.136001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2023] [Accepted: 03/01/2024] [Indexed: 04/14/2024]
Abstract
The polar Kerr effect and the closely related anomalous charge Hall effect are among the most distinguishing signatures of the superconducting state in Sr_{2}RuO_{4}, as well as in several other compounds. These effects are often thought to be derived from chiral superconducting pairing, and different mechanisms have been invoked for the explanation. However, the intrinsic mechanisms proposed previously often involve unrealistically strong interband Cooper pairing. We show in this Letter that, even without interband pairing, nonunitary superconducting states can support the intrinsic anomalous charge Hall effect, thanks to the quantum geometric properties of the Bloch electrons. The key here is to have a normal-state spin Hall effect, for which a nonzero spin-orbit coupling is essential. A finite charge Hall effect then naturally arises at the onset of a spin-polarized nonunitary superconducting pairing. It depends on both the spin polarization and the normal-state electron Berry curvature, the latter of which is the imaginary part of the quantum geometric tensor of the Bloch states. Applying our results to the weakly paired Sr_{2}RuO_{4} we conclude that, if the reported Kerr effect is of intrinsic origin, the superconducting state is most likely nonunitary and has odd parity. Our theory may be generalized to other superconductors that exhibit the polar Kerr effect.
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Affiliation(s)
- Jia-Long Zhang
- Department of Physics, The Hong Kong University of Science and Technology, Hong Kong SAR, China
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
| | - Weipeng Chen
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Hao-Tian Liu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yu Li
- Institute of Quantum Materials and Physics, Henan Academy of Sciences, Zhengzhou, Henan 450046, China
- Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Zhiqiang Wang
- Department of Physics and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| | - Wen Huang
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
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2
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Ma MH, Batsaikhan E, Chen HN, Chen TY, Lee CH, Li WH, Wu CM, Wang CW. Non-conventional superconductivity in magnetic In and Sn nanoparticles. Sci Rep 2022; 12:775. [PMID: 35031677 PMCID: PMC8760274 DOI: 10.1038/s41598-022-04889-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2021] [Accepted: 12/21/2021] [Indexed: 11/23/2022] Open
Abstract
We report on experimental evidence of non-conversional pairing in In and Sn nanoparticle assemblies. Spontaneous magnetizations are observed, through extremely weak-field magnetization and neutron-diffraction measurements, to develop when the nanoparticles enter the superconducting state. The superconducting transition temperature TC shifts to a noticeably higher temperature when an external magnetic field or magnetic Ni nanoparticles are introduced into the vicinity of the superconducting In or Sn nanoparticles. There is a critical magnetic field and a critical Ni composition that must be reached before the magnetic environment will suppress the superconductivity. The observations may be understood when assuming development of spin-parallel superconducting pairs on the surfaces and spin-antiparallel superconducting pairs in the core of the nanoparticles.
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Affiliation(s)
- Ma-Hsuan Ma
- Department of Physics, National Central University, Zhongli, 32001, Taiwan
| | | | - Huang-Nan Chen
- Department of Physics, National Central University, Zhongli, 32001, Taiwan
| | - Ting-Yang Chen
- Department of Physics, National Central University, Zhongli, 32001, Taiwan
| | - Chi-Hung Lee
- Department of Physics, National Central University, Zhongli, 32001, Taiwan
| | - Wen-Hsien Li
- Department of Physics, National Central University, Zhongli, 32001, Taiwan.
| | - Chun-Ming Wu
- National Synchrotron Radiation Research Center, Hsinchu, 30076, Taiwan
| | - Chin-Wei Wang
- National Synchrotron Radiation Research Center, Hsinchu, 30076, Taiwan
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3
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Petsch AN, Zhu M, Enderle M, Mao ZQ, Maeno Y, Mazin II, Hayden SM. Reduction of the Spin Susceptibility in the Superconducting State of Sr_{2}RuO_{4} Observed by Polarized Neutron Scattering. PHYSICAL REVIEW LETTERS 2020; 125:217004. [PMID: 33275021 DOI: 10.1103/physrevlett.125.217004] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2020] [Revised: 07/01/2020] [Accepted: 10/14/2020] [Indexed: 06/12/2023]
Abstract
Recent observations [A. Pustogow et al., Nature (London) 574, 72 (2019).NATUAS0028-083610.1038/s41586-019-1596-2] of a drop of the ^{17}O nuclear magnetic resonance (NMR) Knight shift in the superconducting state of Sr_{2}RuO_{4} challenged the popular picture of a chiral odd-parity paired state in this compound. Here we use polarized neutron scattering (PNS) to show that there is a 34±6% drop in the magnetic susceptibility at the Ru site below the superconducting transition temperature. We measure at lower fields H∼1/3H_{c2} than a previous PNS study allowing the suppression to be observed. The PNS measurements show a smaller susceptibility suppression than NMR measurements performed at similar field and temperature. Our results rule out the chiral odd-parity d=z[over ^](k_{x}±ik_{y}) state and are consistent with several recent proposals for the order parameter including even-parity B_{1g} and odd-parity helical states.
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Affiliation(s)
- A N Petsch
- H.H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
| | - M Zhu
- H.H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
| | | | - Z Q Mao
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
- Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Y Maeno
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - I I Mazin
- Department of Physics and Astronomy, George Mason University and Quantum Science and Engineering Center, Fairfax, Virginia 22030, USA
| | - S M Hayden
- H.H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
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4
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Ghosh SK, Smidman M, Shang T, Annett JF, Hillier AD, Quintanilla J, Yuan H. Recent progress on superconductors with time-reversal symmetry breaking. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 33:033001. [PMID: 32721940 DOI: 10.1088/1361-648x/abaa06] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2019] [Accepted: 07/28/2020] [Indexed: 06/11/2023]
Abstract
Superconductivity and magnetism are adversarial states of matter. The presence of spontaneous magnetic fields inside the superconducting state is, therefore, an intriguing phenomenon prompting extensive experimental and theoretical research. In this review, we discuss recent experimental discoveries of unconventional superconductors which spontaneously break time-reversal symmetry and theoretical efforts in understanding their properties. We discuss the main experimental probes and give an extensive account of theoretical approaches to understand the order parameter symmetries and the corresponding pairing mechanisms, including the importance of multiple bands.
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Affiliation(s)
- Sudeep Kumar Ghosh
- Physics of Quantum Materials, School of Physical Sciences, University of Kent, Canterbury CT2 7NH, United Kingdom
| | - Michael Smidman
- Center for Correlated Matter and Department of Physics, Zhejiang University, Hangzhou 310058, People's Republic of China
- Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, People's Republic of China
| | - Tian Shang
- Laboratory for Multiscale Materials Experiments, Paul Scherrer Institut, Villigen CH-5232, Switzerland
- Physik-Institut, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - James F Annett
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - Adrian D Hillier
- ISIS Facility, STFC Rutherford Appleton Laboratory, Harwell Science and Innovation Campus, Didcot OX11 0QX, United Kingdom
| | - Jorge Quintanilla
- Physics of Quantum Materials, School of Physical Sciences, University of Kent, Canterbury CT2 7NH, United Kingdom
| | - Huiqiu Yuan
- Center for Correlated Matter and Department of Physics, Zhejiang University, Hangzhou 310058, People's Republic of China
- Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, People's Republic of China
- State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou 310027, People's Republic of China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People's Republic of China
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Momentum-resolved superconducting energy gaps of Sr 2RuO 4 from quasiparticle interference imaging. Proc Natl Acad Sci U S A 2020; 117:5222-5227. [PMID: 32094178 DOI: 10.1073/pnas.1916463117] [Citation(s) in RCA: 9] [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
Sr2RuO4 has long been the focus of intense research interest because of conjectures that it is a correlated topological superconductor. It is the momentum space (k-space) structure of the superconducting energy gap [Formula: see text] on each band i that encodes its unknown superconducting order parameter. However, because the energy scales are so low, it has never been possible to directly measure the [Formula: see text] of Sr2RuO4 Here, we implement Bogoliubov quasiparticle interference (BQPI) imaging, a technique capable of high-precision measurement of multiband [Formula: see text] At T = 90 mK, we visualize a set of Bogoliubov scattering interference wavevectors [Formula: see text] consistent with eight gap nodes/minima that are all closely aligned to the [Formula: see text] crystal lattice directions on both the α and β bands. Taking these observations in combination with other very recent advances in directional thermal conductivity [E. Hassinger et al., Phys. Rev. X 7, 011032 (2017)], temperature-dependent Knight shift [A. Pustogow et al., Nature 574, 72-75 (2019)], time-reversal symmetry conservation [S. Kashiwaya et al., Phys. Rev B, 100, 094530 (2019)], and theory [A. T. Rømer et al., Phys. Rev. Lett. 123, 247001 (2019); H. S. Roising, T. Scaffidi, F. Flicker, G. F. Lange, S. H. Simon, Phys. Rev. Res. 1, 033108 (2019); and O. Gingras, R. Nourafkan, A. S. Tremblay, M. Côté, Phys. Rev. Lett. 123, 217005 (2019)], the BQPI signature of Sr2RuO4 appears most consistent with [Formula: see text] having [Formula: see text] [Formula: see text] symmetry.
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6
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Gingras O, Nourafkan R, Tremblay AMS, Côté M. Superconducting Symmetries of Sr_{2}RuO_{4} from First-Principles Electronic Structure. PHYSICAL REVIEW LETTERS 2019; 123:217005. [PMID: 31809152 DOI: 10.1103/physrevlett.123.217005] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2018] [Indexed: 06/10/2023]
Abstract
Although correlated electronic-structure calculations explain very well the normal state of Sr_{2}RuO_{4}, its superconducting symmetry is still unknown. Here we construct the spin and charge fluctuation pairing interactions based on its correlated normal state. Correlations significantly reduce ferromagnetic in favor of antiferromagnetic fluctuations and increase interorbital pairing. From the normal-state Eliashberg equations, we find spin-singlet d-wave pairing close to magnetic instabilities. Away from these instabilities, where charge fluctuations increase, we find two time-reversal symmetry-breaking spin triplets: an odd-frequency s wave, and a doubly degenerate interorbital pairing between d_{xy} and (d_{yz},d_{xz}).
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Affiliation(s)
- O Gingras
- Département de Physique and Regroupement Québécois sur les Matériaux de Pointe, Université de Montréal, C. P. 6128, Succursale Centre-Ville, Montréal, Québec H3C 3J7, Canada
| | - R Nourafkan
- Département de Physique, Institut quantique, Regroupement Québécois sur les Matériaux de Pointe, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
| | - A-M S Tremblay
- Département de Physique, Institut quantique, Regroupement Québécois sur les Matériaux de Pointe, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
- Canadian Institute for Advanced Research, Toronto, Ontario, Canada M5G 1Z8
| | - M Côté
- Département de Physique and Regroupement Québécois sur les Matériaux de Pointe, Université de Montréal, C. P. 6128, Succursale Centre-Ville, Montréal, Québec H3C 3J7, Canada
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Abstract
Recent work done on the time reversal symmetry (TRS) breaking superconductors is reviewed in this paper. The special attention is paid to Sr 2 RuO 4 believed to be spin triplet chiral p-wave superconductor which break TRS and is expected to posses non-trivial topological properties. The family of TRS breaking superconductors is growing relatively fast, with many of its newly discovered members being non-centrosymmetric. However not only Sr 2 RuO 4 but also many other superconductors which possess center of inversion also break TRS. The TRS is often identified by means of the muon spin relaxation ( μ SR) and the Kerr effect. Both methods effectively measure the appearance of the spontaneous bulk magnetic field below superconducting transition temperature. This compound provides an example of the material whose many band, multi-condensate modeling has enjoyed a number of successes, but the full understanding has not been achieved yet. We discuss in some details the properties of the material. Among them is the Kerr effect and by understanding has resulted in the discovery of the novel mechanism of the phenomenon. The mechanism is universal and thus applicable to all systems with multi-orbital character of states at the Fermi energy.
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8
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Wang WS, Zhang CC, Zhang FC, Wang QH. Theory of Chiral p-Wave Superconductivity with Near Nodes for Sr_{2}RuO_{4}. PHYSICAL REVIEW LETTERS 2019; 122:027002. [PMID: 30720289 DOI: 10.1103/physrevlett.122.027002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2018] [Indexed: 06/09/2023]
Abstract
We use the functional renormalization group method to study a three-orbital model for superconducting Sr_{2}RuO_{4}. Although the pairing symmetry is found to be a chiral p wave, the atomic spin-orbit coupling induces near nodes for quasiparticle excitations. Our theory explains a major experimental puzzle between a d-wavelike feature observed in thermal experiments and the chiral p-wave triplet pairing revealed in nuclear-magnetic resonance and the Kerr effect.
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Affiliation(s)
- Wan-Sheng Wang
- Department of Physics, Ningbo University, Ningbo 315211, China
- National Laboratory of Solid State Microstructures & School of Physics, Nanjing University, Nanjing 210093, China
| | - Cong-Cong Zhang
- Department of Physics, Ningbo University, Ningbo 315211, China
| | - Fu-Chun Zhang
- Kavli Institute for Theoretical Sciences & CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Qiang-Hua Wang
- National Laboratory of Solid State Microstructures & School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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9
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Abstract
High-quality single crystals are essentially needed for the investigation of the novel bulk properties of unconventional superconductors. The availability of such crystals grown by the floating-zone method has helped to unveil the unconventional superconductivity of the layered perovskite Sr2RuO4, which is considered as a strong candidate of a topological spin-triplet superconductor. Yet, recent progress of investigations urges further efforts to obtain ultimately high-quality crystalline samples. In this paper, we focus on the method of preparation of feed rods for the floating-zone melting and report on the improvements of the crystal growth. We present details of the improved methods used to obtain crystals with superconducting transition temperatures Tc that are consistently as high as 1.4 K, as well as the properties of these crystals.
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10
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Chung SB, Kim SK, Lee KH, Tserkovnyak Y. Cooper-Pair Spin Current in a Strontium Ruthenate Heterostructure. PHYSICAL REVIEW LETTERS 2018; 121:167001. [PMID: 30387633 DOI: 10.1103/physrevlett.121.167001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2018] [Revised: 07/05/2018] [Indexed: 06/08/2023]
Abstract
It has been recognized that the condensation of spin-triplet Cooper pairs requires not only broken gauge symmetry but also spin ordering as well. One consequence of this is the possibility of a Cooper-pair spin current analogous to the magnon spin current in magnetic insulators, the analogy also extending to the existence of the Gilbert damping of the collective spin-triplet dynamics. The recently fabricated heterostructure of the thin film of the itinerant ferromagnet SrRuO_{3} on bulk Sr_{2}RuO_{4}, the best-known candidate material for a spin-triplet superconductor, offers a promising platform for generating such spin current. We show how such heterostructure allows us to not only realize the long-range spin valve but also electrically drive the collective spin mode of the spin-triplet order parameter. Our proposal represents both a novel experimental realization of superfluid spin transport and a transport signature of the spin-triplet superconductivity therein.
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Affiliation(s)
- Suk Bum Chung
- Department of Physics, University of Seoul, Seoul 02504, Korea
- Natural Science Research Institute, University of Seoul, Seoul 02504, Korea
- Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul National University, Seoul 08826, Korea
- Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
| | - Se Kwon Kim
- Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA
- Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA
| | - Ki Hoon Lee
- Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul National University, Seoul 08826, Korea
- Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
| | - Yaroslav Tserkovnyak
- Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA
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11
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Huang W, Yao H. Possible Three-Dimensional Nematic Odd-Parity Superconductivity in Sr_{2}RuO_{4}. PHYSICAL REVIEW LETTERS 2018; 121:157002. [PMID: 30362809 DOI: 10.1103/physrevlett.121.157002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2018] [Indexed: 06/08/2023]
Abstract
The superconducting pairing in Sr_{2}RuO_{4} is widely considered to be chiral p wave with d[over →]_{k}∼(k_{x}+ik_{y})z[over ^], which belongs to the E_{u} representation of the crystalline D_{4h} group. However, this superconducting order appears hard to reconcile with a number of key experiments. In this Letter, based on symmetry analysis we discuss the possibility of odd-parity pairing with inherent three-dimensional character enforced by the interorbital interlayer coupling and the sizable spin-orbit coupling in the material. We focus on a yet unexplored E_{u} pairing, which contains finite (k_{z}x[over ^], k_{z}y[over ^]) component in the gap function. Under appropriate circumstances a novel time-reversal invariant nematic pairing can be realized. This nematic superconducting state could make contact with some puzzling observations on Sr_{2}RuO_{4}, such as the absence of spontaneous edge current and no evidence of split transitions under uniaxial strains.
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Affiliation(s)
- Wen Huang
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
| | - Hong Yao
- Institute for Advanced Study, Tsinghua University, Beijing 100084, China
- State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
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12
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Towards a Microscopic Theory of the Knight Shift in an Anisotropic, Multiband Type-II Superconductor. MAGNETOCHEMISTRY 2018. [DOI: 10.3390/magnetochemistry4010014] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Komendová L, Black-Schaffer AM. Odd-Frequency Superconductivity in Sr_{2}RuO_{4} Measured by Kerr Rotation. PHYSICAL REVIEW LETTERS 2017; 119:087001. [PMID: 28952759 DOI: 10.1103/physrevlett.119.087001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2017] [Indexed: 06/07/2023]
Abstract
We establish the existence of bulk odd-frequency superconductivity in Sr_{2}RuO_{4} and show that an intrinsic Kerr effect is direct evidence of this state. We use both general two- and three-orbital models, as well as a realistic tight-binding description of Sr_{2}RuO_{4} to demonstrate that odd-frequency pairing arises due to finite hybridization between different orbitals in the normal state, and is further enhanced by finite interorbital pairing.
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Affiliation(s)
- L Komendová
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden
| | - A M Black-Schaffer
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden
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14
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König EJ, Levchenko A. Kerr Effect from Diffractive Skew Scattering in Chiral p_{x}±ip_{y} Superconductors. PHYSICAL REVIEW LETTERS 2017; 118:027001. [PMID: 28128615 DOI: 10.1103/physrevlett.118.027001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2016] [Indexed: 06/06/2023]
Abstract
We calculate the temperature dependent anomalous ac Hall conductance σ_{H}(Ω,T) for a two-dimensional chiral p-wave superconductor. This quantity determines the polar Kerr effect, as it was observed in Sr_{2}RuO_{4} [J. Xia et al., Phys. Rev. Lett. 97, 167002 (2006)]. We concentrate on a single band model with an arbitrary isotropic dispersion relation subjected to rare, weak impurities treated in the Born approximation. As we explicitly show by detailed computation, previously omitted contributions to the extrinsic part of an anomalous Hall response, physically originating from diffractive skew scattering on quantum impurity complexes, appear to the leading order in the impurity concentration. By direct comparison with published results from the literature we demonstrate the relevance of our findings for the interpretation of the Kerr effect measurements in superconductors.
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Affiliation(s)
- Elio J König
- Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Alex Levchenko
- Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
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15
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Kallin C, Berlinsky J. Chiral superconductors. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:054502. [PMID: 27088452 DOI: 10.1088/0034-4885/79/5/054502] [Citation(s) in RCA: 56] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Chiral superconductivity is a striking quantum phenomenon in which an unconventional superconductor spontaneously develops an angular momentum and lowers its free energy by eliminating nodes in the gap. It is a topologically non-trivial state and, as such, exhibits distinctive topological modes at surfaces and defects. In this paper we discuss the current theory and experimental results on chiral superconductors, focusing on two of the best-studied systems, Sr2RuO4, which is thought to be a chiral triplet p-wave superconductor, and UPt3, which has two low-temperature superconducting phases (in zero magnetic field), the lower of which is believed to be chiral triplet f-wave. Other systems that may exhibit chiral superconductivity are also discussed. Key signatures of chiral superconductivity are surface currents and chiral Majorana modes, Majorana states in vortex cores, and the possibility of half-flux quantum vortices in the case of triplet pairing. Experimental evidence for chiral superconductivity from μSR, NMR, strain, polar Kerr effect and Josephson tunneling experiments are discussed.
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16
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Hall BE, Klemm RA. Microscopic model of the Knight shift in anisotropic and correlated metals. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:03LT01. [PMID: 26703085 DOI: 10.1088/0953-8984/28/3/03lt01] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We present a microscopic model of nuclear magnetic resonance in metals. The spin-1/2 local nucleus and its surrounding orbital electrons interact with the arbitrary constant B(0) and perpendicular time-oscillatory magnetic inductions B1(t) and with each other via an anisotropic hyperfine interaction. An Anderson-like Hamiltonian describes the excitations of the relevant occupied local orbital electrons into the conduction bands, each band described by an anisotropic effective mass with corresponding Landau orbits and an anisotropic spin g tensor. Local orbital electron correlation effects are included using the mean-field decoupling procedure of Lacroix. The Knight resonance frequency and corresponding linewidth shifts are evaluated to leading orders in the hyperfine and Anderson excitation interactions. While respectively proportional to (B1/B0)2 and a constant for weak B(0) >> B1, both highly anisotropic shifts depend strongly upon B(0) when a Landau level is near the Fermi energy. Electron correlations affect the anisotropy of the linewidth shift. The model is easily generalizable to arbitrary nuclear spin I.
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Affiliation(s)
- Bianca E Hall
- Department of Physics, University of Central Florida, Orlando, FL 32816-2385 USA
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17
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Snelder M, Golubov AA, Asano Y, Brinkman A. Observability of surface Andreev bound states in a topological insulator in proximity to an s-wave superconductor. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:315701. [PMID: 26189576 DOI: 10.1088/0953-8984/27/31/315701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
To guide experimental work on the search for Majorana zero-energy modes, we calculate the superconducting pairing symmetry of a three-dimensional topological insulator in combination with an s-wave superconductor. We show how the pairing symmetry changes across different topological regimes. We demonstrate that a dominant p-wave pairing relation is not sufficient to realise a Majorana zero-energy mode useful for quantum computation. Our main result is the relation between odd-frequency pairing and Majorana zero energy modes by using Green functions techniques in three-dimensional topological insulators in the so-called Majorana regime. We discuss thereafter how the pairing relations in the different regimes can be observed in the tunneling conductance of an s-wave proximised three-dimensional topological insulator. We discuss the necessity to incorporate a ferromagnetic insulator to localise the zero-energy bound state to the interface as a Majorana mode.
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Affiliation(s)
- M Snelder
- Faculty of Science and Technology and MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands
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Zhang J, Lörscher C, Gu Q, Klemm RA. Is the anisotropy of the upper critical field of Sr2RuO4 consistent with a helical p-wave state? JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:252201. [PMID: 24848586 DOI: 10.1088/0953-8984/26/25/252201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We calculate the angular and temperature T dependencies of the upper critical field Hc2(θ, ϕ, T) for the C4v point group helical p-wave states, assuming a single uniaxial ellipsoidal Fermi surface, Pauli limiting and strong spin-orbit coupling that locks the spin-triplet d-vectors onto the layers. Good fits to the Sr2RuO4 Hc2,a(θ, T) data of Kittaka et al (2009 Phys. Rev. B 80 174514) are obtained. Helical states with d(k) =kˆxxˆ −kˆyy and kˆyxˆ +kˆxy (or kˆxxˆ +kˆyyˆ and kˆyxˆ -kˆxyˆ ) produce Hc2(90°, ϕ, T) that greatly exceed (or do not exhibit) the fourfold azimuthal anisotropy magnitudes observed in Sr2RuO4 by Kittaka et al and by Mao et al (2000 Phys. Rev. Lett. 84 991), respectively.
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Affiliation(s)
- J Zhang
- Department of Physics, University of Science and Technology Beijing, Beijing 100083, People's Republic of China
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19
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Hicks CW, Brodsky DO, Yelland EA, Gibbs AS, Bruin JAN, Barber ME, Edkins SD, Nishimura K, Yonezawa S, Maeno Y, Mackenzie AP. Strong Increase of Tc of Sr2RuO4 Under Both Tensile and Compressive Strain. Science 2014; 344:283-5. [DOI: 10.1126/science.1248292] [Citation(s) in RCA: 222] [Impact Index Per Article: 22.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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20
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Huo JW, Rice TM, Zhang FC. Spin density wave fluctuations and p-wave pairing in Sr2RuO4. PHYSICAL REVIEW LETTERS 2013; 110:167003. [PMID: 23679633 DOI: 10.1103/physrevlett.110.167003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2013] [Indexed: 06/02/2023]
Abstract
Recently, a debate has arisen over which of the two distinct parts of the Fermi surface of Sr(2)RuO(4) is the active part for the chiral p-wave superconductivity exhibited. Early theories proposed p-wave pairing on the two-dimensional γ band, whereas a recent proposal focuses on the one-dimensional (α, β) bands whose nesting pockets are the source of the strong incommensurate spin density wave (SDW) fluctuations. We apply a renormalization group theory to study quasi-one-dimensional repulsive Hubbard chains and explain the form of SDW fluctuations, reconciling the absence of long-range order with their nesting Fermi surface. The mutual exclusion of p-wave pairing and SDW fluctuations in repulsive Hubbard chains favors the assignment of the two-dimensional γ band as the source of p-wave pairing.
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Affiliation(s)
- Jia-Wei Huo
- Department of Physics and Centre of Theoretical and Computational Physics, The University of Hong Kong, Hong Kong SAR, China
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21
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Yonezawa S, Kajikawa T, Maeno Y. First-order superconducting transition of Sr2RuO4. PHYSICAL REVIEW LETTERS 2013; 110:077003. [PMID: 25166397 DOI: 10.1103/physrevlett.110.077003] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2012] [Revised: 10/31/2012] [Indexed: 06/03/2023]
Abstract
By means of the magnetocaloric effect, we examine the nature of the superconducting-normal (S-N) transition of Sr(2)RuO(4), a most promising candidate for a spin-triplet superconductor. We provide thermodynamic evidence that the S-N transition of this oxide is of first order below approximately 0.8 K and only for magnetic field directions very close to the conducting plane, in clear contrast to the ordinary type-II superconductors exhibiting second-order S-N transitions. The entropy release across the transition at 0.2 K is 10% of the normal-state entropy. Our result urges an introduction of a new mechanism to break superconductivity by magnetic field.
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Affiliation(s)
- Shingo Yonezawa
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Tomohiro Kajikawa
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Yoshiteru Maeno
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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22
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Kallin C. Chiral p-wave order in Sr2RuO4. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:042501. [PMID: 22790504 DOI: 10.1088/0034-4885/75/4/042501] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Shortly after the discovery in 1994 of superconductivity in Sr(2)RuO(4), it was proposed on theoretical grounds that the superconducting state may have chiral p-wave symmetry analogous to the A phase of superfluid (3)He. Substantial experimental evidence has since accumulated in favor of this pairing symmetry, including several interesting recent results related to broken time-reversal symmetry (BTRS) and vortices with half of the usual superconducting flux quantum. Great interest surrounds the possibility of chiral p-wave order in Sr(2)RuO(4), since this state may exhibit topological order analogous to that of a quantum Hall state, and can support such exotic physics as Majorana fermions and non-Abelian winding statistics, which have been proposed as one route to a quantum computer. However, serious discrepancies remain in trying to connect the experimental results to theoretical predictions for chiral p-wave order. In this paper, I review a broad range of experiments on Sr(2)RuO(4) that are sensitive to p-wave pairing, triplet superconductivity and time-reversal symmetry breaking and compare these experiments to each other and to theoretical predictions. In this context, the evidence for triplet pairing is strong, although some puzzles remain. The 'smoking gun' experimental results for chiral p-wave order, those which directly look for evidence of BTRS in the superconducting state of Sr(2)RuO(4), are most perplexing when the results are compared with each other and to theoretical predictions. Consequently, the case for chiral p-wave superconductivity in Sr(2)RuO(4) remains unresolved, suggesting the need to consider either significant modifications to the standard chiral p-wave models or possible alternative pairing symmetries. Recent ideas along these lines are discussed.
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Affiliation(s)
- Catherine Kallin
- Department of Physics and Astronomy, McMaster University, Hamilton ON L8S 4M1, Canada.
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23
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Rozbicki EJ, Annett JF, Souquet JR, Mackenzie AP. Spin-orbit coupling and k-dependent Zeeman splitting in strontium ruthenate. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:094201. [PMID: 21339554 DOI: 10.1088/0953-8984/23/9/094201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We compare the relativistic LDA Fermi surface of Sr2RuO4 to direct experimental evidence of spin-orbit coupling from de Haas-van Alphen experiments. The k-dependence of the Zeeman splitting at the Fermi surface is modelled with a range of tight binding models of the quasi-particle bands. Only a very restricted class of parameters are consistent with evidence from the de Haas-van Alphen experiments for a strong k-dependent Zeeman splitting on the alpha Fermi surface sheet. The bare LDA bands do not lead to such a strong k-dependent Zeeman splitting on this sheet, and this suggests that additional charge transfer takes place as suggested by DMFT calculations. We conclude that the overall scale of the spin-orbit coupling must be at least as large as the several hundred kelvin deduced in previous work, and that this must call into question any theory postulating rotation of the triplet d-vector at small magnetic fields.
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Affiliation(s)
- Emil J Rozbicki
- Scottish Universities Physics Alliance, School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK
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24
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Kallin C, Berlinsky AJ. Is Sr(2)RuO(4) a chiral p-wave superconductor? JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2009; 21:164210. [PMID: 21825390 DOI: 10.1088/0953-8984/21/16/164210] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Much excitement surrounds the possibility that strontium ruthenate exhibits chiral p-wave superconducting order. Such order would be a solid state analogue of the A phase of He-3, with the potential for leading to exotic physics relevant to quantum computing. We take a critical look at the evidence for such time reversal symmetry breaking order. The possible superconducting order parameter symmetries and the evidence for and against chiral p-wave order are reviewed, with an emphasis on the most recent theoretical predictions and experimental observations. In particular, attempts to reconcile experimental observations and theoretical predictions for the spontaneous supercurrents expected at sample edges and domain walls of a chiral p-wave superconductor and for the polar Kerr effect, a key signature of broken time reversal symmetry, are discussed.
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Affiliation(s)
- C Kallin
- Department of Physics and Astronomy, McMaster University, Hamilton, ON, L8S 4M1, Canada
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25
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Chung SB, Bluhm H, Kim EA. Stability of half-quantum vortices in p(x)+ip(y) superconductors. PHYSICAL REVIEW LETTERS 2007; 99:197002. [PMID: 18233107 DOI: 10.1103/physrevlett.99.197002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2007] [Indexed: 05/25/2023]
Abstract
We consider the stability conditions for half-quantum vortices in a quasi-two-dimensional p{x}+ip{y} superconductor (such as Sr2RuO4 is believed to be). The predicted exotic nature of these excitations has recently attracted much attention, but they have not been observed yet. We emphasize that an isolated half-quantum vortex has a divergent energy cost in the bulk due to its unscreened spin current, which requires two half-quantum vortices with opposite spin winding to pair. We show that the stability of such a pair is enhanced when the ratio of spin superfluid density to superfluid density rho{sp}/rho{s} is small. We propose using various mesoscopic geometries to stabilize and observe these exotic excitations.
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Affiliation(s)
- Suk Bum Chung
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
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26
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Rostunov T, Demler E, Georges A. Spin-wave contribution to the nuclear spin-lattice relaxation in triplet superconductors. PHYSICAL REVIEW LETTERS 2006; 96:077002. [PMID: 16606127 DOI: 10.1103/physrevlett.96.077002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2005] [Indexed: 05/08/2023]
Abstract
We discuss collective spin-wave excitations in triplet superconductors with an easy axis anisotropy for the order parameter. Using a microscopic model for interacting electrons, we estimate the frequency of such excitations in Bechgaard salts and ruthenate superconductors to be 1 and 20 GHz, respectively. We introduce an effective bosonic model to describe spin-wave excitations and calculate their contribution to the nuclear spin-lattice relaxation rate. We find that, in the experimentally relevant regime of temperatures, this mechanism leads to the power law scaling of 1/T1 with temperature. For two- and three-dimensional systems, the scaling exponents are 3 and 5, respectively. We discuss experimental manifestations of the spin-wave mechanism of the nuclear spin-lattice relaxation.
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Affiliation(s)
- Timofey Rostunov
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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27
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Abstract
Phase-sensitive measurements were made on Sr2RuO4 to establish unambiguously the odd-parity pairing in this material. The critical current of Au(0.5)In(0.5)-Sr2RuO4 superconducting quantum interference devices prepared on Sr2RuO4 single crystals was found to be a maximum for devices with junctions on the same side of the crystal and a minimum for devices with junctions on opposite sides, in the limit of zero magnetic flux; these findings indicate that the phase of the superconducting order parameter in Sr2RuO4 changes by pi under inversion. This result verifies the odd-parity pairing symmetry and the formation of spin-triplet Cooper pairs in Sr2RuO4.
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Affiliation(s)
- K D Nelson
- Department of Physics, Pennsylvania State University, University Park, PA 16802, USA
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28
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Murakawa H, Ishida K, Kitagawa K, Mao ZQ, Maeno Y. Measurement of the 101Ru-Knight shift of superconducting Sr2RuO4 in a parallel magnetic field. PHYSICAL REVIEW LETTERS 2004; 93:167004. [PMID: 15525023 DOI: 10.1103/physrevlett.93.167004] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2004] [Indexed: 05/24/2023]
Abstract
101Ru-Knight shift (101K) in the spin-triplet superconductor Sr2RuO4 was measured under magnetic fields parallel to the c axis (perpendicular to the RuO2 plane), which is the promising superconducting (SC) d-vector direction in a zero field. We succeeded in measuring K(c) in the field range from 200 to 1200 Oe and at temperatures down to 80 mK, using nuclear-quadrupole-resonance spectra. We found that (101)K(c) is invariant with respect to the field and temperature on passing through H(c2) and T(c) above 200 Oe. This indicates that the spin susceptibility along the c axis does not change in the SC state, at least, in the field greater than 200 Oe. The results imply that the SC d vector is in the RuO2 plane when the magnetic field is applied to the c axis.
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Affiliation(s)
- H Murakawa
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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29
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Deguchi K, Mao ZQ, Yaguchi H, Maeno Y. Gap structure of the spin-triplet superconductor Sr2RuO4 determined from the field-orientation dependence of the specific heat. PHYSICAL REVIEW LETTERS 2004; 92:047002. [PMID: 14995396 DOI: 10.1103/physrevlett.92.047002] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2003] [Indexed: 05/24/2023]
Abstract
We report the field-orientation dependent specific heat of the spin-triplet superconductor Sr2RuO4 under the magnetic field aligned parallel to the RuO2 planes with high accuracy. Below about 0.3 K, striking fourfold oscillations of the density of states reflecting the superconducting gap structure have been resolved for the first time. We also obtained strong evidence of multiband superconductivity and concluded that the superconducting gap in the active band, responsible for the superconducting instability, is modulated with a minimum along the [100] direction.
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Affiliation(s)
- K Deguchi
- Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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30
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Suzuki M, Tanatar MA, Kikugawa N, Mao ZQ, Maeno Y, Ishiguro T. Universal heat transport in Sr2RuO4. PHYSICAL REVIEW LETTERS 2002; 88:227004. [PMID: 12059449 DOI: 10.1103/physrevlett.88.227004] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2002] [Indexed: 05/23/2023]
Abstract
We present the temperature dependence of the thermal conductivity kappa(T) of the unconventional superconductor Sr2RuO4 down to low temperatures ( approximately 100 mK). In the T-->0 K limit we found a finite residual term in kappa/T, providing clear evidence for the superconducting state with an unconventional pairing. The residual term remains unchanged for samples with different T(c), demonstrating the universal character of heat transport in this spin-triplet superconductor. The low-temperature behavior of kappa suggests the strong impurity scattering with a phase shift close to pi/2. A criterion for the observation of universality is experimentally deduced.
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Affiliation(s)
- M Suzuki
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
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31
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Santi G, Dugdale SB, Jarlborg T. Longitudinal spin fluctuations and superconductivity in ferromagnetic ZrZn2 from Ab initio calculations. PHYSICAL REVIEW LETTERS 2001; 87:247004. [PMID: 11736533 DOI: 10.1103/physrevlett.87.247004] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2001] [Indexed: 05/23/2023]
Abstract
The recent discovery of superconductivity coexisting with weak itinerant ferromagnetism in the d-electron intermetallic compound ZrZn2 strongly suggests spin-fluctuation mediated superconductivity. Ab initio electronic structure calculations of the Fermi surface and generalized susceptibilities are performed to investigate the viability of longitudinal spin-fluctuation-induced spin-triplet superconductivity in the ferromagnetic state. The critical temperature is estimated to be of the order of 1 K. Additionally, it is shown that in spite of a strong electron-phonon coupling ( lambda(ph) = 0.7), conventional s-wave superconductivity is inhibited by the presence of strong spin fluctuations.
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Affiliation(s)
- G Santi
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
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32
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Morr DK, Trautman PF, Graf MJ. Resonance peak in Sr(2)RuO(4): signature of spin triplet pairing. PHYSICAL REVIEW LETTERS 2001; 86:5978-5981. [PMID: 11415408 DOI: 10.1103/physrevlett.86.5978] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2000] [Indexed: 05/23/2023]
Abstract
We study the dynamical spin susceptibility, chi(q,omega), in the normal and superconducting states of Sr(2)RuO(4). In the normal state, we find a peak in the vicinity of Q(i) approximately (0.72 pi,0.72 pi) in agreement with recent inelastic neutron scattering experiments. We predict that for spin triplet pairing in the superconducting state a resonance peak appears in the out-of-plane component of chi, but is absent in the in-plane component. In contrast, no resonance peak is expected for spin singlet pairing.
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Affiliation(s)
- D K Morr
- Theoretical Division, MS B262, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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33
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Lupien C, MacFarlane WA, Proust C, Taillefer L, Mao ZQ, Maeno Y. Ultrasound attenuation in Sr(2)RuO(4): an angle-resolved study of the superconducting gap function. PHYSICAL REVIEW LETTERS 2001; 86:5986-5989. [PMID: 11415410 DOI: 10.1103/physrevlett.86.5986] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2001] [Indexed: 05/23/2023]
Abstract
We present a study of the electronic ultrasound attenuation alpha in the unconventional superconductor Sr(2)RuO(4). The power law behavior of alpha at temperatures down to T(c)/30 clearly indicates the presence of nodes in the gap. In the normal state, we find an enormous anisotropy of alpha in the basal plane of the tetragonal structure. In the superconducting state, the temperature dependence of alpha also exhibits significant anisotropy. We discuss these results in relation to possible gap functions.
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Affiliation(s)
- C Lupien
- Canadian Institute for Advanced Research, Department of Physics, University of Toronto, Toronto, Canada M5S 1A7
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34
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Tanatar MA, Suzuki M, Nagai S, Mao ZQ, Maeno Y, Ishiguro T. Anisotropy of magnetothermal conductivity in Sr2RuO4. PHYSICAL REVIEW LETTERS 2001; 86:2649-2652. [PMID: 11290002 DOI: 10.1103/physrevlett.86.2649] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2000] [Indexed: 05/23/2023]
Abstract
The dependence of in-plane and interplane thermal conductivities of Sr2RuO4 on temperature, as well as magnetic field strength and orientation, is reported. We found no notable anisotropy in the thermal conductivity for the magnetic field rotation parallel to the conducting plane in the whole range of experimental temperatures and fields, except in the vicinity of the upper critical field H(c2), where the anisotropy of the H(c2) itself plays a dominant role. This finding imposes strong constraints on the possible models of superconductivity in Sr2RuO4 and supports the existence of a superconducting gap with a line of nodes running orthogonal to the Fermi surface cylinder.
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Affiliation(s)
- M A Tanatar
- Department of Physics, Kyoto University, Japan.
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