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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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Khasanov R, Ramires A, Grinenko V, Shipulin I, Kikugawa N, Sokolov DA, Krieger JA, Hicken TJ, Maeno Y, Luetkens H, Guguchia Z. In-Plane Magnetic Penetration Depth in Sr_{2}RuO_{4}: Muon-Spin Rotation and Relaxation Study. PHYSICAL REVIEW LETTERS 2023; 131:236001. [PMID: 38134793 DOI: 10.1103/physrevlett.131.236001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2023] [Revised: 10/02/2023] [Accepted: 10/03/2023] [Indexed: 12/24/2023]
Abstract
We report on measurements of the in-plane magnetic penetration depth (λ_{ab}) in single crystals of Sr_{2}RuO_{4} down to ≃0.015 K by means of muon-spin rotation-relaxation. The linear temperature dependence of λ_{ab}^{-2} for T≲0.7 K suggests the presence of nodes in the superconducting gap. This statement is further substantiated by observation of the Volovik effect, i.e., the reduction of λ_{ab}^{-2} as a function of the applied magnetic field. The experimental zero-field and zero-temperature value of λ_{ab}=124(3) nm agrees with λ_{ab}≃130 nm, calculated based on results of electronic structure measurements reported in A. Tamai et al. [High-resolution photoemission on Sr_{2}RuO_{4} reveals correlation-enhanced effective spin-orbit coupling and dominantly local self-energies, Phys. Rev. X 9, 021048 (2019)PRXHAE2160-330810.1103/PhysRevX.9.021048]. Our analysis reveals that a simple nodal superconducting energy gap, described by the lowest possible harmonic of a gap function, does not capture the dependence of λ_{ab}^{-2} on T, so the higher angular harmonics of the energy gap function need to be introduced.
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Affiliation(s)
- Rustem Khasanov
- Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
| | - Aline Ramires
- Laboratory for Theoretical and Computational Physics, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
| | - Vadim Grinenko
- Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 201210, China
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Ilya Shipulin
- Leibniz Institute for Solid State and Materials Research, 01069 Dresden, Germany
| | - Naoki Kikugawa
- National Institute for Materials Science, Tsukuba, Ibaraki 305-0003, Japan
| | - Dmitry A Sokolov
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Strasse 40, 01187 Dresden, Germany
| | - Jonas A Krieger
- Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
| | - Thomas J Hicken
- Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
| | - Yoshiteru Maeno
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
- Toyota Riken - Kyoto University Research Center (TRiKUC), Kyoto 606-8501, Japan
| | - Hubertus Luetkens
- Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
| | - Zurab Guguchia
- Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
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3
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Azari N, Yakovlev M, Rye N, Dunsiger SR, Sundar S, Bordelon MM, Thomas SM, Thompson JD, Rosa PFS, Sonier JE. Absence of Spontaneous Magnetic Fields due to Time-Reversal Symmetry Breaking in Bulk Superconducting UTe_{2}. PHYSICAL REVIEW LETTERS 2023; 131:226504. [PMID: 38101387 DOI: 10.1103/physrevlett.131.226504] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2023] [Accepted: 10/18/2023] [Indexed: 12/17/2023]
Abstract
We have investigated the low-temperature local magnetic properties in the bulk of molten salt-flux (MSF)-grown single crystals of the candidate odd-parity superconductor UTe_{2} by zero-field muon spin relaxation (μSR). In contrast to previous μSR studies of UTe_{2} single crystals grown by a chemical vapor transport method, we find no evidence of magnetic clusters or electronic moments fluctuating slow enough to cause a discernible relaxation of the zero-field μSR asymmetry spectrum. Consequently, our measurements on MSF-grown single crystals rule out the generation of spontaneous magnetic fields in the bulk that would occur near impurities or lattice defects if the superconducting state of UTe_{2} breaks time-reversal symmetry. This result suggests that UTe_{2} is characterized by a single-component superconducting order parameter.
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Affiliation(s)
- N Azari
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - M Yakovlev
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - N Rye
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
| | - S R Dunsiger
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
- Centre for Molecular and Materials Science, TRIUMF, Vancouver, British Columbia V6T 2A3, Canada
| | - S Sundar
- Scottish Universities Physics Alliance, School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS, United Kingdom
| | - M M Bordelon
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - S M Thomas
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - J D Thompson
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - P F S Rosa
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - J E Sonier
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
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Curran PJ, Bending SJ, Gibbs AS, Mackenzie AP. The search for spontaneous edge currents in Sr 2RuO 4 mesa structures with controlled geometrical shapes. Sci Rep 2023; 13:12652. [PMID: 37542057 PMCID: PMC10403554 DOI: 10.1038/s41598-023-39590-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Accepted: 07/27/2023] [Indexed: 08/06/2023] Open
Abstract
Scanning Hall microscopy has been used to search for spontaneous edge fields in geometrically shaped mesa structures etched into the ab surface of Sr2RuO4 single crystals in order to test recent theories of the direction of edge current flow as a function of facet orientation and band filling. We find no evidence for spontaneous edge fields in any of our mesa structures above our experimental noise floor of ± 25 mG. We do, however, observe pronounced vortex clustering at low fields and temperatures, consistent with the established semi-Meissner scenario whereby a long range attractive component to the vortex-vortex interaction arises due, for example, to the multiband nature of the superconductivity. We also see clear evidence for the formation of a square vortex lattice inside square mesa structures above 1.3 K. Our results are discussed in terms of recent relevant experimental results and theoretical predictions.
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Affiliation(s)
- P J Curran
- Department of Physics, University of Bath, Claverton Down, Bath, BA2 7AY, UK
| | - S J Bending
- Department of Physics, University of Bath, Claverton Down, Bath, BA2 7AY, UK.
| | - A S Gibbs
- School of Chemistry, University of St. Andrews, St. Andrews, KY16 9ST, UK
| | - A P Mackenzie
- School of Physics and Astronomy, University of St. Andrews, St. Andrews, KY16 9SS, UK
- Max-Planck Institute for Chemical Physics of Solids, 01187, Dresden, Germany
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Kim B, Khmelevskyi S, Franchini C, Mazin II. Suppressed Fluctuations as the Origin of the Static Magnetic Order in Strained Sr_{2}RuO_{4}. PHYSICAL REVIEW LETTERS 2023; 130:026702. [PMID: 36706403 DOI: 10.1103/physrevlett.130.026702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2022] [Revised: 10/04/2022] [Accepted: 12/21/2022] [Indexed: 06/18/2023]
Abstract
Combining first-principles density-functional calculations and Moriya's self-consistent renormalization theory, we explain the recently reported counterintuitive appearance of an ordered magnetic state in uniaxially strained Sr_{2}RuO_{4} beyond the Lifshitz transition. We show that strain weakens the quantum spin fluctuations, which destroy the static order, more strongly than the tendency to magnetism. A different rate of decrease of the spin fluctuations vs magnetic stabilization energy promotes the onset of a static magnetic order beyond a critical strain.
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Affiliation(s)
- Bongjae Kim
- Department of Physics, Kunsan National University, Gunsan 54150, Korea
| | - Sergii Khmelevskyi
- Center for Computational Materials Science, Institute for Applied Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 1040 Vienna, Austria
| | - Cesare Franchini
- University of Vienna, Faculty of Physics and Center for Computational Materials Science, Vienna A-1090, Austria
- Dipartimento di Fisica e Astronomia, Università di Bologna, 40127 Bologna, Italy
| | - I I Mazin
- Department of Physics and Astronomy, George Mason University, Fairfax, Virginia 22030, USA
- Quantum Science and Engineering Center, George Mason University, Fairfax, Virginia 22030, USA
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6
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Yazdani-Hamid M. Effect of nonequilibrium order parameter on the optical response of superconductor Sr 2RuO 4. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:455603. [PMID: 36041424 DOI: 10.1088/1361-648x/ac8dd2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2022] [Accepted: 08/30/2022] [Indexed: 06/15/2023]
Abstract
The breaking of time reversal symmetry of the superconducting pairings is expected to manifest itself through characteristic transport properties such as a non-zero Kerr angle which provides fingerprint of the quantum anomalous Hall state. In this work, we theoretically study the Kerr effect or the Hall-type response and also consider how this response is modified by the nonequilibrium shape of order parameter of the superconducting state due to the influence of the electromagnetic radiation for the most favorable candidates of chiral superconducting order parameters and of the non-chiral states in strontium ruthenate (Sr2RuO4). The unique sensitivity of the Hall-type response introduced above to different types of pairings can be used to identify the most favored pairing which is a serious doubt on the superconducting state of this material.
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Affiliation(s)
- Meghdad Yazdani-Hamid
- Department of Physics, Ayatollah Boroujerdi University, Boroujerd, Lorestan 65151-36111, Iran
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7
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Jerzembeck F, Røising HS, Steppke A, Rosner H, Sokolov DA, Kikugawa N, Scaffidi T, Simon SH, Mackenzie AP, Hicks CW. The superconductivity of Sr 2RuO 4 under c-axis uniaxial stress. Nat Commun 2022; 13:4596. [PMID: 35933412 PMCID: PMC9357014 DOI: 10.1038/s41467-022-32177-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2022] [Accepted: 07/19/2022] [Indexed: 11/15/2022] Open
Abstract
Applying in-plane uniaxial pressure to strongly correlated low-dimensional systems has been shown to tune the electronic structure dramatically. For example, the unconventional superconductor Sr2RuO4 can be tuned through a single Van Hove point, resulting in strong enhancement of both Tc and Hc2. Out-of-plane (c axis) uniaxial pressure is expected to tune the quasi-two-dimensional structure even more strongly, by pushing it towards two Van Hove points simultaneously. Here, we achieve a record uniaxial stress of 3.2 GPa along the c axis of Sr2RuO4. Hc2 increases, as expected for increasing density of states, but unexpectedly Tc falls. As a first attempt to explain this result, we present three-dimensional calculations in the weak interaction limit. We find that within the weak-coupling framework there is no single order parameter that can account for the contrasting effects of in-plane versus c-axis uniaxial stress, which makes this new result a strong constraint on theories of the superconductivity of Sr2RuO4. In the superconductor Sr2RuO4, in-plane strain is known to enhance both the superconducting transition temperature Tc and upper critical field Hc2, but the effect of out-of-plane strain has not been studied. Here, the authors find that Hc2 is enhanced under out-of-plane strain, but Tc unexpectedly decreases.
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Affiliation(s)
- Fabian Jerzembeck
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Str 40, 01187, Dresden, Germany.
| | - Henrik S Røising
- Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SE-106 91, Stockholm, Sweden
| | - Alexander Steppke
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Str 40, 01187, Dresden, Germany
| | - Helge Rosner
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Str 40, 01187, Dresden, Germany
| | - Dmitry A Sokolov
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Str 40, 01187, Dresden, Germany
| | - Naoki Kikugawa
- National Institute for Materials Science, Tsukuba, 305-0003, Japan
| | - Thomas Scaffidi
- Department of Physics, University of Toronto, Toronto, ON, M5S 1A7, Canada.,Department of Physics and Astronomy, University of California, Irvine, CA, 92697, USA
| | - Steven H Simon
- Rudolf Peierls Center for Theoretical Physics, Oxford, OX1 3PU, UK
| | - Andrew P Mackenzie
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Str 40, 01187, Dresden, Germany. .,Scottish Universities Physics Alliance, School of Physics and Astronomy, University of St. Andrews, St. Andrews, KY16 9SS, UK.
| | - Clifford W Hicks
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Str 40, 01187, Dresden, Germany. .,School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, UK.
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Abstract
Abstract
Beta-detected NMR is a type of nuclear magnetic resonance that uses the asymmetric property of radioactive beta decay to provide a “nuclear” detection scheme. It is vastly more sensitive than conventional NMR on a per nuclear spin basis but requires a suitable radioisotope. I briefly present the general aspects of the method and its implementation at TRIUMF, where ion implantation of the NMR radioisotope is used to study a variety of samples including crystalline solids and thin films, and more recently, soft matter and even room temperature ionic liquids. Finally, I review the progress of the TRIUMF βNMR program in the period 2015–2021.
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Affiliation(s)
- W. Andrew MacFarlane
- Department of Chemistry , University of British Columbia , Vancouver , BC , 2036, Main Mall, V6T 1Z1 , Canada
- Stewart Blusson Quantum Matter Institute, University of British Columbia, , Vancouver , BC , 2355, East Mall, V6T 1Z4 , Canada
- TRUMF, , Vancouver , BC , 4004 , Wesbrook Mall , V6T 2A3 , Canada
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9
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Nayak S, Batra N, Kumar S. Pairing symmetries in the Zeeman-coupled extended attractive Hubbard model. Sci Rep 2021; 11:22724. [PMID: 34811458 PMCID: PMC8609039 DOI: 10.1038/s41598-021-02175-5] [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: 07/13/2021] [Accepted: 10/22/2021] [Indexed: 11/10/2022] Open
Abstract
By introducing the possibility of equal- and opposite-spin pairings concurrently, we show that the ground state of the extended attractive Hubbard model (EAHM) exhibits rich phase diagrams with a variety of singlet, triplet, and mixed parity superconducting orders. We study the competition between these superconducting pairing symmetries invoking an unrestricted Hartree-Fock-Bogoliubov-de Gennes (HFBdG) mean-field approach, and we use the d-vector formalism to characterize the nature of the stabilized superconducting orders. We discover that, while all other types of orders are suppressed, a non-unitary triplet order dominates the phase space in the presence of an in-plane external magnetic field. We also find a transition between a non-unitary to unitary superconducting phase driven by the change in average electron density. Our results serve as a reference for identifying and understanding the nature of superconductivity based on the symmetries of the pairing correlations. The results further highlight that EAHM is a suitable effective model for describing most of the pairing symmetries discovered in different materials.
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Affiliation(s)
- Swagatam Nayak
- Department of Physical Sciences, Indian Institute of Science Education and Research Mohali, PO 140306, Mohali, Manauli, India
- School of Physical Sciences, National Institute of Science Education and Research (NISER), Bhubaneswar, Odisha, 752050, India
| | - Navketan Batra
- Department of Physical Sciences, Indian Institute of Science Education and Research Mohali, PO 140306, Mohali, Manauli, India
- Department of Physics, Brown University, Providence, RI, 02912, USA
| | - Sanjeev Kumar
- Department of Physical Sciences, Indian Institute of Science Education and Research Mohali, PO 140306, Mohali, Manauli, India.
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