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Babaev E, Svistunov B. Hydrodynamics of Borromean Counterfluids. PHYSICAL REVIEW LETTERS 2024; 133:026001. [PMID: 39073945 DOI: 10.1103/physrevlett.133.026001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2023] [Revised: 02/19/2024] [Accepted: 05/31/2024] [Indexed: 07/31/2024]
Abstract
Counterflow superfluidity in a system with N≥3 components is distinctively different from the N=2 case. The key feature is the difference between the number (N) of elementary vortex excitations and the number (N-1) of independent branches of phonon modes, that is, the number of superfluid modes is larger than the number of ordered phase variables. We formulate a hydrodynamic theory of this state. We show how all the dynamical and statistical aspects of this ("Borromean") type of ordering are naturally described by effective N-component theory featuring compact-gauge invariance. We also discuss how off diagonal intercomponent couplings convert the Borromean supercounterfluid into a Borromean insulator, with an emphasis on the properties of a nontrivial state with broken time-reversal symmetry.
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Affiliation(s)
- Egor Babaev
- Department of Physics, KTH Royal Institute of Technology, Stockholm SE-10691, Sweden
- Department of Physics, Wallenberg Initiative Materials Science for Sustainability, The Royal Institute of Technology, Stockholm SE-10691, Sweden
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Iguchi Y, Shi RA, Kihou K, Lee CH, Barkman M, Benfenati AL, Grinenko V, Babaev E, Moler KA. Superconducting vortices carrying a temperature-dependent fraction of the flux quantum. Science 2023:eabp9979. [PMID: 37262195 DOI: 10.1126/science.abp9979] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Accepted: 05/15/2023] [Indexed: 06/03/2023]
Abstract
Magnetic field penetrates type-II bulk superconductors by forming quantum vortices that enclose a magnetic flux equal to the magnetic flux quantum. The flux quantum is a universal quantity that depends only on fundamental constants. Here we investigate isolated vortices in the hole-overdoped Ba1-xKxFe2As2 (x = 0.77) by using scanning superconducting quantum interference device (SQUID) magnetometry. In many locations, we observed vortices that carried only part of a flux quantum, with a magnitude that varied continuously with temperature. We interpret these features as quantum vortices with non-universally quantized (fractional) magnetic flux whose magnitude is determined by the temperature-dependent parameters of a multiband superconductor. The demonstrated mobility and manipulability of the fractional vortices may enable applications in fluxonics-based computing.
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Affiliation(s)
- Yusuke Iguchi
- Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
| | - Ruby A Shi
- Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
- Department of Physics, Stanford University, Stanford, CA 94305, USA
| | - Kunihiro Kihou
- National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan
| | - Chul-Ho Lee
- National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan
| | - Mats Barkman
- Department of Physics, Royal Institute of Technology, SE-106 91 Stockholm, Sweden
| | - Andrea L Benfenati
- Department of Physics, Royal Institute of Technology, SE-106 91 Stockholm, Sweden
| | - Vadim Grinenko
- Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 201210, China
| | - Egor Babaev
- Department of Physics, Royal Institute of Technology, SE-106 91 Stockholm, Sweden
| | - Kathryn A Moler
- Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
- Department of Physics, Stanford University, Stanford, CA 94305, USA
- Department of Applied Physics, Stanford University, Stanford, CA 94305, USA
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Garaud J, Babaev E. Effective Model and Magnetic Properties of the Resistive Electron Quadrupling State. PHYSICAL REVIEW LETTERS 2022; 129:087602. [PMID: 36053680 DOI: 10.1103/physrevlett.129.087602] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2022] [Revised: 05/09/2022] [Accepted: 06/30/2022] [Indexed: 06/15/2023]
Abstract
Recent experiments [Grinenko et al. Nat. Phys. 17, 1254 (2021)NPAHAX1745-247310.1038/s41567-021-01350-9] reported the observation of a condensate of four-fermion composites. This is a resistive state that spontaneously breaks the time-reversal symmetry, leading to unconventional magnetic properties, detected in muon spin rotation experiments and by the appearance of a spontaneous Nernst effect. In this Letter, we derive an effective model for the four-fermion order parameter that describes the observed spontaneous magnetic fields in this state. We show that this model, which is alike to the Faddeev-Skyrme model can host skyrmions: magnetic-flux-carrying topological excitations.
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Affiliation(s)
- Julien Garaud
- Institut Denis Poisson CNRS-UMR 7013, Université de Tours, 37200 Tours, France
- Nordita, Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden
| | - Egor Babaev
- Department of Physics, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden
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Probing pairing symmetry in multi-band superconductors by quasiparticle interference. Sci Rep 2018; 8:11594. [PMID: 30072766 PMCID: PMC6072734 DOI: 10.1038/s41598-018-30045-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2018] [Accepted: 07/19/2018] [Indexed: 11/08/2022] Open
Abstract
We study momentum and energy dependencies of the quasiparticle interference (QPI) response function in multiband superconductors in the framework of the strong-coupling Eliashberg approach. Within an effective two-band model we study the s± and s++ symmetry cases, corresponding to opposite or equal signs of the order parameters in the bands. We demonstrate that the momentum dependence of the QPI function is strikingly different for s± and s++ symmetries of the order parameter at energies close to the small gap. At the same time, the QPI response becomes indistinguishable for both symmetries at higher energies around the large gap. This result may guide future experiments on probing pairing symmetry in iron pnictides as well as in other unconventional superconductors.
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Zyuzin AA, Garaud J, Babaev E. Nematic Skyrmions in Odd-Parity Superconductors. PHYSICAL REVIEW LETTERS 2017; 119:167001. [PMID: 29099226 DOI: 10.1103/physrevlett.119.167001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2017] [Indexed: 06/07/2023]
Abstract
We study topological excitations in two-component nematic superconductors, with a particular focus on Cu_{x}Bi_{2}Se_{3} as a candidate material. We find that the lowest-energy topological excitations are coreless vortices: a bound state of two spatially separated half-quantum vortices. These objects are nematic Skyrmions, since they are characterized by an additional topological charge. The inter-Skyrmion forces are dipolar in this model, i.e., attractive for certain relative orientations of the Skyrmions, hence forming multi-Skyrmion bound states.
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Affiliation(s)
- A A Zyuzin
- Department of Physics, KTH-Royal Institute of Technology, Stockholm, SE-10691 Sweden
- Ioffe Physical-Technical Institute, 194021 St. Petersburg, Russia
| | - Julien Garaud
- Department of Physics, KTH-Royal Institute of Technology, Stockholm, SE-10691 Sweden
| | - Egor Babaev
- Department of Physics, KTH-Royal Institute of Technology, Stockholm, SE-10691 Sweden
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Garaud J, Silaev M, Babaev E. Thermoelectric Signatures of Time-Reversal Symmetry Breaking States in Multiband Superconductors. PHYSICAL REVIEW LETTERS 2016; 116:097002. [PMID: 26991194 DOI: 10.1103/physrevlett.116.097002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2015] [Indexed: 06/05/2023]
Abstract
We show that superconductors with broken time-reversal symmetry have very specific magnetic and electric responses to inhomogeneous heating. A local heating of such superconductors induces a magnetic field with a profile that is sensitive to the presence of domain walls and crystalline anisotropy of superconducting states. A nonstationary heating process produces an electric field and a charge imbalance in different bands. These effects can be measured and used to distinguish s+is and s+id superconducting states in the candidate materials such as Ba_{1-x}K_{x}Fe_{2}As_{2}.
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Affiliation(s)
- Julien Garaud
- Department of Theoretical Physics and Center for Quantum Materials, KTH-Royal Institute of Technology, Stockholm SE-10691, Sweden
| | - Mihail Silaev
- Department of Theoretical Physics and Center for Quantum Materials, KTH-Royal Institute of Technology, Stockholm SE-10691, Sweden
| | - Egor Babaev
- Department of Theoretical Physics and Center for Quantum Materials, KTH-Royal Institute of Technology, Stockholm SE-10691, Sweden
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Lin SZ. Ground state, collective mode, phase soliton and vortex in multiband superconductors. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:493202. [PMID: 25398159 DOI: 10.1088/0953-8984/26/49/493202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
This article reviews theoretical and experimental work on the novel physics in multiband superconductors. Multiband superconductors are characterized by multiple superconducting energy gaps in different bands with interaction between Cooper pairs in these bands. The discovery of prominent multiband superconductors MgB2 and later iron-based superconductors, has triggered enormous interest in multiband superconductors. The most recently discovered superconductors exhibit multiband features. The multiband superconductors possess novel properties that are not shared with their single-band counterpart. Examples include: the time-reversal symmetry broken state in multiband superconductors with frustrated interband couplings; the collective oscillation of number of Cooper pairs between different bands, known as the Leggett mode; and the phase soliton and fractional vortex, which are the main focus of this review. This review presents a survey of a wide range of theoretical exploratory and experimental investigations of novel physics in multiband superconductors. A vast amount of information derived from these studies is shown to highlight unusual and unique properties of multiband superconductors and to reveal the challenges and opportunities in the research on the multiband superconductivity.
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Affiliation(s)
- Shi-Zeng Lin
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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