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The shear viscosity has been shown to be equal to the product of pressure and relaxation time in normal scale-invariant fluids, but the presence of superfluidity at low temperatures can alter the relation. By using the mean-field BCS-Leggett theory with a gauge-invariant linear response theory for unitary Fermi superfluids, we present an explicit relation between thermodynamic quantities, including the pressure and chemical potential, and transport coefficients, including the shear viscosity, superfluid density, and anomalous shear viscosity from momentum transfer via Cooper pairs. The relation is modified when pairing fluctuations associated with noncondensed Cooper pairs are considered. Within a pairing fluctuation theory consistent with the BCS-Leggett ground state, we found an approximate relation for unitary Fermi superfluids. The exact mean-field relation and the approximate one with pairing flucutaions advance our understanding of relations between equilibrium and transport quantities in superfluids, and they help determine or constrain quantities which can be otherwise difficult to measure.

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“…Here we construct a gauge-invariant vertex by applying the consistent fluctuations of order parameter (CFOP) theory [25,36] and obtain…”

Section: Discussionmentioning

confidence: 99%

Relation connecting thermodynamics and transport of atomic unitary Fermi superfluids

Guo

Cai

et al. 2017

Phys. Rev. A

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“…For simplicity, we consider the T = 0 case. The expressions for the finite temperature coefficients can be calculated in an analogous manner [9,26].…”

Section: Appendixmentioning

confidence: 99%

Collective modes and electromagnetic response of a chiral superconductor

Roy

Kallin

2008

Phys. Rev. B

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Motivated by the recent controversy surrounding the Kerr effect measurements in strontium ruthenate [1], we examine the electromagnetic response of a clean chiral p-wave superconductor. When the contributions of the collective modes are accounted for, the Hall response in a clean chiral superconductor is smaller by several orders of magnitude than previous theoretical predictions and is too small to explain the experiment. We also uncover some unusual features of the collective modes of a chiral superconductor, namely, that they are not purely longitudinal and couple to external transverse fields. The experiment by Xia et al. found a Kerr angle of approximately 60 nanoradians at a frequency, ω ≃ 0.8 eV, which is small compared to the Kerr angle observed in typical ferromagnets, but can be understood qualitatively if one notes that the superconducting gap (or order parameter) for Sr 2 RuO 4 is substantially reduced from that of a typical ferromagnet [1]. The Kerr angle at high frequencies is related to the ac Hall conductivity. Theoretical work, however, is divided on the issue of whether the experimental observation result is consistent with the linear response theory of a clean chiral p-wave superconductor [8,9,10]. Earlier works on the electromagnetic response of a chiral p-wave superconductor, with an isotropic Fermi surface [10,11], found no quasi-particle contribution in the clean limit, even in the presence of particle-hole asymmetry, but did predict a Kerr angle due to the so-called "flapping" collective mode. The predicted magnitude is smaller by several orders of magnitude than that observed in Sr 2 RuO 4 .These earlier theoretical studies neglected the effect of an anomalous density-current correlation function which vanishes for a non-chiral superconductor. It was recently argued that when this anomalous correlation function is taken into account, the linear response theory does predict an ac Hall conductivity which is large enough to account for the experiments [8,9]. In the effective action language, the anomalous correlation function gives rise to a Chern-Simons-like term which is reminiscent of the quantum Hall effect [12]. A similar term in the Ginzburg Landau free energy leads to a small "spontaneous Hall effect" in a finite system [13]. When the dynamics of the spin degrees of freedom which are unimportant for the purposes of the present paper are also considered, the effective action of a chiral superconductor or superfluid also contains a non-abelian Chern Simons term which is responsible for the spin quantum Hall effect in these systems [14,15,16,17].In this paper, we examine afresh the linear response of a chiral p-wave superconductor taking into account the anomalous density-current correlation functions and also the contributions from collective modes. We find that when both factors are taken into account, the ac Hall response is strictly zero for an idealized beam normally incident on the a-b plane, with no in-plane wave vector. This is in contrast to the recent results which also consid...

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“…(17) is proportional to the time derivative of the London supercurrent j s = (ρ s e/2m)[∇ϕ − (2e/c)A]. Obtaining a self-consistent equation of motion for the superconducting phase ϕ is a complicated problem [17]. However, one may argue that the supercurrent contribution in Eq.…”

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confidence: 99%

“…This product can be also written as the vector Ψ×Ψ * pointing alongẑ [14], which is consistent with Eq. (17). It would be very interesting to verify experimentally the Ω −3 frequency dependence of the Kerr angle predicted by Eq.…”

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confidence: 99%

Theory of the High-Frequency Chiral Optical Response of apx+ipySuperconductor

Yakovenko

2007

Phys. Rev. Lett.

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The optical Hall conductivity and the polar Kerr angle are calculated as functions of temperature for a two-dimensional chiral px + ipy superconductor, where the time-reversal symmetry is spontaneously broken. The theoretical estimate for the polar Kerr angle agrees by the order of magnitude with the recent experimental measurement in Sr2RuO4 by Xia et al. [PRL 97, 167002 (2006)]. The theory predicts that the Kerr angle is proportional to the square of the superconducting energy gap and is inversely proportional to the cube of frequency, which can be verified experimentally.

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Cited by 43 publications

References 27 publications

Relation connecting thermodynamics and transport of atomic unitary Fermi superfluids

Relation connecting thermodynamics and transport of atomic unitary Fermi superfluids

Collective modes and electromagnetic response of a chiral superconductor

Theory of the High-Frequency Chiral Optical Response of apx+ipySuperconductor

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