Nonlinear fluctuation phenomena in the transport properties of superconductors

We revisit AdS2 holography with the Sachdev-Ye-Kitaev models in mind. Our main result is to rewrite a generic theory of gravity near an AdS2 throat as a novel hydrodynamics coupled to the correlation functions of a conformal quantum mechanics. This gives a prescription for the computation of n-point functions in the dual quantum mechanics. We thereby find that the dual is maximally chaotic.Introduction. The Sachdev-Ye-Kitaev (SYK) models [1,2] are quantum mechanical systems with random all-to-all interactions. They have been recently argued to have a gravity dual in two dimensions.The basic SYK model is a theory of 2N Majorana fermions ψ a (a = 1, .., 2N ) perturbed by quenched disorder. The Hamiltonian is

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“…Consider an out-of-time-ordered, connected, thermal four-point function [7,8] of two operators W and V ,…”

Section: At O(ℓmentioning

confidence: 99%

“…The second is much more nontrivial. The SYK models saturate the "chaos bound" of [6] on the Lyapunov exponent, which characterizes the rate of growth of certain out-of-time-ordered four-point functions [7,8]. This bound, which exists in any quantum system, is 2πT .…”

mentioning

confidence: 99%

Chaos inAdS2Holography

2016

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“…A short comment would be useful regarding the application of the cut-off procedure to the k-integrals in Eqs. (27) and (22). It could seem more appealing to apply the cut-off on the translated wave-vector magnitude, such as k 2 y + [k x + (e 0 Eτ /2 )] 2 < cξ −2 0 , as it was approximately done, although in a different gauge, by Kajimura and Mikoshiba, 38 while studying the paraconductivity in arbitrary electric field in the two-dimensional case.…”

Section: Solutions With Consideration Of the Uv Cut-offmentioning

confidence: 99%

“…23 and 26. In some more recent derivations of the TDGL, 22,27 however, the original appearance of these parameters is preserved, so that the order parameter relaxation rate is written as depending on the actual temperature. In this mathematically somewhat stricter sense, one could therefore write the life-time of the metastable Cooper pairs as τ (BCS) = π /16k B T ln (T /T 0 ).…”

Section: Tdgl Equation For Arbitrary Electric Fieldmentioning

confidence: 99%

Critical fluctuation conductivity in layered superconductors in a strong electric field

Puica¹,

Lang

2003

Phys. Rev. B

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The paraconductivity, originating from critical superconducting order-parameter fluctuations in the vicinity of the critical temperature in a layered superconductor is calculated in the frame of the self-consistent Hartree approximation, for an arbitrarily strong electric field and zero magnetic field. The paraconductivity diverges less steep towards the critical temperature in the Hartree approximation than in the Gaussian one and it shows a distinctly enhanced variation with the electric field. Our results indicate that high electric fields can be effectively used to suppress orderparameter fluctuations in high-temperature superconductors.

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“…However, as independently predicted by Fulde and Ferrell [21] and Larkin and Ovchinnikov [22], the superconductor may overcome the pair-breaking effect of magnetic field by forming periodic regions of superconductivity separated by domains of aligned spins. In such FFLO-state the order parameter is spatially modulated along the field direction.…”

Section: Introductionmentioning

confidence: 99%

Enhancement of superconductivity by an external magnetic field in magnetic alloys

Borycki

2014

Eur. Phys. J. B

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Abstract. An infinite-volume limit solution of the thermodynamics of a BCS superconductor containing spin 1/2 and 7/2 magnetic impurities, obtained recently in [D. Borycki, J. Maćkowiak, Supercond. Sci. Technol. 24, 035007 (2011)] is exploited to derive the expressions for critical magnetic field Hc(T ). The credibility of the resulting thermodynamically limited theoretical equations, which depend on the magnetic coupling constant g and impurity concentration c, is verified on the experimental data for the following superconducting alloys: LaCe, ThGd and SmRh4B4. Good quantitative agreement with experimental data is found for sufficiently small values of c. The discrepancies between theoretical and experimental values of Hc(T ) for larger values of c in case of LaCe and ThGd are reduced by introducing the concept of the effective temperatureT , which accounts for the Coulomb interactions between the electron gas and impurity ions. At low temperatures, the critical magnetic field is found to increase with decreasing temperature T . This enhancement of the critical magnetic field provides evidence of the Jaccarino-Peter effect, which was experimentally observed in the Kondo systems like LaCe, (La1−xCex)Al2 and also in the pseudoternary compounds, including Sn1−xEuxMo6S8, Pb1−xEuxMo6S8 and La1.2−xEuxMo6S8. The effect of an external magnetic field H on a BCS superconductor perturbed by magnetic impurities was also studied. On these grounds, by analyzing the dependence of superconducting transition temperature Tc on H of (La1−xCex)Al2, we have shown, that for certain parameter values, external magnetic field compensates the destructive effect of magnetic impurities.

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Nonlinear fluctuation phenomena in the transport properties of superconductors

Cited by 112 publications

References 12 publications

Chaos inAdS2Holography

Chaos inAdS2Holography

Critical fluctuation conductivity in layered superconductors in a strong electric field

Enhancement of superconductivity by an external magnetic field in magnetic alloys

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