Critical scaling of the a.c. conductivity for a superconductor above Tc

TL;DR

This paper investigates how critical fluctuations near the superconducting transition temperature affect the a.c. conductivity, using renormalization group methods to verify scaling laws and compute universal functions.

Contribution

It applies dynamic renormalization group analysis to the relaxational Ginzburg-Landau model, explicitly verifying the scaling hypothesis and calculating the universal scaling function for the a.c. conductivity.

Findings

Confirmed the scaling hypothesis for  conductivity near Tc

Computed the universal scaling function S(y) with slight deviations from Gaussian form

Estimated the dynamic exponent z rom the XY-model fixed point

Abstract

We consider the effects of critical superconducting fluctuations on the scaling of the linear a.c. conductivity, \sigma(\omega), of a bulk superconductor slightly above Tc in zero applied magnetic field. The dynamic renormalization- group method is applied to the relaxational time-dependent Ginzburg-Landau model of superconductivity, with \sigma(\omega) calculated via the Kubo formula to O(\epsilon^{2}) in the \epsilon = 4 - d expansion. The critical dynamics are governed by the relaxational XY-model renormalization-group fixed point. The scaling hypothesis \sigma(\omega) \sim \xi^{2-d+z} S(\omega \xi^{z}) proposed by Fisher, Fisher and Huse is explicitly verified, with the dynamic exponent z \approx 2.015, the value expected for the d=3 relaxational XY-model. The universal scaling function S(y) is computed and shown to deviate only slightly from its Gaussian form, calculated earlier. The present theory is compared with experimental measurements of the a.c. conductivity of YBCO near Tc, and the implications of this theory for such experiments is discussed.