Critical scaling of the ac conductivity for a superconductor above Tc

Abstract

We consider the effects of critical superconducting fluctuations on the scaling of the linear ac conductivity, σ(ω), 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 σ(ω) calculated via the Kubo formula to O(ε2) in the ε=4−d expansion. The critical dynamics are governed by the relaxational XY-model renormalization-group fixed point. The scaling hypothesis σ(ω)∼ξ2−d+zS(ωξz) proposed by Fisher, Fisher, and Huse is explicitly verified, with the dynamic exponent z≈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 ac conductivity of YBa2Cu3O7−δ near Tc, and the implications of this theory for such experiments is discussed.

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