Berezinskii-Kosterlitz-Thouless transition in homogeneously disordered superconducting films

TL;DR

This paper develops a comprehensive theory for the Berezinskii-Kosterlitz-Thouless transition in disordered superconducting films, accounting for quantum, mesoscopic, and thermal fluctuations across multiple length scales.

Contribution

It extends the renormalization group approach to the diffusive nonlinear sigma model on the superconducting side of the transition, incorporating mesoscopic fluctuations and microscopic parameters.

Findings

Predicted how vortex unbinding temperature depends on disorder and interactions.

Calculated the impact of fluctuations on superconducting density and resistivity.

Provided a framework to connect microscopic disorder with macroscopic observables.

Abstract

We develop a theory for the vortex unbinding transition in homogeneously disordered superconducting films. This theory incorporates the effects of quantum, mesoscopic and thermal fluctuations stemming from length scales ranging from the superconducting coherence length down to the Fermi wavelength. In particular, we extend the renormalization group treatment of the diffusive nonlinear sigma model to the superconducting side of the transition. Furthermore, we explore the mesoscopic fluctuations of parameters in the Ginzburg-Landau functional. Using the developed theory, we determine the dependence of essential observables (including the vortex unbinding temperature, the superconducting density, as well as the temperature-dependent resistivity and thermal conductivity) on microscopic characteristics such as the disorder-induced scattering rate and bare interaction couplings.