Finite temperature transport at the superconductor-insulator transition in disordered systems

TL;DR

This paper analyzes the temperature-dependent conductivity at the superconductor-insulator transition in disordered systems, revealing a universal behavior with a simple pole at one dimension and estimating the critical conductivity in two dimensions.

Contribution

It introduces an analytic approach to understand the crossover function's behavior across dimensions, providing the first estimate of critical conductivity in disordered boson systems with Coulomb interactions.

Findings

Universal crossover function has a simple pole at d=1.

Estimated critical conductivity in 2D is approximately 0.69 (2e)^2/h.

Results align well with experimental data on thin films.

Abstract

I argue that the incoherent, zero-frequency limit of the universal crossover function in the temperature-dependent conductivity at the superconductor-insulator transition in disordered systems may be understood as an analytic function of dimensionality of system d, with a simple pole at d=1. Combining the exact result for the crossover function in d=1 with the recursion relations in d=1+\epsilon, the leading term in the Laurent series in the small parameter \epsilon for this quantity is computed for the systems of disordered bosons with short-range and Coulomb interactions. The universal, low-temperature, dc critical conductivity for the dirty boson system with Coulomb interaction in d=2 is estimated to be 0.69 (2e)^2 /h, in relatively good agreement with many experiments on thin films. The next order correction is likely to somewhat increase the result, possibly bringing it closer to the self-dual value.