Metal-superconductor transition in two-dimensional electron systems with fractal-like mesoscopic disorder

TL;DR

This paper models the metal-superconductor transition in disordered two-dimensional systems using a random-resistor network, highlighting the impact of local critical temperature distribution and spatial correlations on the transition behavior.

Contribution

It introduces a novel random-resistor network model that incorporates mesoscopic disorder and fractal-like structures, advancing understanding of the transition in disordered 2D systems.

Findings

Distribution of critical temperatures influences transition behavior.

Spatial correlations modify effective medium theory predictions.

Exact calculations highlight the importance of low-connectivity clusters.

Abstract

Motivated by recent experimental data on thin film superconductors and oxide interfaces we propose a random-resistor network apt to describe the occurrence of a metal-superconductor transition in a two-dimensional electron system with disorder on the mesoscopic scale. We explore the interplay between the statistical distribution of local critical temperatures and the occurrence of a lower-dimensional (e.g., fractal-like) structure of a superconducting cluster embedded in the two-dimensional network. The thermal evolution of the resistivity is determined by an exact calculation and, for comparison, a mean-field approach called effective medium theory (EMT). Our calculations reveal the relevance of the distribution of critical temperatures for clusters with low connectivity. In addition, we show that the presence of spatial correlations requires a modification of standard EMT to give qualitative agreement with the exact results.