Percolation model for the superconductor-insulator transition in granular films

TL;DR

This paper models the superconductor-insulator transition in granular films using a percolation network approach, explaining broad resistance tails and identifying critical resistance with analytical and numerical methods.

Contribution

It introduces a two-dimensional resistor percolation model incorporating Josephson and quasiparticle tunneling, providing analytical and numerical insights into the transition.

Findings

Effective resistance expression derived analytically.

Critical resistance value identified.

Model matches experimental temperature dependence.

Abstract

We study the temperature dependence of the superconductor-insulator transition in granular superconductors. Empirically, these systems are characterized by very broad resistance tails, which depend exponentially on the temperature, and the normal state resistance. We model these systems by a two-dimensional random resistor percolation networks in which the resistance between two grains is governed either by Josephson junction coupling or by quasi particle tunneling. Our numerical simulations as well as an effective medium evaluation explain the experimental results over a wide range of temperatures and resistances. Using effective medium approximation we find an analytical expression for the effective resistance of the system and the value of the critical resistance separating conducting from insulating branches.