Percolation of Superconductivity

TL;DR

This paper investigates the conditions under which a disordered lattice system becomes superconducting, identifying a critical concentration of attractive centers necessary for superconductivity using a random Hubbard model.

Contribution

It introduces a model analyzing the percolation of superconductivity in a disordered lattice with random attractive centers, employing CPA and Gorkov decoupling methods.

Findings

Existence of a critical concentration c_0 for superconductivity

Superconductivity depends on the percolation of attractive centers

Below c_0, the system remains non-superconducting

Abstract

In case of superconductors whose electrons attract each other only if they are near certain centers, the question arises 'How many such centers are needed to make the ground state superconducting?' We shall examine it in the context of a random U Hubbard model. In short we study the case where U_i is -|U| and 0 with probability c and 1-c respectively on a lattice whose sites are labelled i using the Gorkov decoupling and the Coherent Potential Approximation (CPA). We argue that for this model there is a critical concentration c_0 below which the system is not a superconductor.