Quantum Superconductor-Metal Transition in a 2D Proximity-Coupled Array

TL;DR

This paper develops a theory describing the quantum phase transition from superconducting to normal states in a 2D array of superconductive islands on a metal film, influenced by island spacing and conductance.

Contribution

It introduces a model for quantum fluctuations in a 2D superconducting array with repulsive interactions, predicting the critical distance for the transition based on conductance and Andreev processes.

Findings

Critical distance for transition depends logarithmically on conductance.

Transition occurs when island spacing exceeds a critical value related to conductance.

Superconductivity persists when islands are sufficiently close, despite electron-electron repulsion.

Abstract

We construct a theory of quantum fluctuatons in a regular array of small superconductive islands connected via low-resistance tunnel contacts to a dirty thin metal film. Electron-electron interaction in the film is assumed to be repulsive. The system is macroscopically superconductive when the distance between neighbouring islands is short enough. The zero-temperature phase transition from superconductive to normal-conductive state is shown to occur with the increase of distance between superconductive islands; the logarithm of the critical distance is proportional to the low-frequency zero-voltage Andreev conductance between the SC island and the film. This critical distance is always much less the than the two-dimensional localization length, so the considered effect develops when weak-localization corrections are still small. The dependence of the critical temperature on the film conductance and inter-island distance is found.