Theory of Fluctuations in a Network of Parallel Superconducting Wires

TL;DR

This paper models a network of parallel superconducting wires under a magnetic field, revealing a critical temperature for phase coherence onset using a quantum-mechanical mapping and mean field approximation.

Contribution

It introduces a novel mapping of the superconducting wire network problem onto a two-dimensional quantum mechanics model with an imaginary magnetic field, and analyzes the phase transition.

Findings

Identifies a critical temperature for phase coherence transition.

Plots transition temperature under magnetic and non-magnetic conditions.

Uses mean field approximation to analyze the system.

Abstract

We show how the partition function of a network of parallel superconducting wires weakly coupled together by the proximity effect, subjected a vector potential along the wires can be mapped onto N-distinguishable two dimensional quantum-mechanics problem with a perpendicular imaginary magnetic field. Then, we show, using a mean field approximation, that, for a given coupling, there is a critical temperature for onset of inter-wire phase coherence. The transition temperature $T_c$ is plotted on both cases for non-magnetic and a magnetic field perpendicular to the wires.