Transport properties of clean and disordered superconductors in matrix field theory

TL;DR

This paper develops a matrix field theory framework to analyze the transport properties of both clean and disordered superconductors, providing a unified approach to study their quantum phase transitions.

Contribution

It introduces a saddle-point solution within matrix field theory for disordered superconductors and derives a general gap equation and correlation functions.

Findings

Derived explicit expressions for ultrasonic attenuation and electrical conductivity.

Analyzed differences between clean and disordered superconductor cases.

Provided a formalism for studying quantum phase transitions in superconductors.

Abstract

A comprehensive field theory is developed for superconductors with quenched disorder. We first show that the matrix field theory, used previously to describe a disordered Fermi liquid and a disordered itinerant ferromagnet, also has a saddle-point solution that describes a disordered superconductor. A general gap equation is obtained. We then expand about the saddle point to Gaussian order to explicitly obtain the physical correlation functions. The ultrasonic attenuation, number density susceptibility, spin density susceptibility and the electrical conductivity are used as examples. Results in the clean limit and in the disordered case are discussed respectively. This formalism is expected to be a powerful tool to study the quantum phase transitions between the normal metal state and the superconductor state.