Transport properties of clean and disordered superconductors in matrix field theory

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.