Isospin Formulation of the Theory of a Granular Superconductor

Abstract

The properties of a granular superconductor are studied with the aid of the isospin formulation of the microscopic theory of superconductivity. The system consists of grains of homogeneous superconductor separated by insulating but tunnelable barriers (Josephson junctions). The general nonlinear equations of motion are set up for the isospins, "spin up" representing the absence, and "spin down" the presence, of a given Cooper pair. These equations are like torque equations for each isospin moving in an effective pseudomagnetic field due to all the other isospins. Linearized solutions result in various single-particle and collective excitations. A certain class of nonlinear solutions is shown to satisfy a Ginzburg-Landau-like differential equation. The effects of electric fields (within the junctions) and real magnetic fields are studied, one result being that there are bulk electromagnetic modes, analogous to the surface modes known to be associated with a single isolated Josephson junction. Consequences of changes in temperature and changes in effective electron-electron interaction are studied.