Gor’kov, Eilenberger, and Ginzburg–Landau Equations

Abstract

One of the most outstanding features of superconductivity is that there can be various stable structures with quasimacroscopic inhomogeneity, such as the flux-line lattice realized in certain superconductors under an applied magnetic field. To describe these structures concisely, we here simplify the BdG equations in three steps. First, we derive the Gor’kov equations (14.26) for the Matsubara Green’s functions, which is equivalent to the BdG equations. Second, we integrate out an independent variable from the Gor’kov equations to derive the Eilenberger equations (14.61) and (14.62) for the quasiclassical Green’s function (14.59). Third, we focus on the region near Tc to simplify the Eilenberger equations further into the Ginzburg–Landau (GL) equations (14.89) and (14.94). Those who are interested mainly in the physical phenomena rather than the microscopic derivations of the standard equations may skip this chapter.