FREE-ENERGY OF AN INHOMOGENEOUS SUPERCONDUCTOR - A WAVE-FUNCTION APPROACH

A method for calculating the free energy of an inhomogeneous supercond uctor is presented. This method is based on the quasiclassical limit ( or Andreev approximation) of the Bogoliubov-de Gennes (or wave functio n) formulation of the theory of weakly coupled superconductors. The me thod is applicable to any pure bulk superconductor described by a pair potential with arbitrary spatial dependence, in the presence of super currents and external magnetic field. We find that both the local dens ity of states and the free energy density of an inhomogeneous supercon ductor can be expressed in terms of the diagonal resolvent of the corr esponding Andreev Hamiltonian, which obeys the so-called Gelfand-Dikii equation. Also, the connection between the well known Eilenberger equ ation for the quasiclassical Green's function and the less known Gelfa nd-Dikii equation for the diagonal resolvent of the Andreev Hamiltonia n is established. These results are used to construct a general algori thm for calculating the (gauge invariant) gradient expansion of the fr ee energy density of an inhomogeneous superconductor at arbitrary temp eratures. [S0163-1829(98)05138-8].