From BCS theory for isotropic homogeneous systems to the complete Ginzburg-Landau equations for anisotropic inhomogeneous systems

Abstract

On the basis of the BCS theory of superconductivity, this paper gives the complete expression for the free-energy density Fs as a function of the superconducting energy gap D(T) and temperature T, valid for the entire superconducting temperature range. Then under the condition D(T)/kT,1, the complete expansion of the phenomenological Ginzburg-Landau free-energy density is derived from the BCS free-energy density. For isotropic inhomogeneous systems and systems in magnetic fields, the complete expansions of these two kinds of free energy and the relations between the microscopic and phenomenological coefficients have been determined. Complete forms of the Ginzburg-Landau equations are obtained for both isotropic and anisotropic systems. Finally, we have found the nonlinear equation of the energy gap and the expression for the current density for anisotropic inhomogeneous systems within the framework of BCS theory. The range of validity of these equations is extended to D(T)/pk,T<Tc rather than the usual T!Tc . @S0163-1829~98!04718-3#