Local Density Approximation for Superconductors

Abstract

A universal LDA-type density functional describing the electronic correlations in superconductors is developed from first principles. The functional is constructed from the exchange-correlation free-energy density, ${f}_{\mathrm{xc}}^{\mathrm{hom}}$, of a homogeneous electron gas exposed to an external translationally invariant pairing field. The quantity ${f}_{\mathrm{xc}}^{\mathrm{hom}}$, which is a function of the density and a functional of the induced order parameter, is calculated by many-body perturbation theory.