DENSITY-FUNCTIONAL THEORY OF NORMAL AND SUPERCONDUCTING ELECTRON LIQUIDS - EXPLICIT FUNCTIONALS VIA THE GRADIENT EXPANSION

The basic idea of density functional theory is to map an interacting m any-particle system on an effective non-interacting system in such a w ay that the ground-state densities of the two systems are identical. T ile non-interacting particles move in an effective local potential whi ch is a functional of tile density. The central task of density functi onal theory is to find good approximations for the density dependence of this local single-particle potential. An overview of recent advance s in the construction of this potential (beyond tile local-density app roximation) will be given along with successful applications in quantu m chemistry and solid state theory. We then turn to the extension of d ensity functional theory to superconductors and first discuss the Hohe nberg-Kohn-Sham-type existence theorems. In the superconducting analog ue of the the normal-state Kohn-Sham formalism, a local single-particl e potential is needed which now depends on two densities, tile ordinar y density n(r) and the anomalous density Delta(r,r'). As a first step towards the construction of such a. potential, a gradient expansion te chnique for superconductors is presented and applied to calculate an a pproximation of the non-interacting kinetic energy functional T-s[n, D elta]. We also obtain a Thomas-Fermi-type variational equation for sup erconductors.