Ab-initio computation of superconducting properties of elemental superconductors and MgB₂

We present ab-initio predictions of superconducting properties of some elemental superconductors and of MgB₂, based on the Super-Conducting Density Functional theory (SC-DFT). This formalism allows a description of superconducting properties at thermal equilibrium by means of three "densities": the ordinary electron density, the superconducting order parameter, and the diagonal of the nuclear N-body density matrix. These quantities are determined through self-consistent solutions of Bogoliubov-de Gennes Kohn-Sham like equations, involving exchange-correlation potentials which are universal functionals of the three above-mentioned quantities. By means of approximate expressions for the relevant functionals, we obtain an ab-initio description of the superconducting state, completely free of empirical parameters. The results of our present implementation of SC-DFT for selected materials are discussed in terms of superconducting energy gap, critical temperature and specific heat, and compared with experiments.