Condensation Energy and Tc within the Density Functional Theory for Superconductors

Abstract

We study the behaviour of the density functional theory for superconductors (SCDFT) for two cases: 1) the Coulomb part of the condensation energy (Ec) of a homogeneous electron gas under pairing potential with high angular momentum, and 2) the Tc of niobium under pressure.In the first case, we treat the electronic correlations at the random phase approximation (RPA) level and we do not find superconductivity for densities with rs up to 9, and only a very weak negative value of Ec for f‐waves and higher angular momentum when rs=10.In the second case, low and high pressure anomalies and the absolute values of Tc are reproduced quite well by the linearized SCDFT gap equation (with a Thomas‐Fermi screening of Coulomb interactions and phonons treated within the Migdal’s theorem). In contrast, the critical temperatures of Nb under pressure obtained from the linearized Eliashberg equation are largely overestimated, even when spin‐fluctuations are included.