Density Functional Theory for Superconductors with Particle-hole Asymmetric Electronic Structure

To extend the applicability of density functional theory for superconductors (SCDFT) to systems with significant particle-hole asymmetry, we construct a new exchange-correlation kernel entering the gap equation. We show that the kernel is numerically stable and does not diverge even in the low temperature limit. Solving the gap equation for model systems with the present kernel analytically and numerically, we find that the asymmetric component of electronic density of states, which has not been considered with the previous kernel, systematically decreases transition temperature (Tc). We present a case where the decrease of Tc amounts to several tens of percent.