Density Functional Theory for Plasmon-Assisted Superconductivity

We review the recent progress in the density functional theory for superconductors (SCDFT). Motivated by the long-studied plasmon mechanism of superconductivity, we have constructed an exchange-correlation kernel entering the SCDFT gap equation, which includes the plasmon effect. In the case of lithium under high pressures, we show that the plasmon effect substantially increases the transition temperature (T_c) by cooperating with the conventional phonon mechanism and results in better agreement between the theoretical and experimentally observed T_c values. Our present formalism will be a first step in density functional theory for unconventional superconductors.