Development of Density-Functional Theory for Plasmon-Assisted Superconducting State: Application to Lithium Under High Pressures

We extend the density-functional theory for superconductors (SCDFT) to take account of the dynamical structure of the screened Coulomb interaction. We construct an exchange-correlation kernel in the SCDFT gap equation on the basis of the random-phase approximation, where electronic collective excitations such as plasmons are properly treated. Through an application to fcc lithium under high pressures, we demonstrate that our new kernel gives higher transition temperatures (Tc) when the plasmon and phonon cooperatively mediate pairing and it improves the agreement between the calculated and experimentally observed Tc. The present formalism opens the door to non-empirical studies on unconventional electron mechanisms of superconductivity based on density functional theory.