  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.
