State of the art and new developments in superconducting density functional theory

We will present the theoretical framework of superconducting density functional theory (SCDFT), a fully parameter-free approach to superconductivity. The advantages and disadvantages of this method will be presented, as well as more recent extensions and perspectives. First I will present the connection of the theory to Eliashberg's method, and discuss some exact limits. Then I will report on how this connection is used to improve the existing phononic functionals. Applications to several materials will be shown. The purely electronic part of the coupling in SCDFT will also be analyzed properties and limits of the static random phase approximation will be discussed. Finally I will report on recent extensions which include dynamical effects in the screened interaction.