Superconducting pairing mediated by spin-fluctuations from first principles

We present the derivation of an ab-initio and parameter free effective electron-electron interaction that goes beyond the screened RPA and accounts for superconducting pairing driven by spin-fluctuations. The construction is based on many body perturbation theory and relies on the approximation of the exchange-correlation part of the electronic self-energy within time dependent density functional theory. This effective interaction is included in an exchange correlation kernel for superconducting density functional theory, in order to achieve a completely parameter free superconducting gap equation. First results from applying the new functional to a simplified two-band electron gas model are consistent with experiments.