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 random phase approximation 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.