Self-consistent GW theory for superconductivity in SrTiO3

Superconductivity in doped SrTiO3, the first superconducting transition discovered in a doped semiconductor more than 60 years ago, remains puzzling due to its unusually low Tc and unconventional electron–phonon interactions that violate the Migdal approximation. Here, we present an efficient implementation of self-consistent GW (renormalized Migdal–Eliashberg) theory for a one-band model with Fröhlich-type coupling, with model parameters obtained from ab initio simulations of SrTiO3. We demonstrate that the G0W0-level calculations without frequency truncation drastically overestimate Tc, whereas the self-consistent (renormalized) theory, by partially incorporating vertex corrections, reduces Tc and provides a more accurate description.