LABORATOIRE DE PHYSIQUE ET MODELISATION DES MILIEUX CONDENSES

Superconductivity is a many-body phenomenon of high interest. In this talk, I will discuss Green's function approaches that incorporate correlation effects beyond a mean-field treatment (i.e., beyond the Hartree–Fock–Bogoliubov (HFB) approximation). The main focus will be the recently proposed Bogoliubov formulation of the GW approximation within the fully self-consistent framework (scGW). I will outline some theoretical foudations and crucial details of its computational implementation. Then, I will compare its performance against (Bogoliubov) self-consistent second-order Green's function based methods (scGF2) using the attractive Hubbard model as a playground for testing. The comparison will highlight the drawbacks of the GW approximation to describe correlation effects in superconductors. In this line, our results indicate the importance of (second-order) exchange corrections for treating these systems. Finally, I will comment on future directions for Green's function approximations in superconductivity.