Modeling superconducting properties with the Eliashberg formalism

Ab initio prediction of superconducting properties remains among the most challenging problems in materials research. Recent advances in computational methodology based on the Eliashberg formalism represent an important milestone in moving toward fully ab initio description of phonon-mediated superconductors. In this talk, I will introduce our computational framework that combines the fully anisotropic Eliashberg theory with electron-phonon interpolation based on maximally-localized Wannier functions. The methodology, implemented in the open-source EPW package, allows one to perform highly accurate calculations of the anisotropic temperature-dependent superconducting gap and critical temperature. I will illustrate the performance of this advanced computational technique on several prototypical systems.