Anisotropic Migdal-Eliashberg theory using Wannier functions

We combine the fully anisotropic Migdal-Eliashberg theory with electron-phonon interpolation based on maximally localized Wannier functions, in order to perform reliable and highly accurate calculations of the anisotropic temperature-dependent superconducting gap and critical temperature of conventional superconductors. Compared with the widely used McMillan approximation, our methodology yields a more comprehensive and detailed description of superconducting properties, and is especially relevant for the study of layered or low-dimensional systems as well as systems with complex Fermi surfaces. In order to validate our method we perform calculations on two prototypical superconductors, Pb and MgB2, and obtain good agreement with previous studies. DOI: 10.1103/PhysRevB.87.024505