Anisotropic Migdal-Eliashberg theory using Wannier functions

TL;DR

This paper introduces an advanced anisotropic Migdal-Eliashberg theory combined with Wannier function interpolation, enabling highly accurate predictions of superconducting properties in complex materials, surpassing traditional approximations.

Contribution

The authors develop a fully anisotropic Migdal-Eliashberg framework integrated with Wannier functions for precise superconductivity calculations, especially in layered and complex Fermi surface systems.

Findings

Accurate calculation of superconducting gaps and critical temperatures for Pb and MgB₂.

Good agreement with previous experimental and theoretical results.

Enhanced description of anisotropic superconducting properties.

Abstract

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 MgB$_2$, and obtain good agreement with previous studies.