Full-bandwidth anisotropic Migdal-Eliashberg theory and its application to superhydrides

TL;DR

This paper advances Migdal-Eliashberg theory by incorporating full electronic structure and non-uniform sampling, enabling more accurate predictions of superconductivity in complex materials like superhydrides.

Contribution

The authors develop a full-bandwidth implementation of Migdal-Eliashberg theory within the EPW code, allowing for detailed electronic structure considerations beyond the Fermi surface.

Findings

Accurate modeling of superconductors with complex electronic features.

Significant differences observed between full-bandwidth and constant-density-of-states approximations.

Enhanced understanding of the role of density of states in doped superconductors.

Abstract

Migdal-Eliashberg theory is one of the state-of-the-art methods for describing conventional superconductors from first principles. However, widely used implementations assume a constant density of states around the Fermi level, which hinders a proper description of materials with distinct features in its vicinity. Here, we present an implementation of the Migdal-Eliashberg theory within the EPW code that considers the full electronic structure and accommodates scattering processes beyond the Fermi surface. To significantly reduce computational costs, we introduce a non-uniform sampling scheme along the imaginary axis. We demonstrate the power of our implementation by applying it to the sodalite-like clathrates YH$_6$ and CaH$_6$, and to the covalently-bonded H$_3$S and D$_3$S. Furthermore, we investigate the effect of maximizing the density of states at the Fermi level in doped H$_3$S and BaSiH$_8$ within the full-bandwidth treatment compared to the constant-density-of-states approximation. Our findings highlight the importance of this advanced treatment in such complex materials.