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

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_3S and D_3S. Furthermore, we investigate the effect of maximizing the density of states at the Fermi level in doped H_3S 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. Migdal-Eliashberg theory is a method for describing conventional superconductors. Here, the authors present an implementation that goes beyond the widely used constant density of states approximation by accommodating scattering processes beyond the Fermi surface, and they show its importance in two classes of near room temperature superhydrides.