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

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.

16 pages, 4 figures. Revised manuscript with minor changes. Supplemental Information available on the journal website (open access)

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