Efficient anisotropic Migdal-Eliashberg calculations with an intermediate representation basis and Wannier interpolation

In this study, we combine the ab initio Migdal-Eliashberg approach with the intermediate representation of the Green's function, enabling accurate and efficient calculations of the momentum-dependent superconducting gap function while fully considering the effect of the Coulomb retardation. Unlike the conventional scheme that relies on a uniform sampling across Matsubara frequencies, demanding hundreds to thousands of points, the intermediate representation works with fewer than 100 sampled Matsubara Green's functions. The developed methodology is applied to investigate the superconducting properties of three representative low-temperature elemental metals: aluminum, lead, and niobium. The results demonstrate the power and reliability of our computational technique to accurately solve the ab initio anisotropic Migdal-Eliashberg equations even at extremely low temperatures below 1 K.