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Gap Anisotropy in Multiband Superconductors Based on Multiple Scattering Theory

We implement the Bogoliubov-de Gennes (BdG) equation in a screened Korringa-Kohn-Rostoker (KKR) method for solving, self-consistently, the superconducting state for 3d crystals. This method combines the full complexity of the underlying electronic structure and Fermi surface geometry with a simple phenomenological parametrisation for the superconductivity. We apply this theoretical framework to the known s-wave superconductors Nb, Pb, and MgB$_2$. In these materials multiple distinct peaks at the gap in the density of states were observed, showing significant gap anisotropy which is in good agreement with experiment. Qualitatively, the results can be explained in terms of the k-dependent Fermi velocities on the Fermi surface sheets exploiting concepts from BCS theory.