  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.

Superconductivity