  We report on the implementation of the Bogoliubov-de Gennes method into the
JuKKR code [https: //jukkr.fz-juelich.de], an implementation of the
relativistic all-electron, full-potential Korringa-Kohn-Rostoker Green function
method, which allows a material-specific description of inhomogeneous
super-conductors and heterostructures on the basis of density functional
theory. We describe the formalism and report on calculations for the s-wave
superconductor Nb, a potential component of the materials platform enabling the
realization of the Majorana zero modes in the field of topological quantum
computing. We compare the properties of the superconducting state both in the
bulk and for (110) surfaces. We compare slab calculations for different
thicknesses and comment on the importance of spin-orbit coupling, the effect of
surface relaxations and the influence of a softening of phonon modes on the
surface for the resulting superconducting gap.
