Andreev and normal reflections at normal metal-superconductor boundaries: Limitations of the semiclassical approximation

We study the scattering of quasiparticles at a normal metal-superconductor interface using Bogoliubov-de Gennes equations, taking the motion parallel to the interface fully into account. We show that while the Andreev reflection is the dominant scattering process in case of nearly perpendicular impacts (as predicted by the semiclassical theory), the normal reflection becomes increasingly important for quasiparticles with large momenta parallel to the interface, and the semiclassical approximation becomes progressively inadequate. We work out consequence of this feature for spectra of bound states in superconductor-normal metal-superconductor junctions.