Electronic Structure of Pinned Abrikosov Vortices: Andreev Theory of Quasiparticle Bound States

Starting from the Bogolubov–de Gennes equations for superconductor with an arbitrary anisotropic Fermi surface we derive the Andreev-type theory accounting for the quasiparticle trajectory interference and corresponding nonquasiclassical quantization effects. The resulting Andreev equations are applied for the analysis of the subgap quasiparticle states localized at the pinned vortex cores. The normal reflection of electrons and holes at the defects is shown to result in the qualitative transformation of the subgap spectra and formation of new types of bound quasiparticle states. We focus on the effect of the Fermi surface anisotropy on the quasiparticle spectral properties including opening of soft and hard minigaps in the spectrum and spatial behavior of the local density of states around pinned vortex cores.