Magnetic field dependence of partially-separated Andreev bound states in semiconductor-superconductor nanowires with finite coherence length

Abstract

We study numerically and analytically magnetic field dependence of partially separated Andreev bound states (ps-ABSs), which are localized on both sides of hybrid semiconductor-superconductor nanowire, considering the spatial inversion symmetry of proximity-induced pairing potential with finite coherence length and tunnel one. Finite coherence length results in the occurrence of topologically nontrivial regions near the ends of the nanowire, where near-zero energy ps-ABSs are energetically degenerate due to the spatial inversion symmetry. With increasing the applied magnetic field, the degeneracy is lifted by the overlap between the ps-ABSs near the opposite ends of the nanowire, leading to the appearance of a robust near-zero energy Majorana bound state (MBS) localized at both ends and a nanowire bulk-like state. Our findings provide a mechanism for coexisting of near-zero energy ps-ABS and bulk-like state in the nanowire.