Majorana fermions in multiband quantum wires: A semiclassical analysis

Abstract

In this paper, we calculate the Andreev bound state spectrum in a half-infinite superconducting wire with an arbitrary number of bands crossing the chemical potential. Electrons in the wire are affected by the asymmetric (Rashba) spin–orbit coupling due to the presence of a substrate. The normal state of the wire is assumed to have an antiunitary symmetry (time reversal or its combination with a point group operation), which may be broken by the superconducting order parameter and/or the boundary. The bound state spectrum is calculated without relying on any particular microscopic model, using the semiclassical approach with the boundary conditions described by a phenomenological scattering matrix.