Majorana Zero Modes in Cylindrical Semiconductor Quantum Wire

Abstract

We study Majorana zero modes properties in cylindrical cross-section semiconductor quantum wires based on the k • p theory and a discretized lattice model. Within this model the influence of disorder potentials in the wire and amplitude and phase fluctuations of the superconducting orderparameter are discussed. We find that for typical wire geometries, pairing potentials, and spin-orbit coupling strengths, coupling between quasi-one-dimensional sub-bands is weak, low-energy quasiparticles near the Fermi energy are nearly completely spin-polarized, and the number of electrons in the active sub-bands of topological states is small.