Majorana Zero Modes in Cylindrical Semiconductor Quantum Wire

TL;DR

This paper investigates the properties of Majorana zero modes in cylindrical semiconductor quantum wires, analyzing effects of disorder, superconducting fluctuations, and sub-band coupling to understand their robustness and characteristics.

Contribution

It provides a detailed theoretical analysis of Majorana zero modes in cylindrical wires using $k \, ext{p}$ and lattice models, highlighting weak inter-sub-band coupling and spin polarization.

Findings

Low-energy quasiparticles are nearly fully spin-polarized.

Coupling between quasi-one-dimensional sub-bands is weak.

The number of electrons in topological active sub-bands is small.

Abstract

We study Majorana zero modes properties in cylindrical cross-section semiconductor quantum wires based on the $k \cdot p$ 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 order-parameter 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.