Emergence of Majorana modes in cylindrical nanowires

TL;DR

This paper investigates the emergence of Majorana modes in cylindrical semiconductor nanowires with superconductivity, analyzing how magnetic field orientation and orbital effects influence their robustness and experimental signatures.

Contribution

It provides a detailed numerical and analytical study of Majorana modes in cylindrical nanowires, highlighting the effects of orbital contributions and magnetic field orientation on their stability.

Findings

Majorana modes are robust with a parallel magnetic field component.

Orbital effects cause anisotropy in the critical magnetic field.

Multiple Majorana modes can coexist on the same edge under certain conditions.

Abstract

We present calculations of Majorana edge modes in cylindrical nanowires of a semiconductor material with proximity-induced superconductivity. We consider a Rashba field along the transverse direction and an applied magnetic field in arbitrary orientation. Our analysis is based on exact numerical diagonalizations for the finite cylinder and on the complex band structure for the semi-infinite one. Orbital effects are responsible for a strong anisotropy of the critical field for which the effective gap vanishes. Robust Majorana modes are induced by the parallel field component and we find regimes with more than one Majorana mode on the same edge. Experimentally, they would manifest as a specific sequence of zero-bias conductances as a function of magnetic field. In the finite cylinder, a degradation of the Majorana modes due to interference of the two edges leads to oscillating non zero energies for large enough fields.