Renormalization of the Majorana bound state decay length in a perpendicular magnetic field

TL;DR

This paper analyzes how a perpendicular magnetic field influences Majorana bound states in semiconductor nanowires, revealing that such a field can actually enhance the formation of topological zero-energy modes by reducing their decay length.

Contribution

It introduces an analytical model explaining the combined effects of magnetic field, spin-orbit interaction, and paramagnetic coupling on Majorana modes in nanowires.

Findings

Perpendicular magnetic field decreases Majorana decay length.

Magnetic field can facilitate topological zero-energy modes.

Analytical model captures orbital and spin effects on Majorana states.

Abstract

Orbital effects of a magnetic field in a proximitized semiconductor nanowire are studied in the context of the spatial extent of Majorana bound states. We develop analytical model that explains the impact of concurring effects of paramagnetic coupling of the nanowire bands via the kinetic energy operator and spin-orbit interaction on the Majorana modes. We find, that the perpendicular field, so far considered as to be detrimental to the Majorana fermion formation, is in fact helpful in establishing the topological zero-energy-modes in a finite system due to significant decrease in the Majorana decay length.