Magnetic-field instability of Majorana modes in multiband quantum wires

TL;DR

This paper studies the stability of Majorana modes in multiband semiconductor quantum wires with Rashba interaction and magnetic fields, revealing that interband mixing generally destroys multiple Majorana modes, but a single mode remains robust.

Contribution

It demonstrates that interband mixing from Rashba spin-orbit coupling hybridizes Majorana pairs, limiting their coexistence, and analyzes the robustness of Majorana modes against magnetic orbital effects.

Findings

Interband mixing hybridizes Majorana pairs from different modes.

Multiple Majorana modes generally do not coexist.

Single transverse mode Majorana physics is robust.

Abstract

We investigate the occurrence of Majorana modes in semiconductor quantum wires in close proximity with a superconductor and when both, Rashba interaction and magnetic field, are present. We consider long, but finite, multiband wires (namely, planar wires with dimensions $L_x\gg L_y$). Our results demonstrate that interband mixing coming from Rashba spin orbit term hybridizes Majorana pairs originating from different transverse modes while simultaneously closing the effective gap. Consequently, multiple Majorana modes do not coexist in general. On the contrary, Majorana physics is robust provided that only one single transverse mode contributes with a Majorana pair. Finally, we analyse the robustness of Majorana physics with respect to magnetic orbital effects.