Majorana End-States in Multi-band Microstructures with Rashba Spin-Orbit Coupling

TL;DR

This paper extends the understanding of Majorana end-states in multi-band Rashba-superconductor structures, revealing new conditions for their existence, including finite size effects and domain boundaries, with implications for quantum wire experiments.

Contribution

It introduces novel insights into Majorana states in Rashba systems, showing they can exist outside traditional topological regimes and under various geometries.

Findings

Majorana end-states can occur outside the Zeeman gap due to finite size effects.

Large induced magnetization reduces the bulk energy gap.

Majorana states can form at ferromagnetic domain ends and with meandering edges.

Abstract

A recent work [1] demonstrated, for an ideal spinless p+ip superconductor, that Majorana end-states can be realized outside the strict one-dimensional limit, so long as: 1) the sample width does not greatly exceed the superconducting coherence length and 2) an odd number of transverse sub-bands are occupied. Here we extend this analysis to the case of an effective p+ip superconductor engineered from Rashba spin-orbit coupled surface with induced magnetization and superconductivity, and find a number of new features. Specifically, we find that finite size quantization allows Majorana end-states even when the chemical potential is outside of the induced Zeeman gap where the bulk material would not be topological. This is relevant to proposals utilizing semiconducting quantum wires, however, we also find that the bulk energy gap is substantially reduced if the induced magnetization is too large. We next consider a slightly different geometry, and show that Majorana end-states can be created at the ends of ferromagnetic domains. Finally, we consider the case of meandering edges and find, surprisingly, that the existence of well-defined transverse sub-bands is not necessary for the formation of robust Majorana end-states.