Robustness of Majorana bound states in the short junction limit

TL;DR

This paper investigates how strong coupling in a short junction limit affects Majorana bound states in superconductor-semiconductor nanowires, showing that a small superconducting gap does not significantly impair Majorana properties.

Contribution

It demonstrates that in the short junction limit, the superconducting gap size does not critically influence Majorana states, and elucidates how magnetic field effects depend on material parameters.

Findings

Superconducting gap size has minimal impact on Majorana states.

Critical magnetic field depends on wire cross section.

Orbital and Zeeman effects are governed by material parameters.

Abstract

We study the effects of strong coupling between a superconductor and a semiconductor nanowire on the creation of the Majorana bound states, when the quasiparticle dwell time in the normal part of the nanowire is much shorter than the inverse superconducting gap. This "short junction" limit is relevant for the recent experiments using the epitaxially grown aluminum characterized by a transparent interface with the semiconductor and a small superconducting gap. We find that the small superconducting gap does not have a strong detrimental effect on the Majorana properties. Specifically, both the critical magnetic field required for creating a topological phase and the size of the Majorana bound states are independent of the superconducting gap. The critical magnetic field scales with the wire cross section, while the relative importance of the orbital and Zeeman effects of the magnetic field is controlled by the material parameters only: $g$-factor, effective electron mass, and the semiconductor-superconductor interface transparency.