# Electronic structure of full-shell InAs/Al hybrid semiconductor-superconductor nanowires: Spin-orbit coupling and topological phase space

## TL;DR

This study uses a detailed quantum model to analyze full-shell InAs/Al nanowires, revealing that the conditions for topological phases are very limited and require precise tuning of wire diameter.

## Contribution

It provides a comprehensive self-consistent analysis of the electronic structure and spin-orbit coupling in full-shell InAs/Al nanowires, highlighting the narrow parameter space for topological phases.

## Key findings

- Weak spin-orbit coupling near Fermi energy sub-bands.
- Small, sparse chemical potential windows for topological phases.
- Topological phase realization requires fine tuning of wire diameter.

## Abstract

We study the electronic structure of full-shell superconductor-semiconductor nanowires, which have recently been proposed for creating Majorana zero modes, using an eight-band $\vec{k} \cdot \vec{p}$ model within a fully self-consistent Schr\"{o}dinger-Poisson scheme. We find that the spin-orbit coupling induced by the intrinsic radial electric field is generically weak for sub-bands with their minimum near the Fermi energy. Furthermore, we show that the chemical potential windows consistent with the emergence of a topological phase are small and sparse and can only be reached by fine tunning the diameter of the wire. These findings suggest that the parameter space consistent with the realization of a topological phase in full-shell InAs/Al nanowires is, at best, very narrow.