# Effects of the electrostatic environment on superlattice Majorana nanowires

## TL;DR

This study investigates how the electrostatic environment influences the formation and detection of Majorana bound states in superlattice nanowires, emphasizing the importance of 3D modeling for accurate phase diagram predictions.

## Contribution

It provides a comprehensive 3D self-consistent numerical analysis of superlattice nanowires, highlighting the role of electrostatics and surface charges in topological phase realization.

## Key findings

- 3D electrostatic environment critically affects Majorana states.
- Surface charge and superlattice dimensions influence topological phases.
- Accurate phase diagrams require detailed electrostatic modeling.

## Abstract

Finding ways of creating, measuring and manipulating Majorana bound states (MBSs) in superconducting-semiconducting nanowires is a highly pursued goal in condensed matter physics. It was recently proposed that a periodic covering of the semiconducting nanowire with superconductor fingers would allow both gating and tuning the system into a topological phase while leaving room for a local detection of the MBS wavefunction. We perform a detailed, self-consistent numerical study of a three-dimensional (3D) model for a finite-length nanowire with a superconductor superlattice including the effect of the surrounding electrostatic environment, and taking into account the surface charge created at the semiconductor surface. We consider different experimental scenarios where the superlattice is on top or at the bottom of the nanowire with respect to a back gate. The analysis of the 3D electrostatic profile, the charge density, the low energy spectrum and the formation of MBSs reveals a rich phenomenology that depends on the nanowire parameters as well as on the superlattice dimensions and the external back gate potential. The 3D environment turns out to be essential to correctly capture and understand the phase diagram of the system and the parameter regions where topological superconductivity is established.