# Vortex Lattice Structure and Topological Superconductivity in the Quantum Hall Regime

## TL;DR

This paper investigates how vortex lattice structure influences the emergence of topological superconductivity and Majorana modes in quantum Hall systems coupled to s-wave superconductors, highlighting the importance of vortex lattice engineering.

## Contribution

It explicitly accounts for Landau quantization in quantum Hall-superconductor systems and links vortex lattice structure to topological phase realization.

## Key findings

- Odd flux vortex lattices support even Majorana edge modes
- Vortex lattice structure determines topological phase transition
- Strategies proposed for engineering chiral topological superconductivity

## Abstract

Chiral topological superconductors are expected to appear as intermediate states when a quantum anomalous Hall system is proximity coupled to an s-wave superconductor and the magnetization direction is reversed. In this paper we address the edge state properties of ordinary quantum Hall systems proximity coupled to s-wave superconductors, accounting explicitly for Landau quantization. We find that the appearance of topological superconducting phases with an odd number of Majorana edge modes is dependent on the structure of the system's vortex lattice. More precisely, vortex lattices containing odd number of superconducting flux quanta per unit cell, always support an even number of chiral edge channels and are therefore adiabatically connected to normal quantum Hall insulators. We discuss strategies to engineer chiral topological superconductivity in proximity-coupled quantum Hall systems by manipulating vortex lattice structure.