# Quantum Anomalous Parity Hall Effect in Magnetically Disordered Topological Insulator Films

## TL;DR

This paper demonstrates a novel quantum anomalous parity Hall phase in magnetically disordered topological insulator films, enabling electrical control of Majorana modes without external magnetic fields.

## Contribution

It introduces the quantum anomalous parity Hall phase arising from magnetic disorder and shows how to manipulate Majorana zero modes electrically in this system.

## Key findings

- Disorder-induced helical edge modes protected by reflection symmetry.
- Electrical creation and manipulation of Majorana zero modes.
- Potential for zero-field topological quantum computing.

## Abstract

In magnetically doped thin-film topological insulators, aligning the magnetic moments generates a quantum anomalous Hall phase supporting a single chiral edge state. We show that as the system de-magnetizes, disorder from randomly oriented magnetic moments can produce a `quantum anomalous parity Hall' phase with \emph{helical} edge modes protected by a unitary reflection symmetry. We further show that introducing superconductivity, combined with selective breaking of reflection symmetry by a gate, allows for creation and manipulation of Majorana zero modes via purely electrical means and at zero applied magnetic field.