# Parafermions, induced edge states and domain walls in the fractional quantum Hall effect spin transitions

## TL;DR

This paper explores the formation of parafermions in fractional quantum Hall systems with spin transitions, proposing experimental setups and analyzing edge states and domain walls that could host non-Abelian excitations for topological quantum computing.

## Contribution

It demonstrates the existence of counter-propagating edge modes at spin transition boundaries and proposes conditions under which these systems can host parafermions coupled with superconductors.

## Key findings

- Counter-propagating edge modes with opposite spins identified
- Parafermions can be realized when coupled to s-wave superconductors
- Feasible experimental setups for hosting parafermions in quantum Hall systems

## Abstract

Search for parafermions and Fibonacci anyons, which are excitations obeying non-Abelian statistics, is driven both by the quest for deeper understanding of nature and prospects for universal topological quantum computation. However, physical systems that can host these exotic excitations are rare and hard to realize in experiments. Here we study the domain walls and the edge states formed in spin transitions in the fractional quantum Hall effect. Effective theory approach and exact diagonalization in a disk and torus geometries proves the existence of the counter-propagating edge modes with opposite spin polarizations at the boundary between the two neighboring regions of the two-dimensional electron liquid in spin-polarized and spin-unpolarized phases. By analytical and numerical analysis, we argue that these systems can host parafermions when coupled to an s-wave superconductor and are experimentally feasible. We investigate settings based on $\nu=\frac{2}{3}$, $\nu=\frac{4}{3}$ and $\nu=\frac{5}{3}$ spin transitions and analyze spin-flipping interactions that hybridize counter-propagating modes. Finally, we discuss spin-orbit interactions of composite fermions.