Parafermion supporting platform based on spin transitions in the fractional quantum Hall effect regime

TL;DR

This paper proposes a feasible system using spin transitions in the fractional quantum Hall regime to realize parafermions, with experimental and numerical evidence supporting the formation of necessary domain walls.

Contribution

It introduces a new platform based on spin transitions for parafermion realization, combining experimental design and numerical analysis.

Findings

Electrostatically induced spin transitions at filling factor 2/3 enable local control.

Formation of helical domain walls with fractionalized charge is demonstrated.

Numerical studies confirm the potential for parafermion formation when coupled to superconductors.

Abstract

We propose an experimentally-feasible system based on spin transitions in the fractional quantum Hall effect regime where parafermions, high-order non-abelian excitations, can be potentially realized. We provide a proof-of-concept experiments showing that in specially designed heterostructures spin transitions at a filling factor 2/3 can be induced electrostatically, allowing local control of polarization and on-demand formation of helical domain walls with fractionalized charge excitations, a pre-requisite ingredient for parafermions formation. We also present exact diagonalization numerical studies of domain walls formed between domains with different spin polarization in the fractional quantum Hall effect regime and show that they indeed possess electronic and magnetic structure needed for parafermion formation when coupled to an s-wave superconductor.