Stability of the k=3 Read-Rezayi state in chiral two-dimensional systems with tunable interactions

TL;DR

This paper proposes that the k=3 Read-Rezayi state, which hosts non-Abelian anyons for topological quantum computing, can be realized in chiral 2D materials like graphene and topological insulators with tunable interactions, enabling experimental study.

Contribution

It introduces a new platform using chiral materials with tunable interactions to realize and investigate the Read-Rezayi state, overcoming limitations of traditional GaAs systems.

Findings

Tunable interactions in chiral materials facilitate realization of the RR state.

External magnetic field and dielectric environment control the energy gaps.

Proposed platform allows exploration of quantum phase transitions.

Abstract

The k=3 Read-Rezayi (RR) parafermion quantum Hall state hosts non-Abelian excitations which provide a platform for the universal topological quantum computation. Although the RR state may be realized at the filling factor \nu=12/5 in GaAs-based two-dimensional electron systems, the corresponding quantum Hall state is weak and at present nearly impossible to study experimentally. Here we argue that the RR state can alternatively be realized in a class of chiral materials with massless and massive Dirac-like band structure. This family of materials encompasses monolayer and bilayer graphene, as well as topological insulators. We show that, compared to GaAs, these systems provide several important advantages in realizing and studying the RR state. Most importantly, the effective interactions can be tuned {\it in situ} by varying the external magnetic field, and by designing the dielectric environment of the sample. This tunability enables the realization of RR state with controllable energy gaps in different Landau levels. It also allows one to probe the quantum phase transitions to other compressible and incompressible phases.