Fractional Quantum Hall Effects in HgTe Quantum Wells

TL;DR

This paper investigates the potential for fractional quantum Hall states in HgTe quantum wells, demonstrating the support for various states and analyzing the effects of well width and Landau level mixing on their stability.

Contribution

It provides the first detailed numerical analysis of fractional quantum Hall states in HgTe quantum wells, highlighting conditions for their stability and dominance.

Findings

Laughlin, Moore-Read, and Read-Rezayi states can be supported in HgTe quantum wells.

Landau level mixing can destroy gaps near the level crossing point.

Well width influences the stability and dominance of different fractional quantum Hall states.

Abstract

We study the possibility of fractional quantum Hall effects in HgTe quantum wells using exact diagonalization. Our results show that Laughlin states, the Moore-Read state, and the Read-Rezayi $Z_3$ state can all be supported. However, near the level crossing point (of the single-particle spectrum), the gap can be destroyed by Landau level mixing, and the Moore-Read state and the Read-Rezayi state dominate over their respective competing states only for wide wells. For smaller well widths the Moore-Read state crosses over to the composite fermion Fermi sea, while the Read-Rezayi state loses its dominance over the hierarchy state.