Non-Abelian $\nu=1/2$ quantum Hall state in $\Gamma_8$ Valence Band Hole Liquid

TL;DR

This paper investigates the fractional quantum Hall effect in a two-dimensional hole system, proposing a new mapping method to identify non-Abelian states with potential applications in quantum computing.

Contribution

It introduces a novel mapping technique for hole states in quantum wells and demonstrates the emergence of a non-Abelian fractional quantum Hall state at half-filling.

Findings

Incompressible fractional quantum Hall state found at half-filling.

State shows significant overlap with Moore-Read Pfaffian, indicating non-Abelian nature.

Excited states also exhibit non-Abelian characteristics.

Abstract

In search of states with non-Abelian statistics, we explore the fractional quantum Hall effect in a system of two-dimensional charge carrier holes. We propose a new method of mapping states of holes confined to a finite width quantum well in a perpendicular magnetic field to states in a spherical shell geometry. This method provides single-particle hole states used in exact diagonalization of systems with a small number of holes in the presence of Coulomb interactions. An incompressible fractional quantum Hall state emerges in a hole liquid at the half-filling of the ground state in a magnetic field in the range of fields where single-hole states cross. This state has a negligible overlap with the Halperin 331 state, but a significant overlap with the Moore-Read Pfaffian state. Excited fractional quantum Hall states for small systems have sizable overlap with non-Abelian excitations of the Moore-Read Pfaffian state.