Non-Abelian $\nu =1/2$ quantum Hall state in ${\Gamma }_8$ Valence Band Hole Liquid

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.

5 pages, 4 figures, 3-page Supplementary Materials. Submitted to Physical Review Letters

References in corpus (16)

• Non-Abelian Anyons and Topological Quantum Computation
• Particle-hole symmetry and the Pfaffian state
• Entanglement entropy in fermionic Laughlin states
• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
• Bipartite entanglement entropy in fractional quantum Hall states
• Observation of a transition from a topologically ordered to a spontaneously broken symmetry phase
• Topological Entanglement Entropy from the Holographic Partition Function
• Observation of a Fractional Quantum Hall State at $\nu =1/4$ in a Wide GaAs Quantum Well
• Topological Quantum Computing with Read-Rezayi States
• Phase Diagram of Fractional Quantum Hall Effect of Composite Fermions in Multi-Component Systems
• Quantum Hall Phase Diagram of Half-filled Bilayers in the Lowest and the Second Orbital Landau Levels: Abelian versus Non-Abelian Incompressible Fractional Quantum Hall States
• Fractional quantum Hall state at ν=1/4 in a wide quantum well
• $\nu =1/2$ Fractional Quantum Hall Effect in Tilted Magnetic Fields
• Fractional quantum Hall effect and electron correlations in partially filled first excited Landau level

Cited by in corpus (1)

• Disorder-generated non-Abelions