Quantum Phase Transitions and the \nu=5/2 Fractional Hall State in Wide Quantum Wells

TL;DR

This paper investigates the /2 fractional quantum Hall state in wide quantum wells, analyzing the effects of subband and Landau level mixing on particle-hole symmetry and the stability of Moore-Read Pfaffian and anti-Pfaffian states.

Contribution

It introduces a novel method to analyze the Moore-Read Pfaffian and anti-Pfaffian states under periodic boundary conditions considering subband and Landau level mixing.

Findings

Anti-Pfaffian state is favored due to symmetry breaking.

Particle-hole symmetry breaking is observed in finite-size systems.

Anti-Pfaffian becomes more robust near the transition to a compressible phase.

Abstract

We study the nature of the \nu=5/2 quantum Hall state in wide quantum wells under the mixing of electronic subbands and Landau levels. We introduce a general method to analyze the Moore-Read Pfaffian state and its particle-hole conjugate, the anti-Pfaffian, under periodic boundary conditions in a "quartered" Brillouin zone scheme containing both even and odd numbers of electrons. We examine the rotational quantum numbers on the torus, and show spontaneous breaking of the particle-hole symmetry can be observed in finite-size systems. In the presence of electronic-subband and Landau-level mixing the particle-hole symmetry is broken in such a way that the anti-Pfaffian is unambiguously favored, and becomes more robust in the vicinity of a transition to the compressible phase, in agreement with recent experiments.