Phase diagram and edge states of the $\nu=5/2$ fractional quantum Hall state with Landau level mixing and finite well thickness

TL;DR

This study investigates the $ u=5/2$ fractional quantum Hall state, revealing how Landau level mixing and finite well thickness influence its edge states, phase transitions, and the stability of candidate ground states like Pfaffian and anti-Pfaffian.

Contribution

It provides the first detailed analysis of Landau level mixing and finite thickness effects on the $ u=5/2$ state using exact diagonalization, highlighting phase transitions and edge state modifications.

Findings

Phase transition from anti-Pfaffian to Pfaffian with LL mixing.

LL mixing increases quasihole size and overcomes edge reconstruction.

Finite thickness enhances these effects and stabilizes energy gaps for Pfaffian and anti-Pfaffian states.

Abstract

The $\nu=5/2$ fractional quantum Hall effect is a system of intense experimental and theoretical interest as its ground state may host non-abelian excitations, but the exact nature of the ground state is still undetermined. We present the results of an exact diagonalization study of an electron system in the disk configuration including the effects of Landau level (LL) mixing and the finite thickness of the quantum well confining the electrons. The degeneracy between the two leading candidates for the ground state, the Pfaffian and anti-Pfaffian, is broken by interactions with a neutralizing background, in addition to the inclusion of two- and three-body interactions via LL mixing. As a result of the neutralizing background in the disc configuration, there is a phase transition from the anti-Pfaffian to the Pfaffian as LL mixing is turned on, in stark contrast to what is observed in a spherical geometry. The LL mixing leads to an increased charge $e/4$ quasihole size. LL mixing interactions are also shown to overcome the effects of edge reconstruction. Due to finite thickness effects, these properties are enhanced dramatically. We also find that only the Pfaffian and anti-Pfaffian states continue to possess energy gaps at finite width, while gaps for compressible stripe states close.