Half-filled 2D bilayers in a strong magnetic field: Revisiting the $\nu=1/2$ fractional quantum Hall effect

TL;DR

This paper investigates the phase diagram of half-filled bilayer quantum Hall systems under strong magnetic fields, concluding that non-Abelian states are unlikely and Abelian states dominate.

Contribution

It provides a detailed numerical analysis showing the unlikelihood of non-Abelian Moore-Read Pfaffian states in the lowest Landau level bilayers.

Findings

Non-Abelian Moore-Read Pfaffian states are unlikely in the system.

Observed FQHE states are most likely described by the Abelian Halperin 331 state.

The phase diagram depends on tunneling strength and layer separation.

Abstract

We examine the quantum phase diagram of the fractional quantum Hall effect in the lowest Landau level in half-filled bilayer structures as a function of tunneling strength and layer separation. Using numerical exact diagonalization we investigate the important question of whether this system supports a fractional quantum Hall effect described by the non-Abelian Moore-Read Pfaffian state in the strong tunneling regime. We find that, although it is in principle possible, it is unlikely that the non-Abelian FQHE exists in the lowest Landau level. We establish that all so far observed FQHE states in half-filled lowest Landau level bilayers are most likely described by the Abelian Halperin 331 state.