Origin of the $\nu=1/2$ fractional quantum Hall effect in wide quantum wells

TL;DR

This paper introduces a three-dimensional fixed phase Monte Carlo method to study the $ u=1/2$ fractional quantum Hall effect in wide quantum wells, revealing it is likely a non-Abelian Pfaffian state.

Contribution

It develops a novel 3D fixed phase Monte Carlo approach that includes Landau level mixing, providing new insights into the nature of the $ u=1/2$ state in wide quantum wells.

Findings

The $ u=1/2$ state is likely a non-Abelian Pfaffian state.

The method accounts for Landau level mixing and finite well width effects.

Results support the one-component nature of the observed state.

Abstract

The nature of the fractional quantum Hall effect at $\nu=1/2$ observed in wide quantum wells almost three decades ago is still under debate. Previous studies have investigated it by the variational Monte Carlo method, which makes the assumption that the transverse wave function and the gap between the symmetric and antisymmetric subbands obtained in a local density approximation at zero magnetic field remain valid even at high perpendicular magnetic fields; this method also ignores the effect of Landau level mixing. We develop in this work a three-dimensional fixed phase Monte Carlo method, which gives, in a single framework, the total energies of various candidate states in a finite width quantum well, including Landau level mixing, directly in a large magnetic field. This method can be applied to one-component states, as well two-component states in the limit where the symmetric and antisymmetric bands are nearly degenerate. Our three-dimensional fixed-phase diffusion Monte Carlo calculations suggest that the observed 1/2 fractional quantum Hall state in wide quantum wells is likely to be the one-component Pfaffian state supporting non-Abelian excitations. We hope that this will motivate further experimental studies of this state.