Fractional quantum Hall state at \nu=1/4 in a wide quantum well

TL;DR

This study uses Monte Carlo and exact diagonalization methods to analyze the quantum Hall state at filling factor 1/4 in a wide quantum well, suggesting a multicomponent nature involving Halperin and Moore-Read states.

Contribution

It provides a detailed numerical analysis of candidate wave functions for the ν=1/4 state in wide quantum wells, highlighting the potential multicomponent nature of the state.

Findings

Overlap with Halperin (5,5,3) and Moore-Read states suggests a multicomponent quantum Hall state.

The Moore-Read Pfaffian state is highly sensitive to interaction parameters.

The observed state likely involves an interplay between different candidate states.

Abstract

We investigate, with the help of Monte-Carlo and exact-diagonalization calculations in the spherical geometry, several compressible and incompressible candidate wave functions for the recently observed quantum Hall state at the filling factor $\nu=1/4$ in a wide quantum well. The quantum well is modeled as a two-component system by retaining its two lowest subbands. We make a direct connection with the phenomenological effective-bilayer model, which is commonly used in the description of a wide quantum well, and we compare our findings with the established results at $\nu=1/2$ in the lowest Landau level. At $\nu=1/4$, the overlap calculations for the Halperin (5,5,3) and (7,7,1) states, the generalized Haldane-Rezayi state and the Moore-Read Pfaffian, suggest that the incompressible state is likely to be realized in the interplay between the Halperin (5,5,3) state and the Moore-Read Pfaffian. Our numerics shows the latter to be very susceptible to changes in the interaction coefficients, thus indicating that the observed state is of multicomponent nature.