Composite Fermions and Landau Level Mixing in the Fractional Quantum Hall Effect

TL;DR

This paper investigates how Landau level mixing affects the energy gaps in the fractional quantum Hall effect at specific filling factors, using variational Monte Carlo with modified composite fermion wave functions.

Contribution

It introduces a modified wave function approach that incorporates Landau level mixing effects into composite fermion theory for the fractional quantum Hall effect.

Findings

Results align with experiments in n-type GaAs.

Landau level mixing alone cannot explain smaller gaps in p-type systems.

Energy gaps decrease with increasing Landau level mixing parameter .

Abstract

The reduction of the energy gap due to Landau level mixing, characterized by the dimensionless parameter $\lambda = (e^2/\epsilon l_0)/\hbar\omega_c$, has been calculated by variational Monte Carlo for the fractional quantum Hall effect at filling fractions $\nu=1/3$ and 1/5 using a modified version of Jain's composite fermion wave functions. These wave functions exploit the Landau level mixing already present in composite fermion wave functions by introducing a partial Landau level projection operator. Results for the energy gaps are consistent with experimental observations in $n$-type GaAs, but we conclude that Landau level mixing alone cannot account for the significantly smaller energy gaps observed in $p$-type systems.