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

Abstract

The reduction of the energy gap due to Landau level mixing, characterized by the dimensionless parameter $λ= (e^2/εl_0)/\hbarω_c$, has been calculated by variational Monte Carlo for the fractional quantum Hall effect at filling fractions $ν=1/3$ 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.