Composite fermion Hall conductivity and the half-filled Landau level

TL;DR

This paper presents a quantum mechanical numerical study showing that the HLR composite fermion theory exhibits a particle-hole symmetric Hall response under disorder, supporting its compatibility with emergent particle-hole symmetry at half-filled Landau levels.

Contribution

The study provides the first quantum numerical evidence that the HLR theory maintains particle-hole symmetry in the Hall response despite disorder, aligning with recent semi-classical and theoretical analyses.

Findings

HLR theory exhibits particle-hole symmetric dc Hall response with disorder

Robustness of the response even with disorder range comparable to Fermi wavelength

Deviations from symmetry appear at high frequencies in ac Hall conductivity

Abstract

We consider the Hall conductivity of composite fermions in the theory of Halperin, Lee, and Read (HLR). We present a fully quantum mechanical numerical calculation that shows, under suitable conditions, the HLR theory exhibits a particle-hole symmetric dc electrical Hall response in the presence of quenched disorder. Remarkably, this response of the HLR theory remains robust even when the disorder range is of the order of the Fermi wavelength. We find that deviations from particle-hole symmetric response can appear in the ac Hall conductivity at frequencies sufficiently large compared to the inverse system size. Our results agree with a recent semi-classical analysis by Wang et al., Phys. Rev. X 7, 031029 (2017) and complement the arguments based on the fully quantum-mechanical model by Kumar et al., Phys. Rev. B 98, 11505 (2018). These results provide further evidence that the HLR theory is compatible with an emergent particle-hole symmetry.