Composite fermion Hall conductivity and the half-filled Landau level

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.

arXiv comment7 pages, 4 figures; v2: New results on the ac Hall conductivity of composite fermions were added. Introduction and discussion sections were rewritten

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• Fluctuations and magnetoresistance oscillations near the half-filled Landau level
• Self-duality of the integer quantum Hall to insulator transition: composite fermion description
• Emergent reflection symmetry from non-relativistic composite fermions
• Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators
• Composite Fermion Nonlinear Sigma Models
• Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions