Manifestation of many-body interactions in the integer quantum Hall effect regime

TL;DR

This paper investigates many-body interactions in the integer quantum Hall regime using self-consistent Hartree-Fock calculations, revealing spin and edge phenomena, and employs a non-equilibrium network model to study transport properties.

Contribution

It introduces a detailed numerical analysis of many-body effects in the IQH regime, highlighting spin interactions, edge stripe formation, and reduced screening effects, with a novel application of a non-equilibrium network model for transport.

Findings

Partly filled Landau levels avoid coexistence of spin states.

Edge stripes with nearly constant filling factor form near half-odd filling.

Screening of disorder is significantly reduced compared to Thomas-Fermi approximation.

Abstract

We use the self-consistent Hartree-Fock approximation for numerically addressing the integer quantum Hall (IQH) regime in terms of many-body physics at higher Landau levels (LL). The results exhibit a strong tendency to avoid the simultaneous existence of partly filled spin-up and spin-down LLs. Partly filled LLs appear as a mixture of coexisting regions of full and empty LLs. We obtain edge stripes with approximately constant filling factor $\nu$ close to half-odd filling at the boundaries between the regions of full and empty LLs, which we explain in terms of the $g$-factor enhancement as a function of a locally varying $\nu$ across the compressible stripes.The many-particle interactions follow a behaviour as it would result from applying Hund's rule for the occupation of the spin split LLs. The screening of the disorder and edge potential appears significantly reduced as compared to screening based on a Thomas-Fermi approximation. For addressing carrier transport, we use a non-equilibrium network model (NNM) that handles the lateral distribution of the experimentally injected non-equilibrium chemical potentials $\mu$.