The microscopic picture of the integer quantum Hall regime

TL;DR

This paper uses advanced self-consistent Hartree-Fock modeling to provide detailed microscopic insights into the integer quantum Hall effect, revealing spatial electron density structures, phase behaviors, and transport phenomena.

Contribution

It demonstrates that Hartree-Fock calculations can quantitatively reproduce and explain microscopic features of the integer quantum Hall regime, including phase formations and transport channels.

Findings

Identification of self-organized electron density clusters.

Observation of bubble and stripe phases in weak disorder regimes.

Reproduction of experimental transport channel characteristics.

Abstract

Computer modelling of the integer quantum Hall effect based on self-consistent Hartee-Fock calculations has now reached an astonishing level of maturity. Spatially-resolved studies of the electron density at near macroscopic system sizes of up to $\sim 1\ \mu m^2$ reveal self-organized clusters of locally fully filled and locally fully depleted Landau levels depending on which spin polarization is favoured. The behaviour results, for strong disorders, in an exchange-interaction induced $g$-factor enhancement and, ultimately, gives rise to narrow transport channels, including the celebrated narrow edge channels. For weak disorder, we find that bubble and stripes phases emerge with characteristics that predict experimental results very well. Hence the HF approach has become a convenient numerical basis to \emph{quantitatively} study the quantum Hall effects, superseding previous more qualitative approaches.