Microscopic Details of the Integer Quantum Hall Effect in an Anti-Hall Bar

TL;DR

This paper uses a Nonequilibrium Network Model to simulate the quantum Hall effect in complex geometries, providing insights into charge inhomogeneities and gating effects that are difficult to measure experimentally.

Contribution

It introduces a simulation approach that accounts for actual sample geometry, enabling detailed analysis of quantum Hall phenomena and charge fluctuations.

Findings

Qualitative agreement with experimental resistance curves

Estimation of carrier concentration and gating potential

Insights into potential fluctuations from charge inhomogeneities

Abstract

Due to the lack of simulation tools that take into account the actual geometry of complicated quantum Hall samples there are lots of experiments that are not yet fully understood. Already some years ago R. G. Mani recorded a shift of the Hall resistance transitions to lower magnetic fields in samples of a Hall bar with embedded anti-Hall bar by using partial gating. We use a Nonequilibrium Network Model (NNM) to simulate this geometry and find qualitative agreement. Fitting the simulated resistance curves to the experimental results we can not only determine the carrier concentration but also obtain an estimate of the screened gating potential and especially the amplitude and lengthscale of potential fluctuations from charge inhomogenities which are not easily accessible by experiment.