On modeling quantum point contacts in quantum Hall systems

TL;DR

This paper introduces two models for quantum point contacts in quantum Hall systems that incorporate spatial extension effects, explaining deviations from traditional models and their impact on tunneling behavior and transport properties.

Contribution

The paper presents two novel models accounting for QPC spatial extension, improving understanding of energy-dependent tunneling in quantum Hall regimes.

Findings

Wide-QPC model predicts decreasing tunneling amplitude away from Fermi level.

Long-QPC model predicts increasing tunneling amplitude away from Fermi level.

Models show opposite energy dependence, affecting transport predictions.

Abstract

Quantum point contacts (QPC) are a key instrument in investigating the physics of edge excitations in the quantum Hall effect. However, at not-so-high bias voltage values, the predictions of the conventional point QPC model often deviate from the experimental data both in the integer and (more prominently) in the fractional quantum Hall regime. One of the possible explanations for such behaviors is the dependence of the tunneling between the edges on energy, an effect not present in the conventional model. Here we introduce two models that take QPC spatial extension into account: wide-QPC model that accounts for the distance along which the edges are in contact; long-QPC model accounts for the fact that the tunneling amplitude originates from a finite bulk gap and a finite distance between the two edges. We investigate the predictions of these two models in the integer quantum Hall regime for the energy dependence of the tunneling amplitude. We find that these two models predict opposite dependences: the amplitude decreasing or increasing away from the Fermi level. We thus elucidate the effect of the QPC geometry on the energy dependence of the tunneling amplitude and investigate its implications for transport observables.