First-Principles Study of Integer Quantum Hall Transitions in Mesoscopic Samples

TL;DR

This study uses first-principles simulations to analyze resistance fluctuations in mesoscopic samples during quantum Hall transitions, reproducing experimental features and explaining fluctuation types through a generalized transport model.

Contribution

It introduces a first-principles numerical approach combined with a generalized Landauer-Büttiker model to explain quantum Hall transition phenomena in mesoscopic samples.

Findings

Reproduces experimental resistance fluctuation features.

Identifies three types of fluctuations near quantum Hall transitions.

Highlights the critical role of the central region in transport.

Abstract

We perform first principles numerical simulations to investigate resistance fluctuations in mesoscopic samples, near the transition between consecutive Quantum Hall plateaus. We use six-terminal geometry and sample sizes similar to those of real devices. The Hall and longitudinal resistances extracted from the generalized Landauer formula reproduce all the experimental features uncovered recently. We then use a simple generalization of the Landauer-B\"uttiker model, based on the interplay between tunneling and chiral currents -- the co-existing mechanisms for transport -- to explain the three distinct types of fluctuations observed, and identify the central region as the critical region.