Correlated mesoscopic fluctuations in integer quantum Hall transitions

TL;DR

This paper uses realistic simulations to explain mesoscopic resistance fluctuations near quantum Hall transitions, revealing the interplay of tunneling and chiral currents as key factors.

Contribution

It provides a unified theoretical explanation for experimental resistance fluctuations in quantum Hall transitions using first-principles simulations and an extended Landauer-Buttiker model.

Findings

Simulations reproduce all experimental fluctuation features.

Identifies the critical region where localization length exceeds sample size.

Explains the three fluctuation regimes based on tunneling and chiral currents.

Abstract

We investigate the origin of the resistance fluctuations of mesoscopic samples, near transitions between Quantum Hall plateaus. These fluctuations have been recently observed experimentally by E. Peled et al. [Phys. Rev. Lett. 90, 246802 (2003); ibid 90, 236802 (2003); Phys. Rev. B 69, R241305 (2004)]. We perform realistic first-principles simulations using a six-terminal geometry and sample sizes similar to those of real devices, to model the actual experiment. We present the theory and implementation of these simulations, which are based on the linear response theory for non-interacting electrons. The Hall and longitudinal resistances extracted from the Landauer formula exhibit all the observed experimental features. We give a unified explanation for the three regimes with distinct types of fluctuations observed experimentally, based on a simple generalization of the Landauer-Buttiker model. The transport is shown to be determined by the interplay between tunneling and chiral currents. We identify the central part of the transition, at intermediate filling factors, as the critical region where the localization length is larger than the sample size.