Conductance fluctuations at the integer quantum Hall plateau transition

TL;DR

This paper numerically investigates conductance fluctuations at the integer quantum Hall plateau transition in mesoscopic systems, revealing a broad, nearly uniform distribution of conductance values consistent with recent experimental observations.

Contribution

It provides a detailed numerical analysis of conductance fluctuations at the quantum Hall transition, highlighting the distribution shape and boundary condition effects.

Findings

Conductance distribution is broad and nearly uniform between 0 and e^2/h.

Results align with recent experimental measurements.

Boundary conditions influence conductance fluctuation characteristics.

Abstract

We study numerically conductance fluctuations near the integer quantum Hall effect plateau transition. The system is presumed to be in a mesoscopic regime, with phase coherence length comparable to the system size. We focus on a two-terminal conductance G for square samples, considering both periodic and open boundary conditions transverse to the current. At the plateau transition, G is broadly distributed, with a distribution function close to uniform on the interval between zero and one in units of e^2/h. Our results are consistent with a recent experiment by Cobden and Kogan on a mesoscopic quantum Hall effect sample.