Measurement of the conductance distribution function at a quantum Hall transition

TL;DR

This paper experimentally investigates conductance fluctuations at the quantum Hall transition, revealing a uniform conductance distribution consistent with random S-matrix theory predictions for single-channel leads in a magnetic field.

Contribution

It provides the first experimental measurement of conductance distribution at a quantum Hall transition, confirming theoretical predictions for conductance behavior in this regime.

Findings

Conductance fluctuations are reproducible between quantum Hall plateaus.

The conductance distribution is approximately uniform between zero and e^2/h.

Results align with random S-matrix theory predictions.

Abstract

We study experimentally the reproducible conductance fluctuations between the quantum Hall plateaus in the conductance of two-terminal submicron silicon MOSFETs. For the dramatic fluctuations at the insulator-to-first-plateau transition we find a conductance distribution that is approximately uniform between zero and $e^2/h$. We point out that this is consistent with the prediction of random $S$-matrix theory for a conductor with single-channel leads in a magnetic field.