Point-Contact Conductances at the Quantum Hall Transition

TL;DR

This paper investigates the statistical properties of point-contact conductances at the quantum Hall transition using a network model, deriving an explicit conductance distribution and revealing multifractal behavior at criticality.

Contribution

It provides an analytical expression for conductance distribution at the quantum Hall transition and identifies the multifractal spectrum related to conductance fluctuations.

Findings

Derived explicit conductance distribution at criticality.

Numerically computed the conductance exponent as X_t = 0.640 +/- 0.009.

Showed multifractality manifests in transport measurements.

Abstract

On the basis of the Chalker-Coddington network model, a numerical and analytical study is made of the statistics of point-contact conductances for systems in the integer quantum Hall regime. In the Hall plateau region the point-contact conductances reflect strong localization of the electrons, while near the plateau transition they exhibit strong mesoscopic fluctuations. By mapping the network model on a supersymmetric vertex model with GL(2|2) symmetry, and postulating a two-point correlator in keeping with the rules of conformal field theory, we derive an explicit expression for the distribution of conductances at criticality. There is only one free parameter, the power law exponent of the typical conductance. Its value is computed numerically to be X_t = 0.640 +/- 0.009. The predicted conductance distribution agrees well with the numerical data. For large distances between the two contacts, the distribution can be described by a multifractal spectrum solely determined by X_t. Our results demonstrate that multifractality can show up in appropriate transport experiments.