Point-contact conductances at the quantum Hall transition

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 $\mathrm{GL}(2|2)$ 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 ${X}_{t}=0.640\ifmmode\pm\else\textpm\fi{}0.009$. 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.