Quantum Hall Plateau Transition — Chalker-Coddington Network

Critical exponent ν≈2.3 · Localization length · Percolation saddle-points

Parameters

ξ/L scaling

CC Model: Saddle points in the random potential landscape scatter electrons between Landau level drifting states. Transmission t through each saddle is tuned by energy.

Critical: At the transition (E=0), ξ(E)∝|E|^{-ν} with ν≈2.3 (numerically). This is a 2D quantum percolation problem.

Plateaux: σ_xy=ne²/h on plateaux, transitions happen only at critical energies.