Percolation, quantum tunnelling and the integer Hall effect

A model is introduced for Anderson localisation in the integer quantum Hall regime. The model represents a system with a disordered potential that varies slowly on the scale of the magnetic length, but includes quantum tunnelling and interference effects. Numerical calculations indicate that the localisation length diverges only at the centre of each Landau band. The scaling behaviour near the mobility edge is analysed: results suggest that quantum tunnelling induces crossover at the classical percolation threshold to critical behaviour similar to that found previously for a rapidly varying potential.