Mesoscopic Effects in the Quantum Hall Regime

We report results of a study of (integer) quantum Hall transitions in a single or multiple Landau levels for non-interacting electrons in disordered two-dimensional systems, obtained by projecting a tight-binding Hamiltonian to corresponding magnetic subbands. In finite-size systems, we find that mesoscopic effects often dominate, leading to apparent non-universal scaling behaviour in higher Landau levels. This is because localization length, which grows exponentially with Landau level index, exceeds the system sizes amenable to numerical study at present. When band mixing between multiple Landau levels is present, mesoscopic effects cause a crossover from a sequence of quantum Hall transitions for weak disorder to classical behaviour for strong disorder. This behaviour may be of relevance to experimentally observed transitions between quantum Hall states and the insulating phase at low magnetic fields.