WEAK-FIELD PHASE-DIAGRAM FOR AN INTEGER QUANTUM HALL LIQUID

We investigate the transition of a two-dimensional electron gas from t he regime of the quantum Hall effect to the regime of weak magnetic fi elds for a tight-binding model. Unlike previous work, we find the foll owing: (1) the linear field dependence of the extended-state energies is not affected by disorder, although the total density of states belo w each level of extended states increases with disorder strength; (2) for each Landau band and disorder strength there exists a critical fie ld B-c below which the extended level disappears, with B-c smaller for lower Landau bands. We show how the experimental findings of level fl otation and direct transition from high Landau level states to the And erson insulating phase may be explained in light of our results.