Anti-levitation in integer quantum Hall systems

The evolution of extended states of two-dimensional electron gas with white-noise randomness and field is numerically investigated by using the Anderson model on square lattices. Focusing on the lowest Landau band we establish an anti-levitation scenario of the extended states: As either the disorder strength W increases or the magnetic field strength B decreases, the energies of the extended states move below the Landau energies pertaining to a clean system. Moreover, for strong enough disorder, there is a disorder-dependent critical magnetic field B-c(W) below which there are no extended states at all. A general phase diagram in the W-1/B plane is suggested with a line separating domains of localized and delocalized states.