Abstract
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 $W\text{\ensuremath{-}}1/B$ plane is suggested with a line separating domains of localized and delocalized states.
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