Quasiclassical approach to the weak levitation of extended states in the quantum Hall effect

The two-dimensional motion of a charged particle in a random potential and a transverse magnetic field is believed to be delocalized only at discrete energies E-N. In strong fields there is a small positive deviation of E-N from the center of the Nth Landau level, which is referred to as the "weak levitation" of the extended state. I calculate the size of the weak levitation effect for the case of a smooth random potential rederiving earlier results of Haldane and Yang [Phys. Rev. Lett. 78, 298 (1997)] and extending their approach to lower magnetic fields. I find that as the magnetic field decreases, this effect remains weak down to the lowest field B-min where such a quasiclassical approach is still justified. Moreover, in the immediate vicinity of B-min, the weak levitation becomes additionally suppressed. This indicates that the "strong levitation" expected at yet even lower magnetic fields must be of a completely different origin. [S0163-1829(98)03519-X].