Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
1997-12-05
Phys. Rev. B 57, 11947 (1998).
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
RevTeX, 4 pages, 1 figure
Scientific paper
10.1103/PhysRevB.57.11947
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 $N$th 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 re-deriving earlier results of Haldane and Yang [PRL 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.
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