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Quasiclassical approach to the weak levitation of extended states in the quantum Hall effect | | M. M. Fogler
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5 Dec 1997 | | Journal: | Phys. Rev. B 57, 11947 (1998). | | Subject: | Mesoscopic Systems and Quantum Hall Effect | cond-mat.mes-hall | | Affiliation: | IAS | | Abstract: | 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. | | Source: | arXiv, cond-mat/9712070 | | Services: | Forum | Review | PDF | Favorites | |
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