The Hall conductivity σxy of a two-dimensional electron system is quantized in units of e2 h when the Fermi level is located in the gap between two Landau levels. We consider the deviation of σxy from a quantized value caused by the thermal activation of electrons to the extended states for the case of a long range random potential. This deviation is of the form σxy*exp( -Δ T). The prefactor σxy* is equal to e2 h at temperatures above a characteristic value T2. Below T2, σxy* decays according to a power law: σxy* = e2 h( T T2)γ. The generalization to fractional Hall plateaux is discussed.
Bibliographical noteFunding Information:
Useful discussionsw ith I. M. Ruzin and D. G. Polya-kov are greatly appreciated.T hii work wss supported by NSF under Grant No. DMR-9321417.
- A. semiconductors D. quantum Hall effect