Activated dissipative conductivity σxx = σ*xx exp(-Δ/T) and the activated deviation of the Hall conductivity from the precise quantization δσxy = σxy-ie2/h = σ*xy exp(-Δ/T) are studied in a plateau range of the quantum Hall effect. The prefactors σ*xx and σ*xy are calculated for the case of a long-range random potential in the framework of a classical theory. There is a range of temperatures T1«T«T2 where σ*xy = e2/h. In this range σ*xy≈(e2/h)(T/T2) 80/21«σ*xx. At large T»T2, on the other hand, σ*xy = e2/h and σ*xx = (e2/h)(T2/T)10/13«σ* xy. Similar results are valid for a fractional plateau near the filling factor p/q if charge e is replaced by e/q.
Bibliographical noteFunding Information:
Useful discussions with I.L. Aleiner, V.I. Perel and I.M. R1;7~n are greatly appreciated. This work was supported by NSF under Grant No. DMR-9321417.
- Hall effect