Activated conductivity in the quantum Hall effect

Activated dissipative conductivity σxx = σ*xxexp(−Δ/T) and the activated deviation of the Hall conductivity from the precise quantization δσxy = σxy −ie2/h= σ*xyexp(−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 = (e2h)(T2T)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.