Activated conductivity in the quantum Hall effect

Abstract

Activated dissipative conductivity σ xx = σ* xxexp(−Δ/ T) and the activated deviation of the Hall conductivity from the precise quantization δσ xy = σ xy − ie 2/ 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 T 1 ≪ T ≪ T 2 where σ* xy = e 2/ h. In this range σ* xy ≈ ( e 2/ h)( T/ T 2) 80/21 ≪ σ* xx. At large T ≫ T 2, on the other hand, σ* xy = e 2/ h and σ* xx = ( e 2h)( T 2 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.