Influence of dissipation on the accuracy of the integral quantum Hall effect

The dc conductivity ${\sigma }_{\mathrm{xx}}$ of a two-dimensional electron gas, in the presence of strong magnetic fields, is evaluated for elastic impurity scattering in the first Born approximation. Short-range, long-range, and Gaussian potentials are considered. The results depend explicitly on the scattering, the temperature (T), and the magnetic field. For low temperatures and high magnetic fields the conductivity shows an activated type of behavior as observed experimentally. For an integer filling factor the deviation Δ${\sigma }_{\mathrm{yx}}$(T) of the Hall conductivity from its zero-temperature quantized value, obtained previously, is equal to α${\sigma }_{\mathrm{xx}}$(T); the coefficient α depends on the scattering, on the magnetic field, and, for constant impurity concentration, on the temperature.