Conductivity tensor of a two‐dimensional electron gas in a strong magnetic field in higher orders of perturbation theory. Quantum hall effect

The components of the conductivity tensor σ are considered for the case of a strong magnetic field H . The investigation of the higher orders in perturbation theory up to the fourth order in static scattering potential shows that for an electric field E under the condition E ≪ E 0 [ heH 3 /2 m 2 c 3 ] 1/2 the Hall conductivityand the transverse conductivity σ yy ∼ exp (− E   0 2 / E 2 here N e , is the carrier concentration. In virtue of the extreme small collisional contribution to the conductivity the picture of the quantum Hall effect is similar to that for an ideal noninteracting two‐dimensional electron gas.