Abstract
The effect of the form of the random potential of impurities and defects on the longitudinal σ xx and Hall σ xy components of conductivity in the mode of the integer quantum Hall effect is theoretically investigated. It is shown that the width of the Hall conductivity plateau as well as the peak values of the longitudinal conductivity heavily depend on the ratio λ/a H between the random potential correlation length and the magnetic length. For the first time, it is established that in the case of the short-wavelength potential λ ≪ a H, the peak values of σ xx (N) are directly proportional to the Landau level number N ≥ 1, σ xx = 0.5Ne 2/h, whereas the peak values of σ xx (N) are independent of the Landau level number in the case of the long-wavelength potential λ ≫ a H, and their magnitude is much lower than 0.5e 2/h. The obtained results are in good agreement with the available experimental data.
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