Integer quantum hall effect and correlated disorder

The effect of the form of the random potential of impurities and defects on the longitudinal sigma(xx) and Hall sigma(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 lambda/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 lambda << a(H), the peak values of sigma((N))(xx) are directly proportional to the Landau level number N >= 1, sigma(xx) = 0.5Ne(2)/h, whereas the peak values of sigma((N))(xx) are independent ofthe Landau level number in the case of the long-wavelength potential lambda >> 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.