The effect of disorder on integer quantized Hall effect

We study the effects of disorder on the integer quantized Hall effect within the screening theory, systematically. The disorder potential is analyzed considering the range of the potential fluctuations. The short-range potential fluctuations (View the MathML source) stems from single impurities and defines the Landau level broadening, whereas, the long-range potential fluctuations (View the MathML source) are calculated from the potential overlap of many-impurities, which in turn determines the widths of the plateaus. The short-range part is taken into account via self-consistent Born approximation hence determining the conductivities and a local version of Ohmʹs law is utilized to define charge transport. We investigate the long range potential fluctuations taking into account interaction effects and explore its effect on the formation of quantum Hall plateaus depending on the number of impurities, the amplitude of the impurity potential and the separation thickness by solving the 3D Poisson equation iteratively. We discuss the long range part of the potential fluctuations by investigating the Coulomb interaction of the two dimension electron gas numerically. We show that the widths of the quantized Hall plateaus increase with increasing disorder, whereas the influence of level broadening is suppressed at narrow Hall bars.