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 (≲20nm) stems from single impurities and defines the Landau level broadening, whereas, the long-range potential fluctuations (≳200nm) 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 Ohm's 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.

Graphical abstractWe plot the estimated long range part of the disorder potential considering various number of impurities NINI and impurity potential amplitude VimpVimp.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► We discuss the effect of disorder on the quantum Hall plateaus. ► We find that the plateau widths depend on the long range fluctuations of the disorder. ► We find that the long range disorder potential is well screened.