Study of integer quantum Hall effect in impurity systems by gauge

In this paper we study the integer quantum Hall effect (IQHE) on the systems with different types of impurities in delta and gaussian forms. The Landau energy levels in the presence of impurity split in two different levels,the extended and localized levels, emerging then the Hall step. Finally, we add a specified form of a quantum dot potential to a system with impurity, and observed that increasing the width and height of quantum dot result in removing the Hall step and disappearing the Hall effect. The numerical calculations are in a good agreement with Laughlin’s argument and Prange’s calculation of quantum hall effect.