A novel microscopic modelling of disorder effects within the non-linear screening theory in the quantized hall regime

In this thesis, we studied the effects of disorder on the integer quantized Hall effect withinthe screening theory, systematically. The disorder potential is analyzed consideringthe range of the potential fluctuations. Short range part of the single impuritypotential is used to define the conductivity tensor elements within the self-consistentBorn approximation, whereas the long range part is treated self-consistently at theHartree level. Briefly, we discussed the extend of the quantized widths Hall plateaus considering the $\emph{mobility}$ of the wafer and the width of the sample, by re-formulating the Ohm?s law at low temperatures and high magneticfields.In the second part of the thesis, discusses a systematic explanation to the unusual non-monotonicbehavior of the Hall resistance observed in two-dimensional electron systems. In the calculations used a semi analytical model based on the interaction theory of the integer quantized Hall effect to investigatethe existence of the anomalous, i.e. overshoot, Hall resistance. The observation of the overshootresistance at low magnetic-field edge of the plateaus is elucidated by means of overlappingevanescent incompressible strips, formed due to strong magnetic fields and interactions. The effects of the sample width, depletion length, disorder strength and magnetic field on the overshoot peaks are investigated in detail.