Abstract
A theory of non-linear screening of a two-dimensional electron gas (2DEG) in a strong magnetic field and in a smooth random potential at T=0 is presented. Only electrons of partly occupied Landau levels (LL) are assumed to take part in the screening. It is shown that a high density of states (DOS) in the middle between two LL's can be explained in the framework of the theory. The width of the QHE plateau is estimated for the case of a strong disorder.
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