Conditions for the quantum Hall effect

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Abstract
The quantum Hall effect occurs in imperfect two-dimensional systems of electrons subjected to strong perpendicular magnetic fields. We determine the conditions on the random imperfection potential, relative to the magnetic field, under which the quantum Hall effect may be expected to occur, if electron-electron interactions are neglected. It is found that all physically reasonable disordered potentials should exhibit the effect in the limit of large field (with electron density increased proportional to the field). This is done by examining the behavior of the eigenstates in various kinds of potentials and collecting the results. Earlier work is reviewed in this context. The consequences for localization in two dimensions in a strong magnetic field are discussed. The mechanism of localization turns out to be qualitatively different from that of Anderson localization.