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Abstract

The quantum Hall effect arises from the interplay between localized and
extended states that form when electrons, confined to two dimensions,
are subject to a perpendicular magnetic field(1). The effect involves
exact quantization of all the electronic transport properties owing to
particle localization. In the conventional theory of the quantum Hall
effect, strong- field localization is associated with a single-
particle drift motion of electrons along contours of constant disorder
potential(2). Transport experiments that probe the extended states in
the transition regions between quantum Hall phases have been used to
test both the theory and its implications for quantum Hall phase
transitions. Although several experiments(3-9) on highly disordered
samples have affirmed the validity of the single- particle picture,
other experiments(10-12) and some recent theories(13-15) have found
deviations from the predicted universal behaviour. Here we use a
scanning single- electron transistor to probe the individual localized
states, which we find to be strikingly different from the predictions
of single- particle theory. The states are mainly determined by Coulomb
interactions, and appear only when quantization of kinetic energy
limits the screening ability of electrons. We conclude that the quantum
Hall effect has a greater diversity of regimes and phase transitions
than predicted by the single-particle framework. Our experiments
suggest a unified picture of localization in which the single- particle
model is valid only in the limit of strong disorder.