Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The microscopic nature of localization in the quantum Hall effect   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. The effect involves exact
quantization of all the electronic transport properties due 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. 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 on highly disordered
samples have affirmed the validity of the single-particle picture, other
experiments and some recent theories 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.

17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol