The microscopic nature of localization in the quantum Hall effect

• Published in: Nature (London) Vol. 427; no. 6972; pp. 328 - 332
• Main Authors: Ilani, S., Martin, J., Teitelbaum, E., Smet, J. H., Mahalu, D., Umansky, V., Yacoby, A.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 22.01.2004; Nature Publishing; Nature Publishing Group
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Electronic structure and electrical properties of surfaces, interfaces, thin films and low-dimensional structures; Electronic transport in interface structures; Exact sciences and technology; Humanities and Social Sciences; letter; multidisciplinary; Physics; Quantum hall effect (including fractional); Science; Science (multidisciplinary); Quantum confinement; Disordered systems; Localized states; Theoretical study; Measuring methods; Quantum Hall effect; Transport processes
• ISSN: 0028-0836; 1476-4687; 1476-4687
• DOI: 10.1038/nature02230

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 , 4 , 5 , 6 , 7 , 8 , 9 on highly disordered samples have affirmed the validity of the single-particle picture, other experiments 10 , 11 , 12 and some recent theories 13 , 14 , 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.