Imaging of localized electronic states in the quantum Hall regime

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Abstract
The concept of electron localization has long been accepted to be essential to the physics of the quantum Hall effect1,2 in a two-dimensional electron gas. The exact quantization of the Hall resistance and the zero of the diagonal resistance over a range of filling factors close to integral are attributed to the localization of electronic states at the Fermi level in the interior of the gas. As the electron density is changed, charging of the individual localized states may occur by single-electron jumps3,4, causing associated oscillations in the local electrostatic potential. Here we search for such a manifestation of localized states in the quantum Hall regime, using a scanning electrometer probe5,6. We observe localized potential signals, at numerous locations, that oscillate with changing electron density. In general, the corresponding spatial patterns are complex, but well-defined objects are often seen which evidently arise from individual localized states. These objects interact, and at times form a lattice-like arrangement.