Imaging of localized electronic states in the quantum Hall regime

The concept of electron localization has long been accepted to be essential to the physics of the quantum Hall effect(1,2) in a two-dimensional electr on gas. The exact quantization of the Ball resistance and the zero of the d iagonal resistance over a range of filling factors close to integral are at tributed 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 i ndividual localized states may occur by single-electron jumps(3,4), causing associated oscillations in the local electrostatic potential. Here we sear ch for such a manifestation of localized states in the quantum Hall regime, using a scanning electrometer probe(5,6). We observe localized potential s ignals, at numerous locations, that oscillate with changing electron densit y. In general, the corresponding spatial patterns are complex, but well-def ined objects are often seen which evidently arise from individual localized states. These objects interact, and at times form a lattice-like arrangeme nt.