Single-electron states in the quantum Hall effect

Spatially localized electronic states in a two-dimensional electron gas in the quantum Hall regime are imaged using a scanning single-electron-transistor probe. Two different regimes of localization are identified depending on the strength of the built-in long-range density fluctuations. In the smoother regions localized states merge into dielectric-like blobs a few μm in extent. In the places with a stronger density gradient complex patterns occur which change markedly with an addition of a single electron. The simplest appearance of the latter is a ring collapsing toward the center as an electron is added to the area.