Electrical imaging of the quantum Hall state

Microscopic images of the local electron compressibility, electrostatic pot ential, and current-induced Hall voltage of a two-dimensional sheet of elec trons in the quantum Hall regime are acquired using a single-electron trans istor as a scanned probe. Regions identified as differing in quantum state (Landau level) occupancy of the electrons appear in interrelated ways in al l of these properties. The compressibility images show quasi-insulating "in compressible" strips, associated with edge states that bound these regions. These strips follow the contours of a constant electron density that match exact occupancy of Landau levels, and shift accordingly with magnetic fiel d and electron density changes. The potential distribution has an overall c orrelation with the density contours marked by the incompressible strips an d a step across the strips that provides a direct measure of the energy gap between Landau levels. The Hall voltage and the inferred current flow patt erns are also guided by these strips. (C) 1999 Elsevier Science Ltd. All ri ghts reserved.