Compressibility images of the quantum Hall state

We have imaged the electronic compressibility of a two-dimensional electron gas in the integer quantum Hall regime. The compressibility images show qu asi-insulating "incompressibie" strips that separate region of electron liq uid of near integer filling. The strips follow the contours of constant ele ctron density that match exact occupancy of the Landau levels, and shift ac cordingly with magnetic field and electron density changes. The surface ele ctrostatic potential distribution has an overall correlation with the compr essibility patterns and the density contours marked by them and an abrupt s tep, at the boundaries, that provides a direct measure of the energy gap be tween the Landau levels. (C) 2001 Elsevier Science B.V. All rights reserved .