Scanning capacitance imaging of compressible and incompressible quantum Hall effect edge strips

We use dynamic scanning capacitance microscopy to image compressible and incompressible strips at the edge of a Hall bar in a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime. This method gives access to the complex local conductance, G_ts, between a sharp metallic tip scanned across the sample surface and ground, comprising the complex sample conductance. Near integer filling factors we observe a bright stripe along the sample edge in the imaginary part of G_ts. The simultaneously recorded real part exhibits a sharp peak at the boundary between the sample interior and the stripe observed in the imaginary part. The features are periodic in the inverse magnetic field and consistent with compressible and incompressible strips forming at the sample edge. For currents larger than the critical current of the QHE break-down the stripes vanish sharply and a homogeneous signal is recovered, similar to zero magnetic field. Our experiments directly illustrate the formation and a variety of properties of the conceptually important QHE edge states at the physical edge of a 2DEG.