Probing the depletion region of a two-dimensional electron system in high magnetic fields

Abstract

To investigate a two-dimensional electron system (2DES) in high magnetic fields and at temperatures below 0.1 K, a metal single-electron transistor (SET) was fabricated as a local electrometer on top of a GaAs/AlGaAs heterostructure containing the 2DES. Probing the bulk of the 2DES, the chemical potential variations of the 2DES versus magnetic field were directly measured and relaxation phenomena on a long time scale were observed within quantum Hall plateau regimes of low Landau-level filling factors. To probe the depletion region of the 2DES, a gate electrode was used to redefine the 2DES edge close to the SET by electrostatical depletion. For a 5 μm distance of the gate electrode's edge to the SET island, the electron concentration under the SET island is only homogeneously reduced by few percent due to the negative voltage applied to the gate electrode. But for a 0.9 μm distance, the SET detects a steep electron concentration gradient, indicating that with increasing the depletion voltage, the 2DES edge is indeed shifted towards the SET. By this approach we mapped out the screening properties and the electrostatic potential variations within the depletion region of the 2DES for magnetic fields corresponding to Landau-level filling factors between ν=1 and ν=4. Compressible and incompressible strips are resolved.