Long time relaxation phenomena of a two-dimensional electron system within integer quantum Hall plateau regimes after magnetic field sweeps

For investigating a two-dimensional electron system (2DES) in high magnetic fields and at temperatures below 0.1 K a single electron transistor (SET) is directly fabricated on top of a GaAs/AlGaAs heterostructure containing the 2DES underneath the surface. By using the SET as a highly sensitive electrostatic potential probe, the variation of the local electrostatic potential in the 2DES under the SET can be observed. Sweeping the magnetic field over a Hall plateau regime, a characteristic hysteresislike dependence of the local electrostatic potential between up and down sweep is observed indicating a nonequilibrium state for the 2DES. Stopping the magnetic field in a Hall plateau regime, the relaxation of the nonequilibrium potential distribution within the 2DES into the thermodynamic equilibrium at very low temperatures can elapse over several hours. The hysteresis effect is interpreted as the fingerprints of eddy currents which are driven by induced electrochemical potential gradients across the incompressible regions of the 2DES.