Spatial potential distribution in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As heterostructures under quantum Hall conditions studied with the linear electro-optic effect

We apply the linear electro-optic effect (Pockels effect) to investigate the spatial potential distribution in GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As heterostructures under quantum Hall conditions. With this method, which avoids electrical contacts and thus does not disturb the potential distribution, we probe the electrostatic potential of the two-dimensional electron gas (2DEG) locally. Scanning across the sample we observe a steep change of the Hall potential at the edges of the 2DEG over a distance of about 70 μm, the lateral resolution of the experimental setup. This change at the edges accounts for more than 80% of the total Hall voltage. The remainder of the Hall potential is distributed in the interior of the sample and varies linearly with the position. The results are interpreted in terms of unscreened charge at the edges.