Potential and Current Distributions Calculated Across a Quantum Hall Effect Sample at Low and High Currents

The potential and current distributions are calculated across the width of a quantum Hall effect sample for applied currents between 0 μA and 225 μA. For the first time, both a confining potential and a current-induced charge-redistribution potential are used. The confining potential has a parabolic shape, and the charge-redistribution potential is logarithmic. The solution for the sum of the two types of potentials is unique at each current, with no free parameters. For example, the charge-depletion width of the confining potential is determined from a localization experiment by Choi, Tsui, and Alavi, and the spatial extent of the conducting two-dimensional electron gas across the sample width is obtained from the maximum electric field deduced from a high-current breakdown experiment by Cage and Lavine, and from the quantum Hall voltage. The spatial extent has realistic cut-off values at the sample sides; e.g., no current flows within 55 magnetic lengths of the sides for currents less than 215 μA. The calculated potential distributions are in excellent agreement with contactless electro-optic effect laser beam measurements of Fontein et al.