SELF-CONSISTENT THOMAS-FERMI CALCULATION OF POTENTIAL AND CURRENT DISTRIBUTIONS IN A 2-DIMENSIONAL HALL BAR GEOMETRY

The electrostatics of a two-dimensional, in-plane-gate-defined Hall ba r is investigated by imposing the electrochemical equilibrium within t he Thomas-Fermi approximation. We calculate the electrostatic potentia l self-consistently with the electron distribution and examine associa ted magnetic-field-induced compressible and incompressible regions as a function of temperature, bare screening length, and gate voltage wit h and without nondissipative currents. We find that the widths of the incompressible and compressible regions depend strongly on temperature and bare screening length. At very low temperature and small screenin g length, our results agree with an analytical work by Chklovskii, Mat veev, and Shklovskii. For a small current applied on the Hall bar, the electron distribution is found to be slightly deformed while the widt h of the incompressible regions is not changed. Neglecting diamagnetic currents, we find that the current densities are distributed over the whole region occupied by electrons.