Self-consistent Thomas-Fermi calculation of potential and current distributions in a two-dimensional Hall bar geometry

Abstract

The electrostatics of a two-dimensional, in-plane--gate-defined Hall bar is investigated by imposing the electrochemical equilibrium within the Thomas-Fermi approximation. We calculate the electrostatic potential self-consistently with the electron distribution and examine associated magnetic-field-induced compressible and incompressible regions as a function of temperature, bare screening length, and gate voltage with 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 screening length, our results agree with an analytical work by Chklovskii, Matveev, and Shklovskii. For a small current applied on the Hall bar, the electron distribution is found to be slightly deformed while the width 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.