Effects of current and gate voltage on compressible and incompressible strips in a Hall bar

Abstract

Abstract We investigate effects of gate voltage and nondissipative current on compressible and incompressible strips in a two-dimensional, in-plane-gate-defined Hall bar under a strong magnetic field. Within the Thomas–Fermi approximation, we calculate the electron distribution self-consistently with the electrostatic potential, leading to the electrochemical equilibrium. At very low temperature, we find that the formation of compressible and incompressible strips depends strongly on gate voltage, especially in the center of the Hall bar. For a small current applied on the Hall bar, the electron distributions are found to be slightly deformed due to the Lorentz force while the resulting potential distributions are drastically different from the case of zero current.