Electric potential and current distributions in a quantum wire under weak magnetic fields

A self-consistent Schrödinger equation is derived to describe the electrostatic potential distribution of a two-dimensional electronic system confined in a narrow wire in a weak magnetic field using the Hartree approximation. Solving the equation numerically in the lowest lateral mode limit, the electric potential and current distributions across the wire are calculated. It is shown that the Hall voltage defined as the electrostatic potential difference between the two edges of the wire is not quenched but retains the classical linear dependence on the magnetic field. The possibility of a novel weakly coupled voltage measurement is also proposed.