Current density in a quantum Hall bar

When current is forced through a quantum Hall bar it is understood that it flows primarily through edge states. These represent extra charges that in turn produce a more widely distributed current density that falls off rather slowly with distance and then drops rapidly as a result of screening by particles beyond the depletion region. We have solved numerically the self consistent Schro{}dinger equation in the Hartree approximation for ideal samples with small widths and sharp boundaries, and combined these results with the Wiener-Hopf technique to obtain an accurate picture of the situation for macroscopically wide samples. Our results indicate that the redistribution of states in the bulk of a quantum Hall bar is a very important effect and that the bulk states contribute to a significant fraction of the total current.