Numerical calculation of the current-voltage dependence in the quantum hall effect regime

We solve numerically the equation for the charge distribution in a 2 D strip in the quantum Hall effect regime, derived earlier [1], and obtain the current-voltage dependence. We find that in the Corbino geometry the current grows exponentially with increasing voltage, in accordance with the experimental data. At high voltages the field distribution across the strip is found to be strongly inhomogeneous, so that all the voltage drop occurs over a narrow region where the local field is very high.