Potential barriers in quantum Hall devices

We investigate numerically the influence of potential barriers on the quantum Hall effect in a six-terminal configuration. The barriers are placed in one of the crossing areas. In agreement with experimental and theoretical results for a simple barrier separating the two crosses, we obtain quantization of the longitudinal resistance R(xx) in addition to the quantization of the Hall resistance R(xy). At a plateau of R(xx) the barrier perfectly separates the edge states into either transmitted states or states deviated along the barrier. For diagonal orientation of the barrier, the two directions of the magnetic field become nonequivalent. In articular, this leads to different plateaus in R(xy) for opposite magnetic fields.