Quantization of the diagonal resistance: Density gradients and the empirical resistance rule in a 2D system

We have observed quantization of the diagonal resistance, R-xx, at the edges of several quantum Hall states. Each quantized R-xx value is close to the difference between the two adjacent Hall plateaus in the off-diagonal resistance, R-xy. Peaks in R-xx occur at different positions in positive and negative magnetic fields. Practically all R-xx features can be explained quantitatively by a 1%/cm electron density gradient. Therefore, R-xx is determined by R-xy and unrelated to the diagonal resistivity rho(xx). Our findings throw an unexpected light on the empirical resistivity rule for 2D systems.