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. 
W. Pan, J.S. Xia, H.L. Stormer, D.C. Tsui, C.L. Vicente, E.D. Adams,   N.S. Sullivan, L.N. Pfeiffer, K.W. Baldwin, and K.W. West