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 $1\%/\mathrm{cm}$ 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.

• Received 20 April 2005

DOI:https://doi.org/10.1103/PhysRevLett.95.066808