Low temperature electronic transports in the presence of a density gradient

In this paper, we review low temperature electronic transport results in high quality two-dimensional electron systems. We discuss the quantization of the diagonal resistance, RxxRxx, at the edges of several quantum Hall states. Each quantized RxxRxx value turns out to be close to the difference between the two adjacent Hall plateaus in the off-diagonal resistance, RxyRxy. Moreover, peaks in RxxRxx occur at different positions in positive and negative magnetic fields. All three RxxRxx features can be explained quantitatively by a ∼1% cm electron density gradient. Furthermore, based on this observation, the well known but still enigmatic resistivity rule, relating RxxRxx to dRxy/dB, finds a simple interpretation in terms of this gradient. In another sample, at 1.2 K, RxxRxx we observe a strongly linear magnetic field dependence. Surprisingly, this linear magnetoresistance also originates from the density gradient. Our findings throw an unexpected light on the relationship between the experimentally measured RxxRxx and the diagonal resistivity ρxxρxx.