Explanation for the resistivity law in quantum Hall systems.

We consider a 2D electron system in a strong magnetic field, where the local Hall resistivity ρxy(r) is a function of position and ρxx(r) is small compared to ρxy. Particularly if the correlations fall off slowly with distance, or if fluctuations exist on several length scales, one finds that the macroscopic longitudinal resistivity Rxx is only weakly dependent on ρxx and is approximately proportional to the magnitude of fluctuations in ρxy. This may provide an explanation of the empirical law Rxx ∝ B dRxy dB where Rxy is the Hall resistance, and B is the magnetic field. PACS: 73.40.Hm,73.40.-c,64.70.Ak Typeset using REVTEX