Explanation for the Resistivity Law in Quantum Hall System

Details Explanation for the Resistivity Law in Quantum Hall System Explanation for the Resistivity Law in Quantum Hall System

1994-06-07

arxiv.org/abs/cond-mat/9406031v3

Physics

Condensed Matter

11 pages (REVTeX 3.0). Revised Version. Complete postscript file for this paper is available on the World Wide Web at http:/

Scientific paper

10.1103/PhysRevLett.73.3278

We consider a 2D electron system in a strong magnetic field, where the local Hall resistivity $\rho_{xy}(\vec r)$ is a function of position and $\rho_{xx}(\vec r)$ is small compared to $\rho_{xy}$. Particularly if the correlations fall off slowly with distance, or if fluctuations exist on several length scales, one finds that the macroscopic longitudinal resistivity $R_{xx}$ is only weakly dependent on $\rho_{xx}$ and is approximately proportional to the magnitude of fluctuations in $\rho_{xy}$. This may provide an explanation of the empirical law $R_{xx} \propto B \frac{dR_{xy}}{dB}$ where $R_{xy}$ is the Hall resistance, and $B$ is the magnetic field.

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