Physics – Condensed Matter
Scientific paper
1996-07-04
Physics
Condensed Matter
7 pages, Revtex, 3 Encapsulated Postscript figures, uses eps.sty
Scientific paper
We model the insulator neighboring the 1/k quantum Hall phase by a random network of puddles of filling fraction 1/k. The puddles are coupled by weak tunnel barriers. Using Kirchoff's laws we prove that the macroscopic Hall resistivity is quantized at $k h/ e^2$ and independent of magnetic field and current bias -- in agreement with recent experimental observations. In addition, for k>1 this theory predicts non linear longitudinal response $V\sim I^\alpha$ at zero temperature, and $V/I\sim T^{1-{1\over \alpha}}$ at low bias. $\alpha$ is determined using Renn and Arovas' theory for the single junction response, and is related to the Luttinger liquid spectra of the edge states straddling the typical tunnel barrier. The dependence of $V(I)$ on the magnetic field is related to the typical puddle size. Deviations of $V(I)$ from a pure power law are estimated using a series/parallel approximation for the two dimensional random nonlinear resistor network. We check the validity of this approximation by numerically solving for a finite square lattice network.
Auerbach Assa
Shimshoni Efrat
No associations
LandOfFree
The Quantized Hall Insulator does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Quantized Hall Insulator, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Quantized Hall Insulator will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-301829