QUANTIZED HALL INSULATOR - TRANSVERSE AND LONGITUDINAL TRANSPORT

We model the insulator neighboring the 1/k quantum Hall phase by a ran dom network of puddles of filling fraction 1/k. The puddles are couple d by weak tunnel barriers. Using Kirchoff's laws we prove that the mac roscopic Hall resistivity is quantized at kh/e(2) and independent of m agnetic field and current bias, in agreement with recent experimental observations. In addition, for k>1 this theory predicts a nonlinear lo ngitudinal response V similar to I-alpha at zero temperature and V/I s imilar to T1-l/alpha at low bias. alpha is determined using Renn and A rovas's theory for the single junction response [Phys. Rev. B 51, 16 8 32 (1995)] and is related to the Luttinger liquid spectra of the edge states straddling the typical tunnel barrier. The dependence of V(I) o n the magnetic field is related to the typical puddle size. Deviations of V(I) from a pure power are estimated using a series/parallel appro ximation for the two-dimensional random nonlinear resistor network. We check the validity of this approximation by numerically solving for a finite square lattice newtwork.