The quantized Hall insulator

We model the insulator neighbouring a 1/k quantum Hall phase by a random network of puddles of filling fraction 1/k. The puddles are coupled by weak tunnel barriers. We prove that the macroscopic Hall resistivity is quantized at kh/e² and independent of magnetic field and current bias, in agreement with recent experimental observations. In addition, for k > 1 this theory predicts a nonlinear longitudinal response V α I^α at zero temperature, and V/I α T^1-1/α at low biases. α is determined by 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.