TY - JOUR

T1 - Quantized Hall insulator

T2 - Transverse and longitudinal transport

AU - Shimshoni, Efrat

AU - Auerbach, Assa

PY - 1997

Y1 - 1997

N2 - 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 Kirchoffșs laws we prove that the macroscopic Hall resistivity is quantized at kh/(Formula presented) 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∼(Formula presented) at zero temperature and V/I∼(Formula presented) at low bias. α is determined using Renn and Arovasșs theory for the single junction response [Phys. Rev. B 51, 16 832 (1995)] 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 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.

AB - 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 Kirchoffșs laws we prove that the macroscopic Hall resistivity is quantized at kh/(Formula presented) 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∼(Formula presented) at zero temperature and V/I∼(Formula presented) at low bias. α is determined using Renn and Arovasșs theory for the single junction response [Phys. Rev. B 51, 16 832 (1995)] 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 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.

UR - http://www.scopus.com/inward/record.url?scp=0000952413&partnerID=8YFLogxK

U2 - 10.1103/physrevb.55.9817

DO - 10.1103/physrevb.55.9817

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0000952413

SN - 1098-0121

VL - 55

SP - 9817

EP - 9823

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

IS - 15

ER -