Conductances, conductance fluctuations, and level statistics on the surface of multilayer quantum Hall states

摘要: Transport properties on the two-dimensional surface of coupled multilayer heterostructures are studied in integer quantum Hall states. We emphasize criticality state and phase-coherent transport thermodynamic limit. A stable numerical algorithm for large-scale conductance calculations transfer-matrix approach is discussed detail. It then applied to a directed network model describing quantum-mechanical tunneling impurity scattering edge calculate two-probe direction parallel external magnetic field, its fluctuations statistical distributions, as functions interlayer strength. Using finite-size scaling, asymptotic scaling ensemble-averaged calculated fixed aspect ratio, found be remarkable agreement with analytical results obtained using supersymmetric nonlinear $\ensuremath{\sigma}$-model approach. The distribution determined quasi-one-dimensional metallic, insulating regime, well crossover regime where comparisons made that at single-layer transition. present detailed study level statistics eigenvalue spectrum transfer matrix. Coexistence metallic observed which attributed emergence finite-range repulsion separating (Wigner-surmise) behavior small spacings from (uncorrelated or Poisson) large spacings.