Thouless conductances of a three-dimensional quantum Hall system

Abstract

We investigate the longitudinal conductance of a disordered three-dimensional (3D) quantum Hall system within a tight-binding lattice model using numerical Thouless conductance calculations. For the bulk, we confirm that the mobility edges are independent of the propagating directions in this anisotropic system. As disorder increases, the conductance peak of the lowest subband in the horizontal direction floats to the central subband as in the two-dimensional (2D) case, while there is no clear evidence of floating in the vertical direction. We thus conclude that for extended states, the longitudinal conductance in the vertical direction behaves like a quasi-one-dimensional (1D) normal metal, while the longitudinal conductance in the horizontal direction is controlled by layered conducting states stacked coherently. Inside the quantum Hall gap, we study the novel 2D chiral surface states at the sidewalls of the sample. We demonstrate the crossover of the surface states between the quasi-1D metal and insulator regimes, which can be achieved by modifying the interlayer hopping strength and the disorder strength in the model. The typical behaviors of the Thouless conductance and the wave functions of the surface states in these two regimes are investigated. Finally, in order to predict the regime of the surface states for arbitrary parameters, we determine an explicit relationship between the localization length of surface states and the microscopic parameters of the model.