Effect of surface disorder on the chiral surface states of a three-dimensional quantum Hall system

Abstract

We investigate the effect of surface disorder on the chiral surface states of a three-dimensional quantum Hall system. Utilizing a transfer-matrix method, we find that the localization length of the surface state along the magnetic field decreases with the surface disorder strength in the weak disorder regime but increases anomalously in the strong disorder regime. In the strong disorder regime, the surface states mainly locate at the first inward layer to avoid the strong disorder in the outmost layer. The anomalous increase of the localization length can be explained by an effective model, which maps the strong disorder on the surface layer to the weak disorder on the first inward layer. Our work demonstrates that surface disorder can be an effective way to control the transport behavior of the surface states along the magnetic field. We also investigate the effect of surface disorder on the full distribution of conductances $P(g)$ of the surface states in the quasi-one-dimensional (1D) regime for various surface disorder strengths. In particular, we find that $P(g)$ is Gaussian in the quasi-1D metal regime and log-normal in the quasi-1D insulator regime. In the crossover regime, $P(g)$ exhibits highly nontrivial forms, whose shapes coincide with the results obtained from the Dorokhov-Mello-Pereyra-Kumar equation of a weakly disordered quasi-1D wire in the absence of time-reversal symmetry. Our results suggest that $P(g)$ is fully determined by the average conductance, independent of the details of the system, in agreement with the single-parameter scaling hypothesis.