Delocalization of surface Dirac electrons in disordered weak topological insulators

The spectrum of massless Dirac electrons on the side surface of a three-dimensional weak topological insulator is significantly affected by whether the number of unit atomic layers constituting the sample is even or odd; it has a finite-size energy gap in the even case while it is gapless in the odd case. The conductivity of such a two-dimensional Dirac electron system with quenched disorder is calculated when the Fermi level is located at the Dirac point. It is shown that the conductivity increases with increasing disorder and shows no clear even-odd difference when the aspect ratio of the system is appropriately fixed. From the system-size dependence of the average conductivity, the scaling function $\beta$ is determined under the one-parameter scaling hypothesis. The result implies that $\beta = 0$ in the clean limit at which the conductivity is minimized, and that $\beta > 0$ otherwise. Hence, the system is a perfect metal in the thermodynamic limit except in the clean limit that should be regarded as an unstable fixed point.