Finite-size effect on quantum percolation in topological insulators.

We study the finite-size effect on quantum percolation in two-dimensional topological insulators. We demonstrate that the percolation threshold in topological insulators strongly depends on the localization length of the edge states in small clusters due to the finite-size effect. Also, we explain why the percolation threshold in the corresponding classical model determines the lower bound of the quantum percolation threshold in topological insulators. In addition, we extend the percolation model to a more general scenario, where the system is composed of both topological and trivial clusters. We find that the quantum percolation threshold can be less than the classical percolation threshold due to quantum tunneling of the edge states.