Weak Topological Insulators in PbTe/SnTe superlattice

It is desirable to realize topological phases in artificial structures by engineering electronic band structures. In this paper, we investigate (PbTe)$_m$(SnTe)$_{2n-m}$ superlattices along the [001] direction and find a robust weak topological insulator phase for a large variety of layer numbers $m$ and $2n-m$. We confirm this topologically non-trivial phase by calculating $Z_2$ topological invariants and topological surface states based on the first-principles calculations. We show that the folding of Brillouin zone due to the superlattice structure plays an essential role in inducing topologically non-trivial phases in this system. This mechanism can be generalized to other systems in which band inversion occurs at multiple momenta, and gives us a brand-new way to engineer topological materials in artificial structures.