Topologically protected mid-gap states induced by impurity in one-dimensional superlattices

Based on the discovery of the nontrivial topological properties of one-dimensional superlattices, we show that mid-gap states emerge in such systems induced by a single on-site impurity. Besides the trivial bound state located at the impurity site, these mid-gap states are localized at the adjacent sites of the impurity in the limit of a strongly attractive/repulsive impurity potential, behaving as edge states under open boundary conditions and thus carrying the information of topological properties. This feature makes it possible to reveal the topological properties of superlattices via the impurity effect and to realize the adiabatic pumping between the opposite sides of the impurity in setups of one-dimensional optical lattices or photonic crystals.