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

TL;DR

This paper demonstrates that a single impurity in one-dimensional superlattices can induce topologically protected mid-gap states, which serve as a tool to detect topology and enable adiabatic pumping in experimental setups.

Contribution

It reveals the emergence of topologically protected mid-gap states caused by impurities in 1D superlattices, linking impurity effects to topological properties.

Findings

Midgap states localized near impurities carry topological information.

Impurities can be used to detect the system's topology.

Adiabatic pumping can be realized via impurity-induced states.

Abstract

Based on the discovery of the nontrivial topology of one-dimensional superlattices, we show that midgap states will emerge in such systems induced by a single on-site impurity. Besides the trivial bound state located at the impurity site, these midgap states are localized at the adjacent sides of the impurity, carrying the information of the topology and behaving like the effect of the open boundary conditions in the limit of a large attractive or repulsive impurity potential. Using this feature, the impurity can be used to detect the topology of the superlattice system and to realize the adiabatic pumping between the opposite sides of the impurity in cold-atom experiments or in photonic crystals.