Boundary-induced topological transition in an open Su-Schrieffer-Heeger model

We consider a Su-Schrieffer-Heeger (SSH) chain to each end of which we attach a semi-infinite undimerized chain (lead). We study the effect of the openness of the SSH model on its properties. A representation of the infinite system using an effective Hamiltonian allows us to examine its low-energy states in more detail. We show that, as one would expect, the edge states of the topological phase hybridize as the coupling between the systems is increased. As this coupling grows, these states are gradually suppressed, disappearing as the coupling goes to infinity. In the topologically trivial phase, in which no edge states exist in the isolated system, the opposite behavior is observed: as the coupling grows, a new type of edge state gradually emerges. These new states, referred to as phase-inverted edge states, are localized low-energy modes very similar to the edge states of the topological phase. Interestingly, localization occurs on a new shifted interface, moving from the first (and last) site to the second (and second to last) site. This suggests that the topology of the system is strongly affected by the leads, with three regimes of behavior. For very small coupling, the system is in a well-defined topological phase; for very large coupling, it is in the opposite phase; in the intermediate region, the system is in a transitional regime.