Cavity-induced topological edge and corner states

We investigate a two-level system with alternating XX coupling in a photon cavity. It is mapped to a free boson model equally coupled to a photon, whose interaction is highly nonlocal. Some intriguing topological phenomena emerge as a function of the photon coupling. The photon energy level anticrosses the zero-energy topological edges at a certain photon coupling, around which the symmetric edge state acquires nonzero energy due to the mixing with the photon. Furthermore, the photon state is transformed into the topological zero-energy edge or corner state when the photon coupling is strong enough. It is a cavity-induced topological edge or corner state. On the other hand, the other topological edge or corner states do not couple with the photon and remains at zero energy even in the presence of the cavity. We analyze a cavity-induced topological edge state in the Su-Schrieffer-Heeger model and a cavity-induced topological corner state in the breathing Kagome model.