Topological transitions induced by cavity-mediated interactions in photonic valley-Hall metasurfaces

Abstract: Topological phases of light exhibit unique properties beyond the realm of conventional photonics. In particular the valley-Hall topological insulator has been realized in a variety of photonic structures because it can be easily induced by breaking certain lattice symmetries. However, the valley-Chern numbers are usually fixed by design and the corresponding topological edge states are forced to propagate in a fixed direction. Here, we propose a mechanism to induce topological transitions via accidental Dirac points in metasurfaces composed of interacting dipole emitters/antennas. For a fixed arrangement of dipoles, we show that the topological phase depends critically on the surrounding electromagnetic environment which mediates the dipole-dipole interactions. To access different topological phases we embed the metasurface inside a cavity waveguide where one can tune the dominant dipolar coupling from short-range Coulomb interactions to long-range photon-mediated interactions by reducing the cavity width; this results in a topological transition characterized by an inversion of the valley-Chern numbers. Consequently, we show that one can switch the chirality of the topological edge states by modifying only the electromagnetic environment in which the dipoles are embedded. This mechanism could have important implications for other topological phases such as photonic higher-order topological insulators.