Scattering-free edge states between heterogeneous photonic topological insulators

We propose a set of three compatible photonic structures emulating quantum topologically insulating phases corresponding to Hall, spin-Hall, and valley-Hall effects. It is shown that an interface between any two of these photonic topological insulators supports scattering-free edge states. Spin and valley degrees of freedom characterizing such topologically protected edge waves determine their unique pathways through complex photonic circuits comprised of multiple heterogeneous interfaces.