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We demonstrate the coexistence of pseudospin- and valley-Hall-like edgestates in a photonic crystal with $C_{3v}$ symmetry, which is composed of threeinterlacing triangular sublattices with the same lattice constants. By tuningthe geometry of the sublattices, three complete photonic band gaps withnontrivial topology can be created, one of which is due to the band inversionassociated with the pseudospin degree of freedom at the $\Gamma$ point and theother two due to the gapping out of Dirac cones associated with the valleydegree of freedom at the $K, K'$ points. The system can support tri-bandpseudospin- and valley-momentum locking edge states at properly designeddomain-wall interfaces. Furthermore, to demonstrate the novel interplay of thetwo kinds of edge states in a single configuration, we design a four-channelsystem, where the unidirectional routing of electromagnetic waves against sharpbends between two routes can be selectively controlled by the pseudospin andvalley degrees of freedom. Our work combines the pseudospin and valley degreesof freedom in a single configuration and may provide more flexibility inmanipulating electromagnetic waves with promising potential for multiband andmultifunctional applications.

Coexistence of pseudospin- and valley-Hall-like edge states in a photonic crystal with $C_{3v}$ symmetry