Coexisting valley and chiral edge states in topological photonic crystals.

We presented the findings on the coexistence of quantum anomalous Hall (QAH) and valley Hall (VH) phases within an identical photonic gap in a hexagonal photonic crystal. The synergistic effect of broken time-reversal symmetry (BTRS) and broken rotation symmetry (BRS) unbuckles the triple-degenerated points at K and K' points, which is crucial for the coexistence of multiple topological phases. The competition of BTRS and BRS adjusts the transition of topological phases. It has been verified that the configuration mainly exhibits the QAH phase through bulk-edge correspondence. The VH phase becomes apparent only after the QAH phase has disappeared. As an application, a circulator with six ports has been further proposed. Our study offers insights into the interplay among photonic topological phases, highlighting potential applications in robust waveguiding and photonic on-chip devices.