Topologically protected edge states of phoxonic crystals

In this paper, we designed a phoxonic crystal (PxC) which simultaneously exhibit the topological states of sound and light. By modulating the impedance ratio between the cylinder scatterers and the matrix in a honeycomb lattice, we found that the inevitable Dirac cones and the accidental double Dirac cone of the phononic mode could be respectively degenerated at the corner and center of the Brillouin zone (BZ). For the photonic mode, we can find that the transverse-magnetic (TM) bands degenerate to Dirac cones at the corner of the BZ and the transverse-electric (TE) bands degenerate to a position-varying Dirac cone along the M Gamma line of the BZ. When the point group symmetry of the PxC is reduced from C-6v to C-3v, the double Dirac cone of the phononic mode is lifted and the topological pseudospin-dependent edge states of sound are induced when we construct a ribbon-shaped supercell with zigzag interface. Under the same operation, the topological valley spin state of the TM mode is excited and the edge state of the TE mode is also realized at the same time. Based on the all full-wave simulations, we simultaneously observed the topologically protected edge propagations of sound and light along the interfaces of two PxCs with the distinct topological phases. Our PxC provides a platform to design the topological optomechanical devices.