Dual-band valley-protected topological edge states in graphene-like phononic crystals with waveguide

Since valley was introduced into phononic crystals, it has promoted far-reaching developments in topologically protected acoustic transmission. However, in the novel research field of valley-Hall phononic topological insulators, most researchers only focus on valley-protected edge state with a single working frequency band. Here, we demonstrate dual-band valley-protected topological edge states in a graphene-like two-dimensional phononic crystal, which consists of columnar air cavities and rigid scatters. It is demonstrated that energy band inversion happens and a gap can be opened at the two Dirac cones at the K ( K ') symmetry points of the Brillouin zone by tuning the radius differences between adjacent columnar air cavities. In addition, we demonstrate the presence of dual-band topologically protected edge states with properties like suppressed back-scattering, one-way transmission, and sharp bend resistance. In these contexts, beam splitting with dual-band is achieved by combining valley vortex states with opposite chirality. Our work may provide a practical method for solving high-efficiency and high-capacity multi-channel acoustic communication in fluid media. Graphical Abstract The dual-band valley-protected topological edge states have been demonstrated in a graphenelike two-dimensional phononic crystal, which consists of columnar air cavities and rigid scatters. The energy band inversion happens and a gap can be opened at the two Dirac cones at the K ( K ’) symmetry points of the Brillouin zone by tuning the radius differences between adjacent columnar air cavities. Based on these, beam splitting with dual-band can be achieved by combining valley vortex states with opposite chirality