Design of GaAs-based valley phononic crystals with multiple complete phononic bandgaps at ultra-high frequency

We report the design of GaAs-based monolithic valley phononic crystals (VPnCs) with multiple complete phononic bandgaps, which support simultaneous valley-protected edge states with different symmetries in the gigahertz range. Rotation of triangular holes in the unit cells breaks the mirror symmetry, and this orientation degree of freedom enables the structures to exhibit different valley vortex chiralities. We numerically demonstrate the transport of multi-band valley-protected edge states with suppressed backscattering at the sharp corners of the interfaces between different VPnCs. Such monolithic semiconductor structures pave the way for ultra-high frequency topological nanophononic applications by using the lithographic technique.