  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 (GHz)
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.
