Topological states of quantum matter exhibit unique disorder-immune surface
states protected by underlying nontrivial topological invariants of the bulk.
Such immunity from backscattering makes topological surface or edge states
ideal carriers for both classical and quantum information. So far, topological
matters have been explored only in the realms of electronics and photonics,
with limited range of bulk properties and largely immutable materials. These
constraints thus impose severe performance trade-offs in experimentally
realizable topologically ordered states. In contrast, phononic metamaterials
not only provide access to a much wider range of material properties, but also
allow temporal modulation in the non-adiabatic regime. Here, from the
first-principles we demonstrate numerically the first phononic topological
metamaterial in an elastic-wave analogue of the quantum spin Hall effect. A
dual-scale phononic crystal slab is used to support two effective spins of
phonon over a broad bandwidth, and strong spin-orbit coupling is realized by
breaking spatial mirror symmetry. By preserving the spin polarization with an
external load or spatial symmetry, phononic edge states are shown to be robust
against scattering from discrete defects as well as disorders in the continuum.
Our system opens up the possibility of realizing topological materials for
phonons in both static and time-dependent regimes.Comment: 19 pages, 6 figure