Backscattering-free edge states below all bands in two-dimensional auxetic media

Unidirectional and backscattering-free propagation of sound waves is of fundamental interest in physics and highly sought-after in engineering. Current strategies utilize topologically protected chiral edge modes in bandgaps, or complex mechanisms involving active constituents or nonlinearity. Here, we propose a new class of passive, linear, one-way edge states based on spin-momentum locking of Rayleigh waves in two-dimensional media in the limit of vanishing bulk to shear modulus ratio, which provides perfect unidirectional and backscattering-free edge propagation that is immune to any edge roughness and has no limitation on its frequency (instead of residing in gaps between bulk bands). We further show that such modes are characterized by a new topological winding number that protects the linear momentum of the wave along the edge. These passive and backscattering-free edge waves have the potential to enable a new class of phononic devices in the form of lattices or continua that work in previously inaccessible frequency ranges.