  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 modulus, which provides $100\%$ unidirectional and
backscattering-free edge propagation at a broad range of frequencies instead of
residing in gaps between bulk bands. We further show that such modes are
characterized by a new topological winding number that is analogous to discrete
angular momentum eigenvalues in quantum mechanics. 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.
