  Designing unconventional interactions between single phonons and spins is
fascinating for its applications in quantum phononics. Here, we propose a
reliable scheme for coupling spins and phonons in phononic dimer and trimer
lattices, with the combination of solid-state defects and diamond phononic
(optomechanical) crystals. The dimer and trimer lattices used are an array of
coupled phononic cavities with spatially modulated hopping rates. We predict a
series of unconventional sound-matter interaction phenomena in this hybrid
quantum system. In the dimer lattice, we show the formation of chiral
spin-phonon bound states and topology-dependent phononic collective radiation.
While in the trimer lattice, chiral bound states still exist and the spin
relaxation is sublattice-dependent. The chiral bound states existed in both
types of lattices are robust to large amount of disorder, which can mediate
chiral and robust spin-spin interactions. This work provides a promising
platform for phonon-based quantum information processing and quantum
simulation.
