Theory of phonon angular momentum transport across smooth interfaces between crystals

We study the spatial profile of phonon angular momentum in a junction between a chiral crystal and a non-chiral (achiral) crystal with a smooth, flat contact at low temperatures. In this junction, the angular momentum is generated by an imbalance in non-equilibrium distributions between transverse acoustic modes. We incorporate the Fresnel coefficients for elastic waves to establish a boundary condition for the phonon distributions, for which we also provide a proof. We demonstrate that the spin angular momentum of phonon induced by a thermal gradient in the chiral crystal diffuses into the adjacent achiral crystal. This diffusion is accompanied by a finite orbital angular momentum stemming from acoustic analog of the Imbert--Fedorov shift in reflected/transmitted wave packets. Concerning angular momentum fluxes that are polarized normal to the interface, the sum of the spin and orbital components is continuous at the interface. This continuity confirms the conservation law of total phonon angular momentum.