Boundary condition for phonon distribution functions at a smooth crystal interface and interfacial angular momentum transfer

TL;DR

This paper develops a comprehensive theoretical framework for phonon boundary conditions at smooth interfaces, incorporating reflection, transmission, mode conversion, and angular momentum transfer, with implications for heat and phonon angular momentum transport.

Contribution

It derives boundary conditions for phonons from classical lattice vibrations, including spatial dependence and angular momentum transfer, advancing the acoustic mismatch model.

Findings

Boundary conditions include reflection, transmission, and mode conversion.

Circularly polarized phonons generate orbital angular momentum at interfaces.

Both spin and orbital angular momentum influence interfacial phonon diffusion.

Abstract

We theoretically elucidate the boundary conditions for phonon distribution functions of long-wavelength acoustic phonons at smooth crystal interfaces. We first derive boundary conditions that fully incorporate reflection, transmission, and mode conversion. We obtain these conditions for phonons from those for classical lattice vibrations, using the correspondence between the quantum and classical descriptions. This formulation provides a theoretical foundation for the acoustic mismatch model, widely used to analyze Kapitza resistance. We then refine the boundary conditions to include spatial dependence parallel to the interface. The refined form captures transverse shifts of elastic wave packets, analogous to the optical Imbert--Fedorov shift, and ensures conservation of total angular momentum. Consequently, circularly polarized phonons carrying spin angular momentum (SAM) generate phonon orbital angular momentum (OAM) at the interface. We analytically determine the spatial profile of this OAM and demonstrate that SAM and OAM are both involved in the interfacial diffusion of chiral phonons. Our theory provides concise boundary conditions for phonons, with applications ranging from heat transport to phonon angular momentum transport.