Theory of phonon angular momentum transport across a smooth crystal interface

TL;DR

This work addresses how phonon angular momentum (AM) is transported across a smooth interface between a chiral crystal and an achiral crystal, a process not fully captured by the conventional acoustic mismatch model. By solving the Boltzmann equation with elasticity-derived boundary conditions and incorporating a chirality-induced RH/LH splitting, the authors show that AM can diffuse into the adjacent crystal even without net heat flow and that the AM density can be amplified near the interface. The key mechanisms involve differences between spin-conserving and spin-flip transmittances (ΔT) and reflectances (ΔR) for RH/LH modes, and a bulk AM density S0 ∝ ∇T arising from the RH/LH population imbalance. The results imply interfacial phonon spin currents that can couple to electron spins, potentially impacting spin caloritronics, phonon Hall effects, and related experimental observations such as inverse spin Hall signals near quartz-metal interfaces; orbital AM is invoked to conserve total angular momentum across the interface.

Abstract

We theoretically elucidate the transfer of phonon angular momentum by acoustic modes across a smooth interface between crystals. We analyze this process, which is difficult to describe with the conventional acoustic mismatch model, using a reformulated boundary condition and the Boltzmann theory. For an interface between a chiral and an achiral crystal, our analysis reveals that thermal gradients in the chiral crystal induce angular momentum, which diffuses into the achiral crystal even without heat flow. Notably, the density of angular momentum can be enhanced near the interface. These findings advance our understanding of phonon transport and its interplay with electron spins.

Figures (2)

• Figure 1: Schematics of a CC/ACC junction and dispersions of the CC as a source of phonon AM $\bm{S}$. (a) Diffusion of AM across the interface at $z = 0$. (b) Acoustic modes in the CC. The AM $\bm{S}$ is generated along the thermal gradient $\bm{\nabla} T$ [(a)] due to the lifting of degeneracy in transverse modes [(b)].
• Figure 2: Diffusion of phonon-AM density $\bm{S}$ (solid curves) and its flux density $\bm{j}^{\text{S}}$ (dashed curves), illustrated for four different interfaces. Each row denotes the case when both the thermal gradient $\bm{\nabla} T$ and polarization of AM are in the direction. (a) normal and (b) parallel to the interface. The insets show enlarged views of the area near the interface. We set parameters as $v_{\text{L}}/v_{\text{T}} = 1.59$ and [Quartz--Vacuum] $\zeta_{\text{T}}/Z_{\text{T}} = 0$, [Quartz--Platinum] $c_{\text{L}}/c_{\text{T}} = 2.25$, $c_{\text{T}}/v_{\text{T}} = 0.493$, and $\zeta_{\text{T}}/Z_{\text{T}} = 3.99$, [Quartz--Lead] $c_{\text{L}}/c_{\text{T}} = 2.84$, $c_{\text{T}}/v_{\text{T}} = 0.183$, and $\zeta_{\text{T}}/Z_{\text{T}} = 0.947$, [Quartz--Quartz] $c_{\text{L}}/v_{\text{T}} = 1.59$ and $c_{\text{T}}/v_{\text{T}} = \zeta_{\text{T}}/Z_{\text{T}} = 1$Rikanempyo2024.