Generalized continuum theory of phonon angular momentum in crystals

TL;DR

This paper develops a generalized continuum model for phonon angular momentum in crystals, incorporating local rotational degrees of freedom to unify optical and acoustic modes.

Contribution

It introduces a local SO(3) material frame into continuum theory, connecting micro-rotation effects with macroscopic phonon angular momentum.

Findings

Derives a continuum expression for phonon angular momentum including displacement and microrotation contributions.

Identifies the locking limit where microrotation reduces to lattice vorticity.

Explains chiral phonon splitting through symmetry-breaking terms.

Abstract

We formulate a generalized continuum theory of phonon angular momentum in crystals by introducing a local SO(3) material frame in addition to the macroscopic displacement field. The local frame represents rotational optical degrees of freedom of the unit cell and brings acoustic displacement modes and optical rotational modes into a common long-wavelength continuum description. In the linearized limit, the co-rotated deformation gradient and the rotational gradient associated with the local material frame recover the Eringen microdeformation and wryness tensors; isotropic micropolar elasticity then appears as a special case. Rotational symmetry and Noether's theorem determine the continuum phonon angular-momentum density, including both the displacement-polarization contribution and the intrinsic microrotation contribution. The theory further identifies the locking limit in which microrotation reduces to lattice vorticity and the improper-symmetry-breaking terms responsible for chiral phonon splitting.