Chiral Phonons in a Cubic Lattice

TL;DR

This paper develops a theoretical framework for understanding chiral phonons in a cubic lattice, revealing that optical triplet modes exhibit intrinsic chirality near zero momentum, described by a Weyl Hamiltonian.

Contribution

It introduces a novel theory describing the energy dispersion of chiral phonons, highlighting the role of a spin-1 Weyl Hamiltonian and pseudoscalar coupling in a cubic lattice.

Findings

Optical triplet phonon modes exhibit intrinsic chirality near k=0.

Energy splitting is described by a spin-1 Weyl Hamiltonian.

Helicity aligns with crystal angular momentum for specific directions.

Abstract

We have developed a theory for the energy dispersion of chiral phonons in a simplest cubic lattice. Among all the phonon modes, only the optical triplet modes exhibit the intrinsic characteristics of chiral phonons near k=0, and we examine their energy splitting in detail by analyzing the dynamical matrix. To first order in k, the splitting is described by a spin-1 Weyl Hamiltonian, and helicity becomes a good quantum number. It asymptotically coincides with the crystal angular momentum for k parallel <111> up to a global sign. The Hamiltonian incorporates a pseudoscalar coupling constant associated with electric toroidal monopoles, determined by the spatial configuration of the stiffness tensors.