Theory of Energy Dispersion of Chiral Phonon

Abstract

We have developed a microscopic theory on phonon energy dispersion in chiral crystals within a harmonic approximation. One of the main issues is about the splitting of sound velocity of acoustic phonons with opposite ``crystal'' angular momentum. We have shown that the splitting must be zero even in chiral crystals and the difference starts from the order of at least $k^2$ or higher in their energy dispersion. Splitting is evident for chiral optical phonons, and we have derived a formula for their $k$-linear splitting. Another important finding is about possible interactions of atomic displacements in microscopic models. We have found that antisymmetric interactions of ${\mathbf{D}}_{ij}\cdot ({\mathbf{d}}_i\times {\mathbf{d}}_j)$ type are not allowed in microscopic Hamiltonians for chiral phonons in compatible with the stability against the Nambu-Goldstone mode. We have identified that the splitting in both acoustic and optical modes arises from the harmonic potentials with the electric toroidal quadrupole of $G_u$-type symmetry. These constraint are important for modeling real materials. Most of our microscopic calculations have been performed for (quasi-)one-dimensional systems with a trigonal crystal symmetry including Te, but these results generally hold also for other chiral phonon systems.

5 pages, 3 figures. To be published in J. Phys. Soc. Jpn

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• Chirality-Induced Selectivity of Phonon Angular Momenta in Chiral Quartz Crystals
• Chiral phonons: circularly polarized Raman spectroscopy and $\text{ab initio}$ calculations in a chiral crystal tellurium
• Weyl phonons in chiral crystals
• Symmetry-adapted modeling for molecules and crystals
• Quantification of chirality based on electric toroidal monopole
• Chirality-induced Phonon-Spin Conversion at an Interface
• Emergence of chirality by multipole interconversion
• Note on Angular Momentum of Phonons in Chiral Crystals
• Theory of spin magnetization driven by chiral phonons
• Electron-Chiral Phonon Coupling, Crystal Angular Momentum, and Phonon Chirality
• Symmetry-adapted closest Wannier modeling based on complete multipole basis set
• Theory of spin Seebeck effect activated by acoustic chiral phonons
• Description of molecular chirality and its analysis with high harmonic generation
• Thermal Einstein-de Haas Effect Induced by Chiral Phonons in Carbon Nanotubes
• Microscopic Theory of Chiral-Phonon-Induced Orbital Selectivity in Helical Crystals
• Dynamical Orbital Angular Momentum Induced by Circularly Polarized Phonons
• Spin-flip Scattering at a Chiral Interface of Helical Chains