Theory of Energy Dispersion of Chiral Phonons

We have developed a microscopic theory on phonon energy dispersion in chiral crystals within harmonic approximation. One of the main issues is about splitting sound velocity acoustic phonons with opposite “crystal” angular momenta. shown that must be zero even and difference starts from order at least k2 or higher their dispersion. Splitting evident for optical phonons, we derived formula k-linear splitting. Another important finding possible interactions atomic displacements models. found antisymmetric Dij · (di × dj) type are not allowed Hamiltonians because stability equilibrium structure. identified both modes arises potentials electric toroidal quadrupole Gu-type symmetry. These constraint modeling real materials. Most our calculations been performed (quasi-)one-dimensional systems trigonal crystal symmetry including Te, but these results generally hold also other systems.