Chirality-Induced Phonon Dispersion in a Noncentrosymmetric Micropolar Crystal

Features of the phonon spectrum of a chiral crystal are examined within the micropolar elasticity theory. This formalism accounts for not only translational micromotions of a medium but also rotational ones. It is found that there appears the phonon band splitting depending on the left- and right-circular polarization in a purely phonon sector without invoking any outside subsystem. The phonon spectrum reveals parity breaking while preserving time-reversal symmetry, i.e., it possesses true chirality. We find that hybridization of the microrotational and translational modes gives rise to the acoustic phonon branch with a rotor . ' minimum reminiscent of the elementary excitations in the superfluid helium-4. We argue that a mechanism of this phenomena is in line with Nozieres' reinterpretation P. Nozieres, [J. Low Temp. Phys. 137, 45 (2004)] of the rotons as a manifestation of an incipient crystallization instability. We discuss a close analogy between the translational and rotational micromotions in the micropolar elastic medium and the Bogoliubov quasiparticles and gapful density fluctuations in He-4.