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/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 micro-rotational and translational modes gives rise to the acoustic phonon branch with a "roton" minimum reminiscent of the elementary excitations in the superfluid helium-4. We argue that a mechanism of this phenomena is in line with Nozi\`{e}res' reinterpretation [J. Low Temp. Phys. \textbf{137}, 45 (2004)] of the rotons as a manifistation 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 ${}^{4}$He.