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 “roton” minimum reminiscent of the elementary excitations in the superfluid helium-4. We argue that a mechanism of this phenomena is in line with Nozières’ reinterpretation P. Nozières, [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 ${}^4\mathrm{He}$.

• Received 15 July 2020
• Accepted 4 November 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.245302

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