Chirality-Induced Phonon Dispersion in a Noncentrosymmetric Micropolar Crystal

Abstract

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 He.

Experimental observation of roton-like dispersion relations in metamaterials

“… ( A ) 3D microstructure unit cell of a metamaterial beam ( 26 ) supporting transverse-like rotons for elastic wave propagation along the z -direction. The blue and red cylinders are responsible for the nearest-neighbor interactions and third-nearest-neighbor interactions, respectively, between the yellow masses.…”

Roton-like acoustical dispersion relations in 3D metamaterials

“…Thus, neither of them captures roton-like behavior. In sharp contrast, it has recently been shown that chiral Eringen micropolar continuum elasticity theory 24 can lead to roton-like dispersion relations for transverse acoustical elastic waves 25 . In their work 25 , chirality has been a necessary mechanism, whereas mechanisms based on periodicity, such as ordinary or extraordinary Bragg reflections, are not accounted for in micropolar elasticity theory 24 .…”

“…In sharp contrast, it has recently been shown that chiral Eringen micropolar continuum elasticity theory 24 can lead to roton-like dispersion relations for transverse acoustical elastic waves 25 . In their work 25 , chirality has been a necessary mechanism, whereas mechanisms based on periodicity, such as ordinary or extraordinary Bragg reflections, are not accounted for in micropolar elasticity theory 24 . More broadly speaking, mechanisms such as ordinary Bragg reflection 26 , 27 , local resonances 28 – 31 , near-ideal joints 32 – 34 introducing soft modes, spatial or temporal symmetry breaking 35 – 38 , topology 39 , 40 , duality 41 , 42 , as well as geometrical nonlinearities 34 , 43 have independently given rise to a wealth of other unusual dispersion relations and quasi-static behaviors of elastic and acoustical metamaterials.…”

Observation of roton-like dispersion relations in acoustic metamaterials

“…Recently, it has been theoretically reported that the roton-like dispersion relations for transverse acoustical elastic waves can be realized in noncentrosymmetric micropolar crystal based on chiral micropolar elasticity theory, where chirality is a necessary condition for roton-like behaviours 30 . Hence, it is natural to ask whether chirality plays an important role in the roton-like behaviours in our airborne acoustic system.…”