Fig. 1.

Chiral phonon eigenmode and unit cell. a Snapshot of a calculated chiral phonon eigenmode with eigenfrequency ω₁ propagating along the z-direction in an infinitely extended 3D chiral micropolar metamaterial crystal. For clarity, all unit cells except for one column along the propagation axis (z-axis) are shown semitransparent and the displacements are largely exaggerated. b Simplified representation only showing the behavior of the unit cells’ centers of mass, forming a helix that is moving along the z-axis versus time. An animation of a and b is shown in Supplementary Video 1. c Single-unit cell (cf. ref. ¹⁹). Geometrical parameters are cubic lattice constant a = 250 μm, d/a = 0.06, r₁/a = 0.32, r₂/a = 0.4, and δ = 34.8°. For the bulk constituent polymer material we have chosen the Young’s modulus E = 4.18 GPa, mass density ρ = 1.15 g cm⁻³, and Poisson’s ratio ν = 0.4. The wave number is k_z = π/(4a) and the angular frequency is ω₁ = 2π × 107 kHz, equivalent to a/λ₀ = 0.0095, with the wavelength λ₀ of pressure waves in the bulk constituent polymer material (cf. Fig. 2)