  Following the discovery of moir\'e-driven superconductivity in twisted
graphene multilayers, twistronics has spurred a surge of interest in tailored
broken symmetries through angular rotations, enabling new properties from
electronics to photonics and phononics. Analogously, in monoclinic polar
crystals a nontrivial angle between non-degenerate dipolar phonon resonances
can naturally emerge due to asymmetries in their crystal lattice, and its
variations are associated with intriguing polaritonic phenomena, including
axial dispersion, i.e., a rotation of the optical axis with frequency, and
microscopic shear effects that result in asymmetric loss distributions. So far
these phenomena were restricted to specific mid-infrared frequencies, difficult
to access with conventional lasers, and fundamentally limited by the degree of
asymmetry and the strength of light-matter interactions available in natural
crystals. Here, we leverage twistronics to demonstrate giant axial dispersion
and loss asymmetry of hyperbolic waves in elastic metasurfaces, by tailoring
the angle between coupled pairs of anisotropic metasurfaces. We show extreme
control over elastic wave dispersion via the twist angle, and leverage the
resulting phenomena to demonstrate reflection-free negative refraction, as well
as the application of axial dispersion to achieve diffraction-free
non-destructive testing, whereby the angular direction of a hyperbolic probe
wave is encoded into its frequency. Our work welds the concepts of twistronics,
non-Hermiticity and extreme anisotropy, demonstrating the powerful
opportunities enabled by metasurfaces for tunable, highly directional surface
acoustic wave propagation, of great interest for applications ranging from
seismic mitigation to on-chip phononics and wireless communications, paving the
way towards their translation into emerging photonic and polaritonic
metasurface technologies.
