Vibrational phenomena in conformally symmetric dilational metamaterials

Recent work has shown that two-dimensional dilational metamaterials possess conformal symmetry, leading to static and low-frequency conformal deformations and novel conserved momenta. In isotropic variants of such systems, the standard elastic formulation of longitudinal and transverse waves simplifies into left- and right-polarized waves (analogous to different spin states) travelling at a common speed of sound. In this talk, we investigate the implications of these degenerate waves for a geometric phase associated with the evolution between different polarization states. Further, we introduce geometric complexities such as interfaces and defects to the bulk dilational structure as a means of controlling and influencing the waves. Finally, we explore how the intrinsic angular momentum of spin-polarized waves can be used to induce torque on the surrounding medium. These phenomena may form the basis of "spincoustic" devices that rely on this novel mechanical degree of freedom, in analogy to spintronic devices leveraging electronic spin.