Rayleigh waves and cyclotron surface modes of gyroscopic metamaterials

We investigate the elastic normal modes of two-dimensional media with broken time-reversal and parity symmetries due to a Lorentz term. Our starting point is an elasticity theory that captures low-energy physics diverse range systems such as gyroscopic metamaterials, skyrmion lattices in thin-film chiral magnets certain Wigner crystals. By focusing on circular disk geometry we analyze finite-size effects study low-frequency shape oscillations disk. demonstrate emergence Rayleigh surface waves from bottom excitation spectrum how curvature disk-boundary modifies their propagation at long wavelengths. Moreover, discover near-cyclotron-frequency wave almost completely localized boundary disk, but distinct wave. It can be distinguished latter by characteristic pattern small region near center