Surface Dynamics and Phononic Properties of 2D Field Tunable Auxetic Crystal

The lattice in-plane dynamics is studied as a function of external field in a model of auxetic crystal consisting of rigid polar rods and of elastic springs. The phase speed of the transverse acoustic wave propagating parallel to the polar rods is shown to be higher than the speed of the longitudinal wave at strong fields. An absolute stop band for the lattice waves opens in the whole Brillouin zone with increasing field. The surface waves and resonances at a surface parallel to the rods are studied. Infinitely narrow resonances called exceptional surface waves are found within bulk bands at certain specific values of the parameters characterizing the surface. Generally, the surface layer should be significantly heavier and stiffer than the substrate for the phenomenon to occur.