Elastic spin-Hall effect in mechanical graphene

Abstract

© 2016 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. We show that spin-orbit interaction and elastic spin-Hall effect can exist in a classical mechanical system consisting of a two-dimensional honeycomb lattice of masses and springs. The band structure shows the presence of splitting at K point induced by the difference of longitudinal and transverse elastic constant, and this splitting can be regarded as an effective Dresselhaus-type spin-orbit coupling. Interestingly, as an initial displacement away from the equilibrium is applied, the time evolution simulation shows that waves of different spin polarization propagates along different directions at the Γ and K point, which is characteristic of spin-Hall effect. Several cases for spin-Hall effect are also discussed.