Elastic Spin Hall effect in Mechanical Graphene

TL;DR

This paper demonstrates that a classical mechanical honeycomb lattice can exhibit spin-orbit coupling and elastic spin-Hall effects, with wave polarization-dependent propagation akin to quantum spin-Hall phenomena.

Contribution

It introduces a mechanical system that mimics spin-orbit interaction and spin-Hall effects, providing a new platform for studying topological phenomena in classical mechanics.

Findings

Band structure shows splitting at K point due to elastic constants.

Wave propagation depends on spin polarization, demonstrating spin-Hall effect.

Different cases of spin-Hall effect are discussed.

Abstract

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 Gamma and K point, which is characteristic of spin-Hall effect. Several cases for spin-Hall effect are also discussed.