Dissipative nonequilibrium synchronization of topological edge states via self-oscillation

The interplay of synchronization and topological band structures with symmetry-protected midgap states under the influence of driving and dissipation is largely unexplored. Here, we consider a trimer chain of electron shuttles, each consisting of a harmonic oscillator coupled to a quantum dot positioned between two electronic leads. Each shuttle is subject to thermal dissipation and undergoes a bifurcation toward self-oscillation with a stable limit cycle if driven by a bias voltage between the leads. By mechanically coupling the oscillators together, we observe synchronized motion at the ends of the chain, which can be explained using a linear stability analysis. Because of the inversion symmetry of the trimer chain, these synchronized states are topologically protected against local disorder. Furthermore, with current experimental feasibility, the synchronized motion can be observed by measuring the dot occupation of each shuttle. Our results open another avenue to enhance the robustness of synchronized motion by exploiting topology.