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 towards self-oscillation with a stable limit cycle if driven by a bias voltage between the leads [1]. 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 [2]. Because of the inversion symmetry of the trimer chain, these synchronized states are topologically protected against local disorder. Our results open another avenue to enhance the robustness of synchronized motion by exploiting topology.

[1] C. W. Wächtler, P. Strasberg, S. H. L. Klapp, G. Schaller, and C. Jarzynski, NJP 21, 07300921 (2019).
[2] C. W. Wächtler, V. Bastidas, G. Schaller, and W. Munro, PRB 102, 14309 (2020).