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Photonic analogs of topological insulators conduct light along their edges scattering-free. Moreover, the flow along the edges is unidirectional, prescribed by the topological invariant, an attribute of the bulk of the system. As long as the topological properties persist, the edge transport is not even perturbed by defects. This connection is enforced by the bulk-boundary correspondence.
However, this correspondence principle is modified under time-periodic driving. In our work we show that for certain defects the protection of an edge state is destroyed, although the topological properties of the bulk are unchanged. Theoretical predictions are verified by experiments in a photonic model systems of 3D printed evanescently coupled dielectric waveguides[1,2].
In particular, we consider a dimer chain (SSH) with a defect in the center of the chain, breaking the dimerization and inducing an edge state [3]. This edge state is protected, as it lies in a bandgap. We drive the defect by periodically modulating its position in the y- direction, leaving the bulk unaltered. The periodic modulation results in Floquet copies [4,5] of the edge state with higher energy, spaced by the driving frequency around zero energy. Whenever the driving frequency is such that the replicas overlap with the bulk bands the edge state couples to the bulk states, i.e. the light does not remain localized at the defect site.
Although the bulk of the system, and as such the topological invariant, remains unchanged, topological protection breaks down for certain driving frequencies.
References
[1] C. Jörg et al., New J. Phys. 19, 083003 (2017).
[2] Z. Cherpakova, C. Jörg et al., arXiv:1807.02321 (2018).
[3] A. Blanco-Redondo et al., Phys. Rev. Lett. 116, 163901 (2016).
[4] M. Holthaus, J. Phys. B: At. Mol. Opt. Phys 49, 013001 (2016).
[5] S. A. Reyes et al., New J. Phys. 19, 043029 (2017).
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