The Su-Schrieffer-Heeger (SSH) model [1] is the prototypical system of a 1D topological insulator. It consists of a chain of identical sites coupled via alternating strong and weak bonds and features two topologically distinct dimerizations. Each interface between the two different dimerizations supports a topologically protected edge mode.
Here, we study the effect of time-periodic perturbations on this topological edge mode. We use arrays of evanescently coupled dielectric-loaded surface plasmon polariton waveguides to implement the SSH model (Fig. 1). Alternating strong and weak bonds with couplings J and J' were realized by choosing two different separations between neighboring waveguides. Periodic temporal fluctuations were implemented by fabricating a meandering waveguide at the interface between two domains. The SPP evolution was monitored by leakage radiation microscopy.
Figure 2 a depicts the real-space intensity distribution for a static interface [2]. Excitation of the central waveguide results in a localized mode at the interface. The corresponding momentum resolved spectrum (Fig. 2 b) reveals a mode in the center of the band gap.
The effect of the time-periodic driving on the topological edge mode depends on the driving frequency ω. We observe both for fast modulations (Fig. 2 c) as well as for slow modulations (Fig. 2 g) a localized mode at the interface between the two dimerizations. In contrast to this, the intensity spreads over the whole array for intermediate modulation frequencies (Fig. 2 e).
The experimental results can be interpreted as follows. Modulation of the central waveguide with frequency ω creates Floquet-replicas of the edge mode, which are shifted in energy by ±nω . For ω>|J+J'| (fast modulation) and ω<|J-J'| (slow modulation), the first replicas do not energetically overlap with the two SSH bands (see arrows in momentum resolved spectrum in Fig. 2 d and e). However, for |J-J'|<ω<|J+J'| the replicas can couple to bulk modes resulting in delocalization. This interpretation is supported by numerical calculations.
In summary, our experiments show that time-periodic perturbations can destroy topological protection.
[1] W. P. Su et al., Phys. Rev. B 22, 2099 (1983).
[2] F. Bleckmann et al., Phys. Rev. B 96, 045417 (2017).
Photonic & plasmonic nanomaterials , Optical properties of nanostructures
