Abstract
Topological insulators are a new class of materials that exhibit robust and scatter-free transport along their edges — independently of the fine details of the system and of the edge — due to topological protection. To classify the topological character of two-dimensional systems without additional symmetries, one commonly uses Chern numbers, as their sum computed from all bands below a specific bandgap is equal to the net number of chiral edge modes traversing this gap. However, this is strictly valid only in settings with static Hamiltonians. The Chern numbers do not give a full characterization of the topological properties of periodically driven systems. In our work, we implement a system where chiral edge modes exist although the Chern numbers of all bands are zero. We employ periodically driven photonic waveguide lattices and demonstrate topologically protected scatter-free edge transport in such anomalous Floquet topological insulators.
Highlights
Topological insulators are a new class of materials that exhibit robust and scatter-free transport along their edges — independently of the fine details of the system and of the edge — due to topological protection
After the discovery of topological insulators[2,3,4,5,6,7], the concept of topology was transferred to the photonic domain of electromagnetic waves[8] with the first realization in the microwave regime implementing the photonic analogue of the quantum Hall effect[9]
It is commonly accepted that for two-dimensional spin-decoupled topological systems a complete topological characterization is provided by the Chern numbers of each band, which represent a set of integer topological invariants[20,21]
Summary
Topological insulators are a new class of materials that exhibit robust and scatter-free transport along their edges — independently of the fine details of the system and of the edge — due to topological protection. The Chern numbers of all bands lying below a certain gap cannot be summed up since there exists no lowest band in the (periodic) band structure In such systems chiral edge modes are possible[10,23], the Chern numbers of all bands may be zero (see Fig. 1 for an illustrative sketch). These materials are called anomalous Floquet topological insulators (A-FTI)[22,24]. To date the experimental demonstration of an A-FTI in an explicitly driven system is still elusive
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