Figure 2. Opening of a topological band gap by subwavelength structural modifications.

(a) Starting from the honeycomb lattice in the extended unit cell picture of Fig. 1e, we shrink the size of the hexagonal arrangement of resonators composing each unit cell, obtaining a triangular lattice of hexagonal metamolecules (circled in green). Conversely, in b we expand the size of the hexagons, obtaining an array composed of a different metamolecule involving a trimer of resonator pairs (circled in green). (c,d) The resonant modes of the two metamolecules, responsible for the six bands observed in the band structures of the two crystals (e,f). (e) The band structure of the lattice of shrunk hexagons, and the associated electric field distribution for the Bloch modes of the six bands at the Γ point. (f) Similar to e for the lattice of extended hexagons, except that the p and d bands are now inverted with respect to the bandgap. As demonstrated in the text, the bandgap (blue shaded area) in e is topologically trivial, whereas the one in f is associated with a non-trivial topology.