Helical boundary modes from synthetic spin in a plasmonic lattice

Artificial lattices have been used as a platform to extend the application of topological physics beyond electronic systems. Here, using the two-dimensional Lieb lattice as a prototypical example, we show that an array of disks which each support localized plasmon modes give rise to an analog of the quantum spin Hall state enforced by a synthetic time reversal symmetry. We find that an effective next-nearest-neighbor coupling mechanism intrinsic to the plasmonic disk array introduces a nontrivial $Z_2$ topological order and gaps out the Bloch spectrum. A faithful mapping of the plasmonic system onto a tight-binding model is developed and shown to capture its essential topological signatures. Full wave numerical simulations of graphene disks arranged in a Lieb lattice confirm the existence of propagating helical boundary modes in the nontrivial band gap.