  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.
