  Edge states occurring in Chern and quantum spin-Hall phases are signatures of
the topological electronic band structure in two-dimensional (2D) materials.
Recently, a new topological electromagnetic phase of graphene characterized by
the optical N-invariant has been proposed. Optical N-invariant arises from
repulsive Hall viscosity in hydrodynamic many-body electron systems,
fundamentally different from the Chern and Z2 invariants. In this paper, we
introduce the topologically protected edge excitation -- optical N-plasmon of
interacting many-body electron systems in the topological optical N-phase.
These optical N-plasmons are signatures of the topological plasmonic band
structure in 2D materials. We demonstrate that optical N-plasmons exhibit
fundamentally different dispersion relations, stability, and edge profiles from
the topologically trivial edge magneto plasmons. Based on the optical
N-plasmon, we design an ultra sub-wavelength broadband topological hydrodynamic
circulator, which is a chiral quantum radio-frequency circuit component crucial
for information routing and interfacing quantum-classical computing systems.
Furthermore, we reveal that optical N-plasmons can be effectively tuned by the
neighboring dielectric environment without breaking the topological properties.
Our work provides a smoking gun signature of repulsive Hall viscosity and opens
practical applications of topological electromagnetic phases of two-dimensional
materials.
