Topological hydrodynamic circulator in graphene's viscous Hall fluid

Viscous Hall electron fluid in graphene has emerged at the forefront of many-body interacting electron systems due to its low dimensionality and impurity density. It is the first candidate for a non-local topological electromagnetic phase of matter. This 2D topological viscous Hall insulator is characterized by an optical N invariant, fundamentally different from the Chern and quantum spin Hall insulators. Here, we show that with broken time-reversal symmetry, this viscous Hall fluid is in a topological electromagnetic phase arising from the repulsive nature of Hall viscosity. This feature is evident by studying the edge magneto-plasmons, which close the low-frequency electromagnetic bandgap for graphene and have dispersion relations independent of fluid boundary conditions. Based on the unidirectional topological edge plasmons immune to back-scattering, we design and simulate a topological circulator, which is a chiral quantum radio-frequency (RF) circuit component crucial for information routing and interfacing quantum-classical computing systems. Our work opens practical applications of graphene's viscous Hall fluid and simultaneously provides an experimental platform for studying topological hydrodynamics of light.