Optical N-invariant of graphene's topological viscous Hall fluid.

Over the past three decades, graphene has become the prototypical platform for discovering topological phases of matter. Both the Chern [Formula: see text] and quantum spin Hall [Formula: see text] insulators were first predicted in graphene, which led to a veritable explosion of research in topological materials. We introduce a new topological classification of two-dimensional matter - the optical N-phases [Formula: see text].

Spin photonic forces in non-reciprocal waveguides.

Optical forces acting on particles - controlled by the intensity, polarization and direction of optical beams - have become an important tool in manipulation, sorting and analysis of nano/micro-particles. The nature of these forces has been well understood in reciprocal structures exhibiting time-reversal symmetries. Here, we investigate the nature of optical forces in non-reciprocal structures with non-degenerate counter-propagating modes.