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]. This topological quantum number is connected to polarization transport and captured solely by the spatiotemporal dispersion of the susceptibility tensor χ. We verify N ≠ 0 in graphene with the underlying physical mechanism being repulsive Hall viscosity. An experimental probe, evanescent magneto-optic Kerr effect (e-MOKE) spectroscopy, is proposed to explore the N-invariant. We also develop topological circulators by exploiting gapless edge plasmons that are immune to back-scattering and navigate sharp defects with impunity. Our work indicates that graphene with repulsive Hall viscosity is the first candidate material for a topological electromagnetic phase of matter.

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. We consider the specific case of non-reciprocity induced via translational motion and show that the two counter-propagating modes in a moving slab-waveguide are not degenerate which results in a non-zero lateral and longitudinal force on a nanoparticle. We prove that these anomalous forces are fundamentally connected to near-field photonic spin in optical waveguides and explain their directionality using universal spin-momentum locking of evanescent waves. The presented results show that the interplay of photon spin and non-reciprocity can lead to unique avenues of controlling nanoscale optical forces on-chip.