Optically induced topological spin-valley Hall effect for exciton polaritons

We consider exciton-polaritons in a honeycomb lattice of micropillars subjected to circularly polarized $({\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}$) incoherent pumps, which are arranged to form two domains in the lattice. We predict that the nonlinear interaction between the polaritons and the reservoir excitons gives rise to the topological valley Hall effect where in each valley two counterpropagating helical edge modes appear. Under a resonant pump, ${\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}$ polaritons propagate in different directions without being reflected around bends. The polaritons propagating along the interface have extremely high effective lifetimes and show fair robustness against disorder. This paves the way for robust exciton-polariton spin separating and transporting channels in which polaritons attain and maintain high degrees of spin polarization, even in the presence of spin relaxation.