Modulational instability and solitary waves in polariton topological insulators

Optical microcavities supporting exciton-polariton quasi-particles offer one of the most powerful platforms for the investigation of the rapidly developing area of topological photonics in general,and of photonic topological insulators in particular. Energy bands of the microcavity polariton graphene are readily controlled by a magnetic field and influenced by the spin-orbit (SO) coupling effects,a combination leading to the formation of linear unidirectional edge states in polariton topological insulators as very recently predicted. In this work we depart from the linear limit of non-interacting polaritons and predict instabilities of the nonlinear topological edge states resulting in the formation of the localized topological quasi-solitons,which are exceptionally robust and immune to backscattering wave packets propagating along the graphene lattice edge. Our results provide a background for experimental studies of nonlinear polariton topological insulators and can influence other subareas of photonics and condensed matter physics,where nonlinearities and SO effects are often important and utilized for applications.