Oscillating edge states in polariton topological insulators

We show that slow time-periodic variation of the external magnetic field applied to a polariton topological insulator based on a honeycomb array of microcavity pillars with pronounced TE-TM splitting results in oscillations of the edge states along the boundary of the insulator accompanied by slow transverse drift of the center of mass of the edge state along the boundary. The oscillations and drift are due to time-periodic variation of the sign of the instantaneous group velocity of the edge state with selected central Bloch momentum triggered by the variation of the Zeeman splitting in the external magnetic field. These oscillations are also accompanied by periodic exchange of norm between two polarization components of the edge state. Oscillating edge states survive despite the fact that the magnetic field periodically vanishes resulting in closure of the topological gap in the instantaneous spectrum of the system. The direction of the drift and amplitude of oscillations of the edge state strongly and nonmonotonically depend on its initial central Bloch momentum.