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We theoretically study laser driven nonequilibrium states in the Kitaevhoneycomb model with a magnetoelectric cross coupling. We show that atopological spin liquid with a gapless chiral edge mode emerges when we applyan elliptically or circularly polarized laser. This is a strongly correlatedquantum spin version of the Floquet topological insulator. In the topologicalphase, the edge mode is made from Majorana fermions and the bulk has gappednon-Abelian anyon excitations.

Floquet Majorana Edge Mode and Non-Abelian Anyons in a Driven Kitaev Model