  We propose that a Floquet Weyl semimetal state can be induced in
three-dimensional topological insulators, either nonmagnetic or magnetic, by
the application of off-resonant light. The virtual photon processes play a
critical role in renormalizing the Dirac mass and so resulting in a topological
semimetal with vanishing gap at Weyl points. The present mechanism via
off-resonant light is quite different from that via on-resonant light, the
latter being recently suggested to give rise to a Floquet topological state in
ordinary band insulators.
