  We theoretically investigate the nature of laser-irradiated Kondo insulators.
Using Floquet theory and slave boson approach, we study a periodic Anderson
model and derive an effective model which describes the laser-irradiated Kondo
insulators. In this model, we find two generic effects induced by laser light.
One is the dynamical localization, which suppresses hopping and hybridization.
The other is the laser-induced hopping and hybridization, which can be
interpreted as a synthetic spin-orbit coupling or magnetic field. The first
effect drastically changes the behavior of the Kondo effect. Especially, the
Kondo effect under laser light qualitatively changes its character depending on
whether the hybridization is on-site or off-site. The second effect triggers
topological phase transitions. In topological Kondo insulators, linearly
polarized laser light realizes phase transitions between trivial, weak
topological, and strong topological Kondo insulators. Moreover, circularly
polarized laser light breaks time-reversal symmetry and induces Weyl
semimetallic phases. Our results pave the new way to dynamically control the
Kondo effect and topological phases in heavy fermion systems. We also discuss
experimental setups to detect the signatures.
