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We show that a strong infrared laser beam obliquely incident on graphene canexperience a parametric instability with respect to decay into lower-frequency(idler) photons and THz surface plasmons. The instability is due to a strongin-plane second-order nonlinear response of graphene which originates from itsspatial dispersion. The parametric decay leads to efficient generation of THzplasmons and gives rise to quantum entanglement of idler photons and surfaceplasmon states. A similar process can be supported by surface states oftopological insulators such as Bi$_2$Se$_3$.

Laser-driven parametric instability and generation of entangled photon-plasmon states in graphene and topological insulators