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We theoretically studied the Floquet state of gated bilayer graphene, whichis irradiated by normally incident focused Gaussian beam with orbital angularmomentum (OAM). According to the Floquet theory, in-plane and out-of-planeelectric field of the OAM beam periodically perturbs the intralayer andinterlayer hopping, which are equivalent to the presence of effective staggeredsublattice potential and next-nearest neighboring interlayer hopping within thelight spot region, respectively. The combination of the effective terms and thegated voltage form an effective trapping potential, which hosts localizedquantum states with energy level being within the energy gap of thenon-irradiated gated bilayer graphene. The energy spectrum can be tuned by theamplitude of the optical beam and additional static magnetic field. Byengineering the parameters, valley-polarized two-fold degenerated zero energyFloquet states can be induced.

Localized Floquet states in gated bilayer graphene induced by focused optical beam with orbital angular momentum