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We theoretically studied the Floquet state of gated bilayer graphene, which is irradiated by normally incident focused Gaussian beam with orbital angular momentum (OAM). According to the Floquet theory, in-plane and out-of-plane electric field of the OAM beam periodically perturbs the intralayer and interlayer hopping, which are equivalent to the presence of effective staggered sublattice potential and next-nearest-neighboring interlayer hopping within the light spot region, respectively. The combination of the effective terms and the gated voltage form an effective trapping potential, which hosts localized quantum states with energy level being within the energy gap of the nonirradiated gated bilayer graphene. The energy spectrum can be tuned by the amplitude of the optical beam and additional static magnetic field. By engineering the parameters, valley-polarized twofold degenerated zero-energy Floquet states can be induced.
Ma Luo (Mon,) studied this question.