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A method is derived to solve the massless Dirac-Weyl equation describingelectron transport in a mono-layer of graphene with a scalar potential barrierU(x,t), homogeneous in the y-direction, of arbitrary x- and time dependence.Resonant enhancement of both electron backscattering and currents, across andalong the barrier, is predicted when the modulation frequencies satisfy certainresonance conditions. These conditions resemble those for Shapiro-steps ofdriven Josephson junctions. Surprisingly, we find a non-zero y-component of thecurrent for carriers of zero momentum along the y-axis.

Current resonances in graphene with time dependent potential barriers