  We demonstrate how to control the spectra and current flow of Dirac electrons
in both a graphene sheet and a topological insulator by applying either two
linearly polarized laser fields with frequencies $\omega$ and $2\omega$ or a
monochromatic (one-frequency) laser field together with a spatially periodic
static potential(graphene/TI superlattice). Using the Floquet theory and the
resonance approximation, we show that a Dirac point in the electron spectrum
can be split into several Dirac points whose relative location in momentum
space can be efficiently manipulated by changing the characteristics of the
laser fields. In addition, the laser-field controlled Dirac fermion band
structure -- Dirac fermion time-Floquet crystal -- allows the manipulation of
the electron currents in graphene and topological insulators. Furthermore, the
generation of dc currents of desirable intensity in a chosen direction occurs
when applying the bi-harmonic laser field which can provide a straightforward
experimental test of the predicted phenomena.
