  Based on the quantum master equation approach, the nonlinear electric
conductivity of graphene is investigated under static electric fields for
various chemical potential shifts. The simulation results show that, as the
field strength increases, the effective conductivity is firstly suppressed,
reflecting the depletion of effective carriers due to the large displacement in
the Brillouin zone caused by the strong field. Then, as the field strength
exceeds $1$~MV/m, the effective conductivity increases, overcoming the carrier
depletion via the Landau--Zener tunneling process. Based on the nonlinear
behavior of the conductivity, the charge transport induced by few-cycle THz
pulses is studied to elucidate the ultrafast control of electric current in
matter.
