  We apply the recently-developed partition-free time-dependent
Landauer-B\"uttiker (TD-LB) formalism to the study of periodically-driven
transport in graphene nanoribbons (GNR). When an AC driving is applied, this
formalism can be used to prove generic conditions for the existence of a
non-zero DC component of the net current (pump current) through the molecular
device. Time-reversal symmetry breaking in the driving field is investigated
and found to be insufficient for a non-zero pump current. We then derive
explicit formulas for the current response to a particular biharmonic bias. We
calculate the pump current through different GNR configurations and find that
the sign and existence of a non-zero pump current can be tuned by simple
alterations to the static parameters of the TD bias. Further, we investigate
transient currents in different GNR configurations. We find a selection rule of
even and odd harmonic response signal depending on a broken dynamical inversion
symmetry in the bias.
