  We propose an experimental setup using 3D Dirac semimetals to access a novel
phenomenon induced by the chiral anomaly. We show that the combination of a
magnetic field and a circularly polarized laser induces a finite charge density
with an accompanying axial current. This is because the circularly polarized
laser breaks time-reversal symmetry and the Dirac point splits into two Weyl
points, which results in an axial-vector field. We elucidate the appearance of
the axial-vector field with the help of the Floquet theory by deriving an
effective Hamiltonian for high-frequency electric fields. This anomalous charge
density, i.e. the chiral pumping effect, is a phenomenon reminiscent of the
chiral magnetic effect with a chiral chemical potential. We explicitly compute
the pumped density and the axial-current expectation value. We also take
account of coupling to the chiral magnetic effect to calculate a balanced
distribution of charge and chirality in a material that behaves as a chiral
battery.
