  The bulk photovoltaic effect (BPVE) refers to current generation due to
illumination by light in a homogeneous bulk material lacking inversion
symmetry. In addition to the intensively studied shift current, the ballistic
current, which originates from asymmetric carrier generation due to scattering
processes, also constitutes an important contribution to the overall kinetic
model of the BPVE. In this letter, we use a perturbative approach to derive a
formula for the ballistic current resulting from the intrinsic electron-phonon
scattering in a form amenable to first-principles calculation. We then
implement the theory and calculate the ballistic current of the prototypical
BPVE material \ch{BaTiO3} using quantum-mechanical density functional theory.
The magnitude of the ballistic current is comparable to that of shift current,
and the total spectrum (shift plus ballistic) agrees well with the
experimentally measured photocurrents. Furthermore, we show that the ballistic
current is sensitive to structural change, which could benefit future
photovoltaic materials design.
