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.
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