  Shift current and ballistic current have been proposed to explain the bulk
photovoltaic effect (BPVE), and there have been experiments designed to
separate the two mechanisms. These experiments are based on the assumption that
under magnetic field, ballistic current can have a Hall effect while the shift
current cannot, which is from some energy-scale arguments and has never been
proven. A recent work [Phys. Rev. B 103, 195203 (2021)] using quantum transport
formalism achieves a conclusion that shift current indeed has a Hall current,
seemingly contradicting the previous assumption and making the situation more
confusing. Moreover, the behavior of BPVE under strong magnetic field is still
unexplored. In this Letter, using a minimal 2D tight-binding model, we carry
out a systematic numerical study of the BPVE under weak and strong magnetic
field by treating the field in a non-perturbative way. Our model clearly shows
the appearance of the magnetically-induced ballistic current along the
transverse direction, which agrees with the previous predictions, and
interestingly a sizable longitudinal response of the shift current is also
observed, a phenomenon that is not captured by any existing theories where the
magnetic field is treated perturbatively. More surprisingly, drastically
different shift current is found in the strong-field regime, and the evolution
from weak to strong field resembles a phase transition. We hope that our work
could resolve the debate over the behavior of BPVE under magnetic field, and
the strong-field behavior of shift current is expected to inspire more studies
on the relation between nonlinear optics and quantum geometry.
