The bulk photovoltaic effect (BPVE) refers to the direct current generation in a noncentrosymmetric material under illumination and can be applied to solar energy technology. BPVE includes injection and shift currents, driven by the change of velocity and displacement of wave packets during optical transitions, respectively. We focus on two-dimensional systems and derive the constraints on the conductivity tensors imposed by mirror-time ($\mathcal{MT}$) symmetry, which leads to orthogonal shift and injection current. For the Haldane model, we show that linearly polarized light can induce shift and injection currents. In contrast, circularly polarized light induces neither shift nor injection currents, as constrained by the three-fold rotation symmetry. Across the topological phase transition, the injection current does not change sign since the group velocity's sign remains unchanged. In contrast, shift current shows a sign flip, as a result of band inversion. Furthermore, we analyze the quantum geometric origins of the response, revealing that vortices in the symplectic connection lead to a suppression of the shift current magnitude in the topological regime. Experimentally, the predicted BPVE can be measured in the antiferromagnetic ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ family, where the symmetry can be tuned by an external electric field, as well as in ultracold atomic systems.

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• Chern insulators
• Geometric & topological phases
• Photoconductivity
• Second order nonlinear optical processes
• Honeycomb lattice
• PT-symmetry
• Tight-binding model