The shift current photovoltaic effect is conventionally understood as the real-space displacement of a wave packet induced by photoexcitation. However, this interpretation becomes insufficient in flat-band systems, where quasiparticles are too massive to accelerate in real space under the optical electric field. Here, we developed a physically consistent method to decompose the shift current into real-space and momentum-space components. A surprising pure momentum-space shift current is found theoretically in flat-band Mott insulator ${\mathrm{Nb}}_3{X}_8$ $(X=\mathrm{Cl}, \mathrm{Br}, \mathrm{I})$ monolayers. This work underscores that significant shift current responses can emerge even in systems with zero polarization change, highlighting the potential for exploring novel bulk photovoltaic effects in flat-band Mott insulators.

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• Flat bands
• Nonlinear optical susceptibility
• Photovoltaic effect
• Monolayer films