Domain-Selective Enhancement of Second Harmonic Generation in Monolayer MoS$_2$ via Ferroelectricity-Controlled Photodoping

Hybrid heterostructures combining two-dimensional semiconductors with ferroelectric materials offer a versatile route to actively control light-matter interactions at the nanoscale. Here, we report all-optical, light-induced domain-selective control of second-harmonic generation (SHG) in monolayer molybdenum disulfide (MoS$_2$) integrated with periodically poled lithium niobate (LiNbO$_3$). Spatially resolved SHG imaging reveals a pronounced modulation of the nonlinear optical response of monolayer MoS$_2$ governed by the ferroelectric domain pattern of the underlying substrate. A strong SHG contrast is observed between domains of opposite polarization, with a marked dependence on both the excitation wavelength and the incident optical power. The comparison between ferroelectric domains that either enable or do not exhibit light-driven photodoping in the MoS$_2$ monolayer provides a direct assessment of the role of carrier density in the nonlinear optical response. We find that ferroelectric-polarization-controlled photodoping at the MoS$_2$/LiNbO$_3$ interface enhances the effective second-order susceptibility, $\chi^2$, producing an increase in SHG intensity of up to ~70% under resonant excitation conditions. Ab initio calculations corroborate that charge doping modifies the electronic band structure of MoS$_2$ and strongly affects $\chi^2$ in the resonant regime, providing microscopic support for the experimentally observed modulation. The results highlight the combination of light intensity and ferroelectricity as a powerful knob for band-structure modulation in 2D materials and reconfigurable nonlinear optical responses, opening pathways toward programmable frequency conversion, smart light modulators, and advanced nonlinear photonic functionalities in integrated hybrid platforms.