Fourth-order Optoelectronic Response from Cascaded Circular Photogalvanic and Nonlinear Hall Effects

The interplay between nonlinear optical transitions and topological band structure offers a route to control photocurrents. We reveal a fourth-order optoelectronic response that emerges due to an interlink between the circular photogalvanic effect (CPGE) and the Berry curvature dipole (BCD) in noncentrosymmetric 2D materials. Using monolayer $\Td$-WTe$_2$ as a prototype, we predict that circularly polarized mid-infrared light produces a steady dc injection current that induces an internal electric field, which in turn drives a transverse nonlinear Hall response through BCD. The resulting cascaded photovoltage scales as the fourth power of the optical field $E_0^4$. By mapping the full injection current tensor, we show that this cascaded voltage is strongly tunable by the optical geometry: normal incidence drives an in-plane resonance $\mathrm{Im}(\eta_{yxy})$, whereas oblique illumination ($\theta = 45^{\circ}$) recruits a dominant out-of-plane component $\mathrm{Im}(\eta_{yyz})$ and amplifies the signal by more than two orders of magnitude (${\sim}10^2~\mu$V). While the massive linear Drude background typically screens nonlinear responses in semimetals, we argue that the amplitude modulation of the optical pump allows lock-in detection to cleanly isolate the frequency-doubled cascaded response. The proposed mechanism converts mid-infrared light into a gate-tunable transverse signal, providing a route for probing quantum geometry and realizing topological photodetectors and frequency doublers.