The electromotive force transverse to a bias field under irradiation of circularly polarized light, namely the photovoltaic Hall response or light-induced anomalous Hall effect, has attracted considerable attention to investigate the topologically nontrivial states in Floquet engineering and the inverse spin Hall effect of spin-polarized carriers in spintronics. However, taking into account inversion symmetry breaking by the bias field, the circularly polarized light can excite photocarriers with asymmetric momentum distribution, which generates injection current transverse to the bias field. Therefore, the field-induced circular photogalvanic effect (FI-CPGE) should also emerge in the very same experimental configuration for light-induced anomalous Hall effect but has been overlooked in the literature. In this work, using terahertz pulses as a bias field for a semiconductor GaAs, we conduct two-dimensional Fourier analysis and demonstrate that the FI-CPGE can play a major role in the photovoltaic Hall response. Counterintuitively, the FI-CPGE is significantly enhanced when the photocarriers are excited near the band gap with small density of states and low group velocity, which can be explained by a three-level resonant nonlinear interaction near the band degeneracy point. We also clarified that the FI-CPGE would be further largely detected in the contact-type measurement using electrodes because of the absence of a filtering effect inherent to terahertz pulses. This work provides a comprehensive, generalized view of the photovoltaic Hall response in biased materials, paving a different avenue for detecting topological monopoles in momentum space hidden in equilibrium using third-order nonlinear responses.

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• Anomalous Hall effect
• Berry curvature
• Photogalvanic effect
• III-V semiconductors
• Optical-pump terahertz-probe spectroscopy