Photogalvanic effect and second-harmonic generation from radio to infrared wavelengths in the WTe2 monolayer

Second-order nonlinear optical responses, including photogalvanic effect (PGE) and second harmonic generation (SHG), are fundamental and important physical phenomena in nonlinear optics and optoelectronics. The PGE and SHG associated with linearly and circularly polarized light are called the linear photogalvanic effect (LPGE), circular photogalvanic effect (CPGE), linear second harmonic generation, and circular second harmonic generation, respectively. In this paper, we use the quantum kinetics under the relaxation time approximation to investigate the dependence of second-order nonlinear optical responses on the Fermi level and frequency under different out-of-plane electric fields in ${T}_{d}\text{\ensuremath{-}}{\mathrm{WTe}}_{2}$ monolayer from radio to infrared region. We find that the maximum frequency at which the Berry curvature dipole mechanism for the nonlinear Hall effect plays a major role is about 1 THz. From the aspect of the Fermi level, in the radio and microwave regions, the two large peaks of nonlinear conductivities occur when the Fermi level is equal to the energy corresponding to the vicinity of the gap-opening points in the band dispersion. From the aspect of frequency, in the radio region, the LPGE and SHG conductivities maintain a large constant while the CPGE conductivity almost disappears. In the microwave region, the LPGE and SHG conductivities start to decrease gradually with increasing frequency while the CPGE conductivity is large. In the infrared region, the frequency and Fermi-level dependence of second-order nonlinear optical responses is complicated. In the 125 THz--300 THz region and in the $y$ direction, the presence of dc current without the disturbance of second harmonic current under circularly polarized light may be useful for the fabrication of unique optoelectronic devices. Moreover, we illustrate that when calculating the nonlinear Hall effect or second-order nonlinear optical responses of practical materials, the theories in the clean limit fail and it is necessary to use a theory that takes into account scattering effects (e.g., relaxation time approximation). Our study is promising to promote the more accurate calculation of second-order nonlinear optical responses in practical materials.