Strain-Induced Tuning of Third-Harmonic Generation in Monolayer Black Phosphorene

Based on the tight-binding model and the semiconductor Bloch equations, this work systematically reveals the microscopic mechanism of strain engineering in turning of third-harmonic generation (THG) in monolayer black phosphorene (BP). % The results show that under strain-free conditions, monolayer BP exhibits significant in-plane anisotropy, and its dominant susceptibility component reaches a maximum of $\chi^{(3);xxxx} = 1.8 \times 10^{-17} \, \text{m}^2/\text{V}^2$, agreeing well with the experimental results. % By applying uniaxial and biaxial strains along the armchair ($x$), zigzag ($y$), and out-of-plane ($z$) directions, we find that the THG response presents strong direction dependence and unique spectral shifting behaviors: in-plane compressive strain and out-of-plane tensile strain both significantly enhance the THG conductivity and induce a redshift, whereas in-plane tensile strain and out-of-plane compression lead to suppression and a blueshift, with the tuning efficiency following the order of $z > y > x$. The microscopic origin of these phenomena is identified as the synergistic modulation of the bandgap and Berry connection by strain. % Furthermore, the synergistic or competitive effects of biaxial strain further enrich the manipulation of THG signals. % Strain engineering can serve as an effective strategy for dynamically controlling nonlinear optical processes in two-dimensional materials, and it also lays a theoretical foundation for the development of high-performance reconfigurable infrared photonic devices.