Monolayer ${\mathrm{WSe}}_2$ (ML ${\mathrm{WSe}}_2$) exhibits orders of magnitude enhancement in second-harmonic-generation efficiency under single one-photon (1-p) or two-photon (2-p) resonant excitation. Here, we propose a strain engineering approach to greatly boost the in-plane second-order nonlinear susceptibility (${\chi }_{yyy}$) of ML ${\mathrm{WSe}}_2$ by strain shifting the $K$-valley A-exciton and a high-lying exciton (HX) into double resonance. We first identify the A-exciton and HX from the two-dimensional (2D) Mott-Wannier model for pristine ML ${\mathrm{WSe}}_2$ and calculate the ${\chi }_{yyy}$ for 1-p and 2-p resonance excitations, and observe a $\sim 40$-fold ${\chi }_{yyy}$ enhancement arising from the 2-p HX resonance state (compared with the A-exciton case). By applying a small uniform biaxial strain (0.16%), we observe an exciton double-resonance state ($E_{\mathrm{HX}}=2E_{\mathrm{A}}$; $E_{\mathrm{HX}}$ and $E_{\mathrm{A}}$ are the exciton absorption energies), which yields up to an additional $\sim 50$-fold enhancement in ${\chi }_{yyy}$ (compared to the 2-p HX resonance state), indicating an overall $\sim 2000$-fold enhancement (compared with the single 2-p A-exciton resonance case). Further exploration of the strain-engineered exciton states (for a $\sim 0.16$% biaxial strain) reveals that double resonance also occurs at other wave vectors near the $K$ valley, leading to additional enhancements in ${\chi }_{yyy}$. This confirms that strain engineering is an effective approach for enhancing ${\chi }_{yyy}$. Our findings suggest different avenues for strain engineering optical properties of 2D materials for novel nonlinear optical and optoelectronic applications.

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• Second order nonlinear optical processes
• Transition metal dichalcogenides
• First-principles calculations
• Optical second-harmonic generation
• Strain engineering