Exciton-driven linear and nonlinear optical responses in metal monoxide monolayers M O ( M = Mg ,Ca,Cd) from first-principles calculations

We study the linear and nonlinear [second-harmonic generation (SHG)] spectra of metal monoxide $\mathrm{MO}$ ($M$=Mg,Ca,Cd) monolayers by using a first-principles approach based on many-body theory. Our results indicate that the strongly bound excitons in $\mathrm{MO}$ with planar structure characterize the optical properties, including both linear and SHG spectra. The optical bandgap ${E}_{\text{opt}}$ is 4.63, 3.71, and 1.27 eV, while the exciton binding energy is as large as 2.49, 2.37, and 1.13 eV, for MgO, CaO, and CdO, respectively. Moreover, the largest SHG coefficient of 586 pm/V is found in CdO monolayer with the smallest bandgap among the three $\mathrm{MO}$ materials. Most importantly, we find a linear relationship between the SHG coefficient and $\mathrm{Qd}/{E}_{\text{opt}}$ ($Q$ is the transferred Bader charge and $d$ is the bond length) which can be used as a descriptor to search for new two-dimensional nonlinear materials.