First-principles study on physical properties of a single ZnO monolayer with graphene-like structure

The elastic, piezoelectric, electronic, and optical properties of a single ZnO monolayer (SZOML) with graphene-like structure are investigated from the first-principles calculations. The phonon dispersion curves contain three acoustic and three optical branches. At $\mathrm{\Gamma }$ point, the out-of-plane acoustic mode has an asymptotic behavior $\omega (q)=B{q}^2$ with $B=1.385 \times 10^{-7}$m$^2$\mathrm{/}s,whiletwoin-planeacousticmodeshavesoundvelocities$2.801$km\mathrm{/}sand$8.095$ km/s; the other three optical modes have frequencies 250 cm${}^{-1}$, 566 cm${}^{-1}$, and 631 cm${}^{-1}$. The elastic and piezoelectric constants are obtained from the relaxed ion model. It is found that the SZOML is much softer than graphene, while it is a piezoelectric material. The electronic band gap is 3.576 eV, which implies that the SZOML is a wide band gap semiconductor. Many peaks exist in the linear optical spectra, where the first peak at 3.58 eV corresponds to the band gap of SZOML.