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 $\Gamma$ point, the out-of-plane acoustic mode has an asymptotic behavior $\omega (q)=Bq^2$ with $B=1.385 \times 10^{-7}$ m$^2$/s, while two in-plane acoustic modes have sound velocities $2.801$ km/s and $8.095$ 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.