Strain effects on electronic and optic properties of monolayer C$_2$N holey two-dimensional crystals

A new two-dimensional material, the C$_2$N holey 2D (C$_2$N-$h$2D) crystal, has recently been synthesized. Here we investigate the strain effects on the properties of this new material by first-principles calculations. We show that the material is quite soft with a small stiffness constant and can sustain large strains $\geq 12\%$. It remains a direct gap semiconductor under strain and the bandgap size can be tuned in a wide range as large as 1 eV. Interestingly, for biaxial strain, a band crossing effect occurs at the valence band maximum close to a 8\% strain, leading to a dramatic increase of the hole effective mass. Strong optical absorption can be achieved by strain tuning with absorption coefficient $\sim10^6$ cm$^{-1}$ covering a wide spectrum. Our findings suggest the great potential of strain-engineered C$_2$N-$h$2D in electronic and optoelectronic device applications.