Strain effect on electronic properties of low-dimensional $\gamma$-graphyne : first principles study

Using first-principles calculations, we study the interplay between structural and electronic properties of $\gamma$-graphyne nanotubes ($\gamma$GNTs) consisting of hexagonal carbon rings and acetylenic linkages. We first identify the equilibrium structures of various $\gamma$GNTs classified in terms of chirality: $(n,0)$ denotes an armchair-type tube, whereas $(n,n)$ does a zigzag-type, in contrast with CNTs. Then their Young's moduli are calcuated to be a few hundreds in GPa, which are smaller than those of CNTs. We verify that all $\gamma$GNTs are intrinsic semicondutors with energy gap ($\alt 1.22$ eV) decreasing with tube diameter. It is, however, found that axial strain can significantly modifies the electronic structures of semiconducting $\gamma$GNTs. Very intriguingly, even semiconductor-metal transition occurs under compressive strain: all armchair $\gamma$GNTs, exept for (3,0) $\gamma$GNT with small diameter, become metallic, while only some types of zigzag $\gamma$GNTs metallic under compression. To explain the origin of such electronic structure modifications, we examine the effect of structural change on the band structures of two-dimensional $\gamma$-graphyne sheet under strains and match them with the band structure of $\gamma$GNTs using the zone-folding scheme.