Periodicity of band gaps of chiral α-graphyne nanotubes

Electronic structures of zigzag (n,0), armchair (n,n), and chiral (n,m) α-graphyne nanotubes (αGNTs) with n = 2-7 were investigated using density functional tight binding calculations. Oscillatory behavior of the band gaps with a period of every (n - m) = 3 was found for each tube. According to the periodicity, αGNTs could be classified into three families, and their band gaps were in the increasing order of (n - m) = 3a < 3a + 1 < 3a + 2. Among the three families, αGNTs with (n - m) = 3a became effectively semimetallic when the tube size was larger than approximately 2 nm, while the other families remained semiconducting.