Definitive Band Gaps for Single-Wall Carbon Nanotubes

We report ab initio quantum mechanical calculations of band structures of single-walled carbon nanotubes (SWNTs) using the B3LYP flavor of density functional theory. In particular, we find excellent agreement with the small band gaps in "metallic" zigzag SWNTs observed by Lieber et al. [0.079 vs 0.080 eV for (9,0), 0.041 vs 0.042 eV for (12,0), and 0.036 eV vs 0.029 eV for (15,0)]. This contrasts with the results from LDA and PBE, which lead to band gaps 70−100% too small, and with those from the GW correction to LDA, which leads to a gap two times too large. Interestingly we find that the (5,0) system, expected to be a large gap semiconductor, is metallic. These results show that B3LYP leads to very accurate band gaps for CNTs, suggesting its use in designing CNT devices. We find that the effective mass of the CNT (significant in designing CNT devices) scales inversely proportional to the square of the diameter.