First-principles Study On The Band Gaps Of Zigzag Single-walled Carbon Nanotubes

Carbon nanotubes are belieVed to be basic structural unit of new nanometer-scale electronic deVices. Their unique electronic properties are derived from their band structures, and the value of energy gap is one of the important parameters of electronic deVices. Therefore, to research the band structures and the band gaps of carbon nanotubes become one hot topic among condensed matter physicists. The band structures and the band gaps of some single-walled carbon nanotubes(SWNTs) were calculated and their conductivities were predicted. HoweVer, most of them are for isolated SWNTs, and they don't agree with experimental data very well. On the other hand, the most existing studies were carried out by using tight-binding model and first-principles calculations within the local density approximation (LDA). In this paper, first-principles calculations within the generalized gradient approximation (GGA) are carried out on the band gaps of zigzag SWNTs (7,0) (8,0) (9,0) and (12,0). Our calculation includes isolated tubes as well as the corresponding ropes. Comparing our results with those of others, we come to the following conclusions: (1) The lattice constants of the ropes of (7,0) (8,0) (9,0) and (12,0) are 0.955nm 1.015nm 1.124nm 1.335nm respectively, they agree well with the experimental data and the theoretical values of Gao GH. This shows that our calculational scheme is reasonable. (2) The band gaps of isolated tubes of (7,0) (8,0) (9,0) and (12,0) are 0.237eV 0.626eV 0.070eV and 0.045eV, respectively. As for (9,0) and (12,0) , they were predicted to be metallic by the simple π-orbital tight binding model, while our results and experimental data of M. Ouyang show that they are narrow-gap semiconductors. (3) For the band gap of isolated tubes, there is small discrepancy between our results and experimental data, but big discrepancy occurs between our results and the expected values of the simple π-orbital tight binding model. Our analysis indicates that the radius of selected tubes is small, curvature effect is too important to be neglected, as a result, the conclusions derived from the simple πorbital tight binding model are wrong for small radius tubes. (4) The band gaps of selected ropes of (7,0) (8,0) (9,0) and (12,0) are 0.237eV 0.626eV 0.070eV and 0.045eV, respectively. Comparing with those of the corresponding isolated tubes,they decrease, which is still no seen reported in domestic journals. Our analysis indicates that the intertube coupling causes the band gaps decrease due to the electrons in the rope are less confined than those in the isolated tube. Although some of our results still need to be modified by experiments, they have some certain directive purport and reference worth on further investigating curvature effect and intertube coupling effect on electronic structure of carbon nanotubes.