Band structures of carbon nanotubes: the sp3s* tight-binding model

We present a simple sp 3 s* tight-binding model for use in calculating the band structures of single-walled carbon nanotubes. The 2s, 2p x , 2p y , 2p z , and s* orbitals of each carbon atom are used as the basis set for expressing the tight-binding model, and the interatom interaction between neighbouring sites is fully taken into account. The elements of the Hamiltonian matrix and related parameters are obtained by adjusting the model to fit the primary reflectivity and photoemission band-structure data. We have employed this tight-binding model in investigating [ n ,0] ( n = 6,7,8,9) carbon nanotubes. Our band-structure and band-gap results show that [6,0] and [9,0] tubes are narrow-gap semiconductors rather than metallic ones, which is at variance with the findings of previous work.