Electronic structure characteristic of carbon nanotubules

Abstract

Electronic structure near the Fermi energy of single-shell carbon nanotubules has been studied within the framework of the tight-binding approximation. The electronic density of states (DOS) of tubules shows a structure consisting of many spike-like peaks. An analytical expression in a π-electron model is derived which predicts not only the energy gap (Eg) of semiconducting tubules, but also the energy positions of those spike-like peaks in the π-DOS near the Fermi energy in any tubule. The limitation of the π-electron model in tubules is discussed by investigating the effect of σ-πmixing. The position of σ component edge in the DOS is also investigated as a function of tubule radius (R) and chiral angle (θ). It is found that this edge energy is very sensitive to θ and largely changes with R, because the dominant contribution of θ to its change is given by g(θ)/R in contrast to f(θ)/R2 for Eg.