An analytical derivation of the density of states, effective mass, and carrier density for achiral carbon nanotubes

An analytical electron density of states (DOS) for zigzag and armchair single-wall carbon nanotubes (CNTs) are derived in this paper. The derivation originates from the tight-binding energy dispersion relation for CNTs and reveals the essential physics such as periodic van-Hove singularities and its dependence on chirality. The DOS derivation is exact and contains no additional approximations or assumptions, except those inherent in the nearest neighbor tight-binding model. In addition, we derive analytical expressions for the group velocity, effective mass, and nondegenerate equilibrium carrier density.