The Electronic Band Structure of Graphene and Carbon Nanotubes

The density of states expressions for graphene and Zigzag carbon nanotubes for different geometries had been rederived using the dispersion relation obtained by the well-known tight-binding method. In addition, our numerical results for the density of states of graphene and zigzag carbon nanotubes had been produced and the results support both the conducting and the semiconducting behavior of the nanotubes. Also we had been used the derived expression for the energy gap of the semiconducting zigzag carbon nanotubes to compute it numerically. Furthermore, we had studied the relativistic Dirac Hamiltonian behavior of the particle in graphene material near the Dirac points and the particle is found to behave as a massless particle. We also compared our numerical results against the very recently experimental and theoretical reported ones.