Radial oscillations of local density of states in carbon nanotubes

By performing an analytical study of the electronic structure of metallic carbon nanotubes, we show that the local density of states exhibits well-defined oscillations as a function of the nanotube radius. The periods of such oscillations are obtained from size quantization effects derived from folding up finite graphene sheets into tubular structures. A clear analogy with the de Haas--van Alphen effect in metals is established to explain the origin and features of such oscillations. Results of energy change calculations for impurity-doped carbon nanotubes also show the same type of oscillations.