Theory of superconductivity in carbon nanotubes and graphene

The energy spectrum of the pi-electrons near the Fermi level of graphene consists of not only delocalized bulk states but also localized edge states. The edge states play a decisive role at the interface between carbon nanotube and an electronic contact because they enhance the local density of states. The contact is also important for emergence of superconductivity observed in multi-wall carbon nanotubes. Thus, it is valuable to examine the effect of the edge states on the superconductivity. Using the Eliashberg equation, we obtain an appreciable transition temperature for the edge states. As a result, a metallic zigzag carbon nanotube having open boundaries can be regarded as a natural Superconductor/Normal Metal/Superconductor junction system, in which superconducting states are developed locally at both ends of the nanotube and a normal metal exists in the middle. In this case, a signal of the edge state superconductivity appears as the Josephson current which is sensitive to the bandwidth of the edge states, the position of the Fermi energy and the length of a nanotube. (arXiv:cond-mat/0611452)