Theory of superconductivity in multiwalled carbon nanotubes

We devise an approach to describe the electronic instabilities of doped multiwalled nanotubes, where each shell has in general a manifold of Fermi points. Our analysis relies on the scale dependence of the different scattering processes, showing that a pairing instability arises for a large enough number of Fermi points as a consequence of their particular geometric arrangement. The instability is enhanced by the tunneling of Cooper pairs between nearest shells, giving rise to a transition from the Luttinger liquid to a superconducting state in a wide region of the phase diagram.

Figure 1

(Color online) Schematic representation of the location of the Fermi points for the shells of a doped MWNT, referred to the hexagonal Brillouin zone (BZ) of graphene. The horizontal lines correspond to different low-energy subbands, arising from the conical dispersion around the corners of the BZ. The full (dashed) hexagon stands for the case of an armchair (zig-zag) geometry. The $c_{a,b}$ $\left(t_{a,b}\right)$ couplings label the intratube (intertube) scattering of Cooper pairs at zero total momentum.

Figure 2

Phase diagram of doped MWNTs in terms of the average radius $R$ of the shells and the doping level, represented by the shift in the Fermi energy ${\epsilon }_F$ with respect to the value in the undoped system. The upper region corresponds to a SC phase with $p$-wave symmetry. The density plot represents in gray scale the values of the logarithm of the transition scale ${\omega }_c$, ranging from $-\ln ({\omega }_c∕\mathrm{\Delta }E)\approx 4$ (black) to $\approx 6$ (white).