Insulating, Superconducting, and Large-Compressibility Phases in Nanotube Ropes

The superconducting properties of carbon nanotube ropes are studied using a new computational framework that incorporates the renormalization of intratube interactions and the effect of intertube Coulomb screening. This method allows one to study both the limits of thin and thick ropes ranging from purely one-dimensional physics to the setting of 3D Cooper-pair coherence, providing good estimates of the critical temperature as a function of the rope physical parameters. We discuss the connection of our results with recent experiments.

Figure 1

Plot of the low-energy linear branches of carbon nanotubes. The spinors in the inside (outside) correspond to the relative electron amplitudes in the two sublattices of graphene rolled up to form a zigzag (armchair) nanotube.

Figure 2

Diagrams contributing to the screening of Coulomb interactions between currents $l_a$, $l_b$ of well-defined chirality and spin inside a rope. The second term takes into account the polarization of the $n$ metallic nanotubes in the rope.

Figure 3

Phase diagram of undoped armchair (left) and doped zigzag (right) nanotubes as a function of the number of metallic nanotubes $n$ in the rope and the strength of the attractive interaction $G=4|g|/\pi v_F$. Thick lines represent the phase boundaries between a 3D phase-coherent superconducting phase and the 1D phases characterized by the breaking of the parameters $K_{+}$ and $K_{-}$ (the narrow phase to the left of the second diagram corresponds to the divergence of the latter). Thin lines are contours of constant critical frequency ${\omega }_c$, starting from above with $\ln (E_c/{\omega }_c)=2,4,6,\dots$.