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Disorder-induced superconductivity in ropes of carbon nanotubes

We study the interplay between disorder and superconductivity in a rope of metallic carbon nanotubes. Based on the time dependent Ginzburg Landau theory, we derive the superconducting transition temperature T$_c$ taking into account the critical superconducting fluctuations which are expected to be substantially strong in such low dimensional systems. Our results indicate that, contrary to what is expected, T$_c$ increases by increasing the amount of disorder. We argue that this behavior is due to the dynamics of the tubes which reduces the drastic effect of the local disorder on superconductivity by enhancing the intertube Josephson tunneling. We also found that T$_c$ is enhanced as the effective dimensionality of the rope increases by increasing the number N of the tubes forming the rope. However, T$_c$ tends to saturate for large values of N, expressing the establishment of a bulk three dimensional (3D) superconducting order.