Disorder induced transverse delocalisation in ropes of carbon nanotubes

A rope of carbon nanotubes is constituted of an array of parallel single wall nanotubes with nearly identical diameters. In most cases the individual nanotubes within a rope have different helicities and 1/3 of them are metallic. In the absence of disorder within the tubes, the intertube electronic transfer is negligeable because of the longitudinal wave vector mismatch between neighboring tubes of different helicities. The rope can then be considered as a number of parallel independent ballistic nanotubes. On the other hand, the presence of disorder within the tubes favors the intertube electronic transfer. This is first shown using a very simple model where disorder is treated perturbatively inspired by the work in reference \cite{maarouf00}. We then present numerical simulations on a tight binding model of a rope. Disorder induced transverse delocalisation shows up as a spectacular increase of the sensitivity to the transverse boundary conditions in the presence of small disorder. This is accompanied by an increase of the longitudinal localisation length. Implications on the nature of electronic transport within a rope of carbon nanotubes are discussed.