Using Bogoliubov-de Gennes formalism for inhomogeneous systems, we have studied superconducting properties of a bundle of packed carbon nanotubes, making a triangular lattice in the bundle's transverse cross-section. The bundle consists of a mixture of metallic and doped semiconducting nanotubes, which have different critical transition temperatures. We investigate how a spatially averaged superconducting order parameter and the critical transition temperature depend on the fraction of the doped semiconducting carbon nanotubes in the bundle. Our simulations suggest that the superconductivity in the bundle will be suppressed when the fraction of the doped semiconducting carbon nanotubes will be less than 0.5, which is the percolation threshold for a two-dimensional triangular lattice. Single wall carbon nanotubes (SWCNTs) represent a unique class of quasione-dimensional nanoscale systems exhibiting various interesting phenomena. Among other exciting features, it was demonstrated that individual single wall carbon nanotubes may have intrinsic superconducting properties [1]. However, because of their extremely small diameter (just few nanometers), and thus strongly one-dimensional character, the superconducting order parameter may have significant “phase slips” due to thermal and quantum fluctuations, leading to a finite conductivity in the system below the critical temperature [2, 3]. Carbon nanotubes can also form bundles and ropes [4], with tens and hundreds of individual SWCNTs in the bundle, coupled to each other by dispersive Van der Waals forces. Such kind of system may exhibit reduced “phase slips” effects and as a result, much stronger conductivity drop below the critical temperature. The overall length of a SWCNT in the bundle also plays a significant role. For example, reducing the bundle’s length to 300？nm may destroy the superconductivity in the system due to increasingly high quantum fluctuations [2]. Generally speaking, for nanoscale systems with the quantum level spacing approaching the superconducting gap energy , the superconductivity vanishes [5]. It is expected that doping of SWCNTs in a bundle by, for example, boron, may significantly improve their superconducting properties [6]. At a proper level of doping, the Fermi level may be at a one-dimensional singularity of the energy spectrum that gives a higher density of states (DOSs), that will lead to a higher critical temperature . In particular, we assume here that such kind of mechanism of doping enhanced may be much better pronounced in the case of semiconducting SWCNTs, which may
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