Theoretical approach to electronic screening and correlated superconductivity in carbon nanotubes

A theoretical analysis of the superconductivity observed recently in carbon nanotubes is proposed. We argue that ultrasmall (diameter $\sim 0.4\mathrm{nm}$) single wall carbon nanotubes (with transition temperature $T_c\sim 15\mathrm{K}$) and entirely end-bonded multiwalled ones $(T_c\sim 12\mathrm{K})$ can superconduct by an electronic mechanism, basically the same in both cases. By a Luttinger liquidlike approach, one finds enhanced superconducting correlations due to the strong screening of the long-range part of the Coulomb repulsion. Based on this finding, we perform a detailed analysis on the resulting Hubbard-like model, and calculate transition temperatures of the same order of magnitude as the measured ones.

Figure 1

(Color online) We assume that all shells of an entirely end-bonded MWNT are resistors in a parallel connection. For $T>T_c$ the current is due to the flow of electrons in the outermost shells with the typical behavior of a Luttinger liquid. For $T<T_c$ a superconducting transition is allowed in the innermost shell; thus the transport is due to Cooper pairs.