Effective low-energy theory of superconductivity in carbon nanotube ropes

TL;DR

This paper develops a low-energy theoretical framework for superconductivity in carbon nanotube ropes, incorporating interactions and quantum fluctuations, and compares predictions with experimental data showing good agreement.

Contribution

It introduces a systematic low-energy theory including quantum fluctuations and phase slips for superconductivity in nanotube ropes, aligning well with experimental observations.

Findings

Quantum phase slips depress the critical temperature below mean-field predictions.

Temperature-dependent resistance appears below the critical temperature.

Theoretical results match experimental data with minimal fitting parameters.

Abstract

We derive and analyze the low-energy theory of superconductivity in carbon nanotube ropes. A rope is modelled as an array of metallic nanotubes, taking into account phonon-mediated as well as Coulomb interactions, and arbitrary Cooper pair hopping amplitudes (Josephson couplings) between different tubes. We use a systematic cumulant expansion to construct the Ginzburg-Landau action including quantum fluctuations. The regime of validity is carefully established, and the effect of phase slips is assessed. Quantum phase slips are shown to cause a depression of the critical temperature $T_c$ below the mean-field value, and a temperature-dependent resistance below $T_c$. We compare our theoretical results to recent experimental data of Kasumov {\sl et al.} [Phys. Rev. B {\bf 68}, 214521 (2003)] for the sub-$T_c$ resistance, and find good agreement with only one free fit parameter. Ropes of nanotubes therefore represent superconductors in the one-dimensional few-channel limit.