Large N Effects and Renormalization of the Long-Range Coulomb Interaction in Carbon Nanotubes

Abstract

We develop a dimensional regularization approach to deal with the low-energy effects of the long-range Coulomb interaction in 1D electron systems. The method allows us to avoid the infrared singularities arising from the long-range Coulomb interaction at D = 1, providing at the same time insight about the fixed-points of the theory. We show that the effect of increasing the number N of subbands at the Fermi level is opposite to that of approaching the bare Coulomb interaction in the limit D --> 1. Then, we devise a double scaling limit, in which the large N effects are able to tame the singularities due to the long-range interaction. Thus, regular expressions can be obtained for all observables right at D = 1, bearing also a dependence o the doping level of the system. Our results imply a variation with N in the value of the exponent for the tunneling density of states, which is in fair agreement with that observed in different transport experiments involving carbon nanotubes. As the doping level is increased in nanotubes of large radius and multi-walled nanotubes, we predict a significant reduction of order N^{-1/2} in the critical exponent of the tunneling density of states.

arXiv comment16 pages, 5 figures, PACS codes: 73.40, 11.10.G

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• Suppression of electron-electron repulsion and superconductivity in Ultra Small Carbon Nanotubes
• Crossover from Luttinger liquid to Coulomb blockade regime in carbon nanotubes
• Single Wall Nanotubes: Atomic Like Behaviour and Microscopic Approach
• Electronic screening and correlated superconductivity in carbon nanotubes
• Transport through a double barrier for interacting quasi one-dimensional electrons in a Quantum Wire in the presence of a transverse magnetic field
• Magnetic field effects and renormalization of the long-range Coulomb interaction in Carbon Nanotubes
• Modulation of Luttinger liquid exponents in multi-walled carbon nanotubes
• Influence of dimensionality on superconductivity in carbon nanotubes