Magnetic field effects and renormalization of the long-range Coulomb interaction in Carbon Nanotubes

TL;DR

This paper develops theoretical methods to analyze how magnetic fields influence the Coulomb interactions in carbon nanotubes, revealing a transition from Luttinger liquid to chiral liquid states with observable effects on tunneling behavior.

Contribution

It introduces two approaches—Renormalization Group and dimensional regularization—for studying long-range Coulomb interactions in one-dimensional systems, applied specifically to carbon nanotubes under magnetic fields.

Findings

Magnetic field alters the critical exponent for tunneling density of states.

Dimensional regularization predicts the disappearance of Luttinger liquid behavior at high magnetic fields.

Results align with recent experimental observations on carbon nanotubes.

Abstract

We develop two theoretical approaches for dealing with the low-energy effects of the repulsive interaction in one-dimensional electron systems. Renormalization Group methods allow us to study the low-energy behavior of the unscreened interaction between currents of well-defined chirality in a strictly one-dimensional electron system. A dimensional regularization approach is useful, when dealing with the low-energy effects of the long-range Coulomb interaction. This method allows us to avoid the infrared singularities arising from the long-range Coulomb interaction at $D = 1$. We can also compare these approaches with the Luttinger model, in order to analyze the effects of the short range term in the interaction. Thanks to these methods, we are able to discuss the effects of a strong magnetic field $B$ in quasi one-dimensional electron systems, by focusing our attention on Carbon Nanotubes. Our results imply a variation with $B$ in the value of the critical exponent $\alpha$ for the tunneling density of states, which is in fair agreement with that observed in a recent transport experiment involving carbon nanotubes. The dimensional regularization allows us to predict the disappearance of the Luttinger liquid, when the magnetic field increases, with the formation of a chiral liquid with $\alpha=0$.