# Magnetic field effects and renormalization of the long-range Coulomb interaction in 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, 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.

- Authors:

- INFN, Laboratori Nazionali di Frascati, P.O. Box 13, 00044 Frascati (Italy). E-mail: Stefano.Bellucci@lnf.infn.it
- INFN, Laboratori Nazionali di Frascati, P.O. Box 13, 00044 Frascati (Italy)
- (Italy)

- Publication Date:

- OSTI Identifier:
- 20767004

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics (New York); Journal Volume: 321; Journal Issue: 4; Other Information: DOI: 10.1016/j.aop.2005.08.010; PII: S0003-4916(05)00190-9; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CARBON; CHARGED-PARTICLE TRANSPORT; CHIRALITY; ELECTRONS; INTERACTIONS; MAGNETIC FIELDS; NANOTUBES; ONE-DIMENSIONAL CALCULATIONS; RENORMALIZATION; SINGULARITY; TUNNEL EFFECT

### Citation Formats

```
Bellucci, S., Onorato, P., and Dipartimento di Scienze Fisiche, Universita di Roma Tre, Via della Vasca Navale 84, 00146 Rome.
```*Magnetic field effects and renormalization of the long-range Coulomb interaction in carbon nanotubes*. United States: N. p., 2006.
Web. doi:10.1016/j.aop.2005.08.010.

```
Bellucci, S., Onorato, P., & Dipartimento di Scienze Fisiche, Universita di Roma Tre, Via della Vasca Navale 84, 00146 Rome.
```*Magnetic field effects and renormalization of the long-range Coulomb interaction in carbon nanotubes*. United States. doi:10.1016/j.aop.2005.08.010.

```
Bellucci, S., Onorato, P., and Dipartimento di Scienze Fisiche, Universita di Roma Tre, Via della Vasca Navale 84, 00146 Rome. Sat .
"Magnetic field effects and renormalization of the long-range Coulomb interaction in carbon nanotubes". United States.
doi:10.1016/j.aop.2005.08.010.
```

```
@article{osti_20767004,
```

title = {Magnetic field effects and renormalization of the long-range Coulomb interaction in carbon nanotubes},

author = {Bellucci, S. and Onorato, P. and Dipartimento di Scienze Fisiche, Universita di Roma Tre, Via della Vasca Navale 84, 00146 Rome},

abstractNote = {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, 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.},

doi = {10.1016/j.aop.2005.08.010},

journal = {Annals of Physics (New York)},

number = 4,

volume = 321,

place = {United States},

year = {Sat Apr 15 00:00:00 EDT 2006},

month = {Sat Apr 15 00:00:00 EDT 2006}

}