skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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:
 [1];  [2];  [3]
  1. INFN, Laboratori Nazionali di Frascati, P.O. Box 13, 00044 Frascati (Italy). E-mail: Stefano.Bellucci@lnf.infn.it
  2. INFN, Laboratori Nazionali di Frascati, P.O. Box 13, 00044 Frascati (Italy)
  3. (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}
}
  • The instantaneous Coulomb interaction is studied in the SU(2) Yang-Mills theory. The Coulomb Green's function and instantaneous Coulomb potential of a static quark-antiquark pair are evaluated for a background gauge field A/sup i//sub a/( x ) that is spherically symmetric and of long range, i.e., that is of order vertical-bar x vertical-bar/sup -1/ as vertical-bar x vertical-bar ..-->.. infinity. The field A/sup i//sub a/( x ) is of the same form as the Wu-Yang magnetic-monopole field. Expansion of the Coulomb Green's function in vector spherical harmonic functions reduces the problem to a radial problem. It is shown that the backgroundmore » field changes the asymptotic form of the instantaneous Coulomb interaction; specifically for the monopole field the correction term is of the same magnitude as the ordinary Coulomb interaction at large distances. In addition, the instanton contribution to the qq-bar potential energy is calculated in the temporal-gauge formulation of the theory, and compared to the instantaneous Coulomb interaction. This calculation illustrates the interpretation of instantons as tunneling field configurations. The possibility that long-range field fluctuations with the magnetic-monopole form occur in an ionized meron phase of quantum chromodynamics is discussed.« less
  • We study the effect of a weak long-range Coulomb interaction on the interband absorption in a strongly correlated half-filled-band Hubbard chain such as low-dimensional charge-transfer organic salts by introducing a small nearest-neighbor Coulomb repulsion (U/sub 1/) to the Hubbard model. A long-range interaction gives rise to an attractive potential well between the doubly occupied site and the hole and distorts the interband absorption line shape for transitions to the upper Hubbard band. Also, it leads to formation of, and additional transitions to, a bound excitonic state. With an increasing value of U/sub 1/, the intensity leaks gradually from the formermore » transitions to the latter, while the total intensity is conserved.« less
  • Regularization and renormalization is discussed in the context of low energy effective field theory treatments of two or more heavy particles (such as nucleons). It is desirable to regulate the contact interactions from the outset by treating them as having a finite range. The low energy physical observables should be insensitive to this range provided that the range is of a similar or greater scale than that of the interaction. Alternative schemes, such as dimensional regularization, lead to paradoxical conclusions such as the impossibility of repulsive interactions for truly low energy effective theories where all of the exchange particles aremore » integrated out. This difficulty arises because a nonrelativistic field theory with repulsive contact interactions is trivial in the sense that the S matrix is unity and the renormalized coupling constant zero. Possible consequences of low energy attraction are also discussed. It is argued that in the case of large or small scattering lengths, the region of validity of effective field theory expansion is much larger if the contact interactions are given a finite range from the beginning. {copyright} {ital 1997} {ital The American Physical Society}« less
  • Carbon nanotubes (CNTs) are widely explored for biomedical applications, but there is very limited information regarding their in vivo biodistribution and biocompatibility. Here, we report the in vivo biodistribution and long-term effects of functionalized multi-walled carbon nanotubes (MWCNTs) in developing zebrafish. The fluorescent-labeled MWCNTs were introduced into zebrafish embryos at 1-cell stage and at 72 h post fertilization through microinjection. After single injection, both acute and long-term interactions between zebrafish and functionalized MWCNTs were studied. The injected FITC-BSA-MWCNTs (at 1-cell stage) were allocated to all blastoderm cells of the embryos through proliferation, and were distinctively excluded from the yolk cell.more » When introduced into the circulation system, FITC-BSA-MWCNTs moved easily in the compartments and finally were cleaned out by the body at 96 h after the loading. At early stages, the treated zebrafish embryos generated immune response by accumulating circulating white blood cells at the trunk region. Under transmission electron microscope, many lysosome-like vesicles were observed in the blastoderm cells of the treated embryos. The zebrafish loaded with MWCNTs had normal primordial germ cells at early stage and produced second generation later on. However, the larvae of the second generation had obviously lower survival rates as compared to the untreated groups, suggesting a negative effect on the reproduction potential. These results suggest that extensive purification and functionalization processes can help improve the biocompatibility of CNTs. This study also indicates that purified CNTs may have long-term toxicity effects when they were delivered into the body.« less
  • A double-fluid theory is used to find the electromagnetic wave absorption of carbon monoxide with iron-catalyzed high-pressure disproportionation (HiPco)-grown single-walled carbon nanotubes (SWNTs). The electromagnetic wave absorption of carbon monoxide with HiPco SWNTs is obtained and is studied numerically. The absorption is then deduced and their functional dependence on the number density, collision frequency, cyclotron frequency, and angle of propagation is studied. The double-fluid theory predicts that there is an electromagnetic frequency dependency on the energy absorption properties of the system under investigation. The calculation results show that effects of magnetic field strength and the angle of microwave propagation onmore » the absorption coefficient as well as the frequency band of resonant absorption are very significant.« less