Electronic and transport properties of nanotubes
Jean-Christophe Charlier
*
Unité de Physico-Chimie et de Physique des Matériaux (PCPM), Université Catholique de
Louvain, 1 Place Croix du Sud, B-1348 Louvain-la-Neuve, Belgium
Xavier Blase
†
Université de Louvain, F-69000, France, Laboratoire de Physique de la Matière
Condensée et Nanostructures, Université Lyon I, CNRS, UMR 5586, Domaine scientifique
de la Doua, F-69622 Villeurbanne Cedex, France
Stephan Roche
‡
Commissariat à l’Energie Atomique, DSM/DRFMC/SPSMS/GT, 17 rue des Martyrs, 38054
Grenoble Cedex 9, France

Published 16 May 2007
This article reviews the electronic and transport properties of carbon nanotubes. The focus is mainly
theoretical, but when appropriate the relation with experimental results is mentioned. While simple
band-folding arguments will be invoked to rationalize how the metallic or semiconducting character of
nanotubes is inferred from their topological structure, more sophisticated tight-binding and ab initio
treatments will be introduced to discuss more subtle physical effects, such as those induced by
curvature, tube-tube interactions, or topological defects. The same approach will be followed for
transport properties. The fundamental aspects of conduction regimes and transport length scales will
be presented using simple models of disorder, with the derivation of a few analytic results concerning
specific situations of short- and long-range static perturbations. Further, the latest developments in
semiempirical or ab initio simulations aimed at exploring the effect of realistic static scatterers

chemical impurities, adsorbed molecules, etc. or inelastic electron-phonon interactions will be
emphasized. Finally, specific issues, going beyond the noninteracting electron model, will be
addressed, including excitonic effects in optical experiments, the Coulomb-blockade regime, and the
Luttinger liquid, charge density waves, or superconducting transition.
DOI: 10.1103/RevModPhys.79.677 PACS number
s: 73.63.Fg, 73.22.
f, 78.67.Ch, 61.46.Fg
CONTENTS
I. Introduction 678
II. Structure of Carbon Nanotubes 679
III. Electronic Properties of Carbon Nanotubes 681
A. From graphite to nanotubes 682
B. Tight-binding model of graphene 683
C. Zone-folding approximation 684
1. Metallic nanotubes 684
2. Semiconducting nanotubes 684
D. Band structures and densities of states 686
E. Band structures in a magnetic field 688
1. Aharonov-Bohm quantum phase 688
2. Parallel field: The band-gap opening and
orbital degeneracy splitting 689
3. Perpendicular field: The onset of Landau
levels 691
F. Curvature effects: Beyond the zone-folding model 692
G. Nanotube bundle and multiwall system 694
H. Structural defects in carbon nanotubes 695
1. Finite length and capping topologies 695
2. Connecting nanotubes 696
3. Vacancies, adatoms, Stone-Wales, etc. 697
I. Optical properties and excitonic effects 698
IV. Transport Properties of Carbon Nanotubes 700
A. Preliminary remarks 700
B. The clean limit 702
1. Ballistic motion and conductance
quantization 702
2. Transport properties of CNT-based
junctions and contact resistance 702
C. Effect of disorder on transport 704
1. Electronic eigenstates and pseudospin
symmetry 704
2. Long-range disorder and the absence of
backscattering 705
3. Short-range disorder and elastic mean free
path: Model analysis 706
4. Influence of doping on transport properties 707
5. Multishell conduction 709
a. Commensurate multiwalled nanotubes 709
b. Incommensurate multiwalled nanotubes 710
c. Crossed carbon nanotubes junctions,
bending and twisting deformations 711
D. Quantum interference effects 711
1. Weak localization and the Aharonov-Bohm
*
Electronic address: charlier@pcpm.ucl.ac.be
†
Electronic address: xblase@lpmcn.univ-lyon1.fr
‡
Electronic address: stephan.roche@cea.fr
REVIEWS OF MODERN PHYSICS, VOLUME 79, APRIL–JUNE 2007
0034-6861/2007/79
2/677
56 2007 The American Physical Society677

effect 711
a. Application to metallic
armchair carbon
nanotubes 712
2. From weak to strong localization 714
E. Inelastic scattering 714
1. Electron-phonon coupling 714
2. Inelastic transport length scales 716
3. Electron-electron scattering and
Luttinger-liquid models 717
4. Transport spectroscopy in the Coulomb
blockade regime 721
F. Superconducting and charge-density-wave
instabilities 722
G. Field emission from nanotubes 724
V. Conclusion 726
Acknowledgments 726
References 726
I. INTRODUCTION
The physics of one-dimensional
1D systems has been
a rich and active playground for theorists for more than
50 years, with major conceptual breakthroughs arising
from the specific properties of the confined electron gas.
While the reduced dimensionality is often used in intro-
ductory textbooks as a convenient way to simplify the
analytic study of electronic properties, the enhanced in-
teraction between electrons in 1D yields several insta-
bilities that are not reproduced by standard tools devel-
oped for 3D solids. This richness and complexity
involved in extending the basics of condensed matter
physics to low-dimensionality systems explain the wealth
of work and theories developed to deal with 1D solids or
molecular chains.
The difficulty in synthesizing clean 1D systems with
metallic behavior has for many decades confined this
theoretical work to formal developments and unverified
predictions. However, progress in synthesis and charac-
terization techniques in the late 1970s allowed a con-
frontation between theory and experiments. Besides
these fundamental aspects, the technological interest in
controlling the properties of nanosized and/or plastic
conductors was a strong driver for exploring this field.
The attribution of the chemistry Nobel prize in 2000 to
A. J. Heeger, A. G. MacDiarmid, and H. Shirakawa for
the “discovery and development of conductive poly-
mers” was a clear recognition from the community of
the importance, and the difficulty, of obtaining conju-
gated one-dimensional metallic systems. Further, even
when metallic, the conductivity in such systems has been
shown to usually remain very low, with in most cases
polaron-assisted transport leading to very large effective
masses for the carriers. As a paradigmatic example, the
conducting
and even superconducting properties of
DNA, at the frontiers of physics, chemistry, and biology,
are currently generating fierce controversies in the lit-
erature.
The field of nanotubes has strongly benefited from
this broad fundamental and technological interest. Not
only can nanotubes be metallic, they are also mechani-
cally very stable and strong, and their carrier mobility is
equivalent to that of good metals, suggesting that they
would make ideal interconnects in nanosized devices.
Further, the intrinsic semiconducting character of other
tubes, as controlled by their topology, allows us to build
logic devices at the nanometer scale, as already demon-
strated in many laboratories. Finally, the large fullerene
community
yet another area recognized by the Nobel
prize in chemistry in 1996, and the even larger family of
researchers interested in carbon-based systems, natu-
rally joined this novel and promising field. This merging
of interests and communities can certainly explain the
formidable success and burgeoning activity generated by
the discovery of nanotubes in 1991.
A nanotube is a honeycomb lattice rolled into a hol-
low cylinder with nanometric diameter and m length.
Depending on the community, specific interests, and tar-
geted applications, nanotubes are regarded as either
single molecules or quasi-one-dimensional crystals with
translational periodicity along the tube axis. As there
are an infinite number of ways of rolling a sheet into a
cylinder, the large variety of possible helical geometries,
defining the tube chirality, provides a family of nano-
tubes with different diameters and microscopic struc-
tures. Some properties of these nanotubes, such as the
elastic ones, can be explained within a macroscopic
model of a homogeneous cylinder. Others depend cru-
cially on the atomic configuration. For instance, the elec-
tronic and transport properties, which constitute the
scope of the present review, are certainly among the
most significant physical properties of carbon nanotubes,
and crucially depend on the diameter and chirality. This
dependence on the atomic configuration, an effect ex-
plained below, is quite unique in solid-state physics. This
sensitivity constitutes a challenge for synthesis tech-
niques, since well-controlled properties are often de-
sired, but it is also a source of innovation for applica-
tions.
In the following sections, we show how carbon nano-
tubes can be either
semimetallic or semiconducting,
with a band gap varying from zero to a few tenths of an
eV, depending on their diameter and chirality. Further,
the band gap of semiconducting tubes, or the energy
difference between the peaks in the electronic density of
states
the so-called van Hove singularities, can be
shown to first order to be simply related to the tube
diameter. Such remarkable results can be obtained from
a variety of considerations, starting from the so-called
band-folding approach, based on knowledge of the elec-
tronic properties of the graphene sheet, to the direct
study of nanotubes using semiempirical tight-binding ap-
proaches. The comparison with more sophisticated ab
initio calculations, and with available experimental re-
sults, allows us to set the limits of these simple treat-
ments, with the introduction of finer considerations,
such as curvature or trigonal warping effects.
Knowledge of the electronic properties of nanotubes
further permits one to study their response to external
probes. This is a crucial issue as it conditions most of the
potentiality for the integration of tubes in real devices
678
Charlier, Blase, and Roche: Electronic and transport properties of nanotubes
Rev. Mod. Phys., Vol. 79, No. 2, April–June 2007