Families of carbon nanotubes: Graphyne-based nanotubes
V. R. Coluci,
1,2,
* S. F. Braga,
1
S. B. Legoas,
1
D. S. Galva
˜
o,
1
and R. H. Baughman
2
1
Instituto de Fı ´sica ‘‘Gleb Wataghin,’’Universidade Estadual de Campinas, C.P. 6165, 13083-970 Campinas SP, Brazil
2
NanoTech Institute and Department of Chemistry, University of Texas, Richardson, Texas830688, USA
Received 28 February 2003; published 30 July 2003
New families of carbon single-walled nanotubes are proposed and their electronic structures are investigated.
These nanotubes, called graphynes, result from the elongation of covalent interconnections of graphite-based
nanotubes by the introduction of yne groups. Analogously to ordinary nanotubes, armchair, zigzag, and chiral
graphyne nanotubes are possible. We here predict the electronic properties of these unusual nanotubes using
tight-binding and ab initio density functional methods. Of the three graphyne nanotube families analyzed here,
two provide metallic behavior for armchair tubes and either metallic or semiconducting behavior for zigzag
nanotubes. A diameter- and chirality-independent band gap is predicted for the other investigated graphyne
family, as well as an oscillatory dependence of the effective mass on nanotube diameter.
DOI: 10.1103/PhysRevB.68.035430 PACS numbers: 81.05.Uw, 73.22.-f, 73.63.Fg, 85.35.-p
I. INTRODUCTION
The early report of graphite-based carbon nanotubes
CNT’s by Iijima
1
generated an enormous amount of re-
search activity. New and exciting phenomena have been
observed,
2
including field emission,
3
quantum conductance,
4
superconductivity,
5
higher thermal conductivity than
diamond,
6
and constant-force nanosprings
7
as well as pro-
posals of CNT-based nanodevices.
8,9
Depending upon struc-
ture, the nanotubes are either metallic or semiconducting,
which is a feature that has been intensively investigated and
exploited in prototype devices.
2
Alternative structures containing heteroatoms N, B, etc.
in the nanotubes, as well as various carbon-free nanofibers,
have been recently synthesized.
2
While previous work has
focused on graphitic nanotubes, we believe that other types
of pure carbon nanotubes are feasible using different acces-
sible hybridization states of carbon. One possibility that has
been overlooked in the literature is to use graphyne sheets as
the structural motif for carbon nanotubes. Graphyne is an
allotropic form of carbon proposed by Baughman, Eckhardt,
and Kertesz
10
in 1987, which has recently become the focus
of new investigations.
11–13
Graphyne is the name for the
lowest-energy member of a family of carbon phases consist-
ing of planar molecular sheets containing only sp and sp
2
carbon atoms. The presence of acetylenic groups in these
structures introduces a rich variety of optical and electronic
properties that are quite different from those of ordinary car-
bon nanotubes.
As there are many different types of graphynes,
10
various
new families of pure carbon nanotubes can be generated that
have different electronic and structural characteristics. Just as
a sheet of graphite graphene can be rolled to form different
types of CNT’s, armchair, zigzag, or chiral, various
graphyne-based nanotubes GNT’s are similarly possible
Fig. 1. In addition, the usual ( n , m ) nomenclature used to
describe CNT’s can be preserved.
In this paper, we report electronic properties for three
families of graphynes as both infinite planar sheets and
nanotubes using tight-binding TB and ab initio density
functional methods. While one of these nanotube families
behaves like CNT’s, unusual characteristics are predicted for
the others. Among these characteristics are a fractional rule
for metallic zigzag nanotubes and a band gap independent
from diameter and chirality values.
II. METHODOLOGY
A single-walled CNT can be considered heuristically as
formed by rolling a graphene sheet to make a seamless
cylinder.
2,14
In the same way we can imagine GNT’s as
formed by rolling graphyne sheets to form quite different
seamless cylinders. Figure 1 represents this process for
graphene Fig. 1a and for two types of graphyne sheets
Figs. 1b and 1c. Figure 2 shows three-dimensional
FIG. 1. The structural relationships between carbon sheets and
single-wall carbon nanotubes for sheets of a graphene a graphite
sheet, b -graphyne, and c -graphyne. Depending upon the
axis used for rolling the carbon sheet to make a seamless cylinder,
the nanotube is armchair a and b, right, zigzag c, right, or
chiral.
PHYSICAL REVIEW B 68, 035430 2003
0163-1829/2003/683/0354306/$20.00 ©2003 The American Physical Society 68 035430-1