Page 389 - Fiber Fracture

ATOMIC TRANSFORMATIONS 37 1

ELECTRON TRANSPORT PROPERTIES OF STRAINED NANOTUBES

Graphite is a semi-metal and the electronic structure of carbon nanotubes can be
derived from that of graphene, a single sheet of graphite. It turns out that single-walled
carbon nanotubes can be either metallic or semiconducting, depending on their helicity.
In particular, nanotubes with indices (n,m) are predicted to be metallic if n - m = 3q
with q = integer (we do not discuss the many-body effects that may lead to insulating
behavior at temperatures near 0 K). While armchair NTs are always metallic, diameter
plays an important role in modifying the electronic properties of chiral and zigzag NTs.
In particular, in small-diameter NTs, the hybridization of s and p orbitals of carbon can
give rise to splitting of the 7c and E* bands responsible for metallic behavior (Blase et
al., 1994). For example, (3q,O) zigzag nanotubes of diameters up to 1.5 nm are always
small-gap semiconductors.
The unique electronic and conducting properties nanotubes have attracted the atten-
tion of a number of experimental and theoretical groups (Song et a]., 1994; Langer et
ai., 1994, 1996; Tian and Datta, 1994; Chico et al., 1996; Collins et al., 1996; Saito et
al., 1996; Tamura and Tsukada, 1997, 1998; Tans et al., 1997; Anantran and Govindan,
1998; Bezryadin et al., 1998; Bachtold et al., 1999; Buongiorno Nardelli, 1999; Buon-
giorno Nardelli and Bernholc, 1999; Choi and Ihm, 1999; Farajian et al., 1999; Paulson
et al., 1999; Rochefort et al., 1999). Below, we discuss the quantum conductance
properties of nanotubes under strain or in the presence of strain-generated defects.
We begin with the analysis of the electrical behavior of bent nanotubes. It has
recently been observed (Bezryadin et al., 1998) that in individual carbon nanotubes
deposited on a series of electrodes three classes of behavior can be distinguished: (1)
non-conducting at room temperature and below, (2) conducting at all temperatures, and
(3) partially conducting. The last class represents NTs that are conducting at a high
temperature but at a low temperature behave as a chain of quantum wires connected in
series. It has been argued that the local barriers in the wire arise from bending of the
tube near the edge of the electrodes.
In Fig. 12 we show the conductance of a (53 armchair nanotube (d = 0.7 nm) that
has been symmetrically bent at angles 0 = 6", 18", 24", 36". 8 measures the inclination
of the two ends of the tubes with respect to the unbent axis. No topological defects are
present in the tubes. For 0 larger than 18" the formation of a kink is observed, which
is a typical signature of large-angle bending in carbon nanotubes (Iijima et al., 1996).
Although armchair tubes are always metallic because of their particular band structure,
the kink is expected to break the degeneracy of the n and 7c* orbitals, thus opening a
pseudo-gap in the conductance spectrum (Ihm and Louie, 1999). However, if the bend-
ing is symmetric with respect to the center of the tube, the presence of the kink does
not alter drastically the conductance of the system (Rochefort et al., 1999), since the
accidental mirror symmetry imposed on the system allows the bands to cross. When this
accidental symmetry is lifted, a small pseudo-gap (-6 meV) occurs for large bending
angles (8 ?24"), see the inset of Fig. 12. The same calculations have been repeated
for a (10,lO) tube (d = 1.4 nm), and no pseudo-gap in the conductance spectrum was
observed in calculations with energy resolution of 35 meV, even upon large-angle asym-
metric bending. Our calculations thus indicate that even moderate-diameter armchair