ISSN 1063-7761, Journal of Experimental and Theoretical Physics, 2007, Vol. 105, No. 1, pp. 210–213. © Pleiades Publishing, Inc., 2007.
Original Russian Text © V.A. Margulis, M.A. Pyataev, 2007, published in Zhurnal Éksperimental’no
œ
i Teoretichesko
œ
Fiziki, 2007, Vol. 132, No. 1, pp. 237–240.
210
Owing to its unique physical properties, carbon nan-
otubes are considered as one of promising materials for
the electronics of the future. It is obvious that the design
of integrated circuits on the basis of carbon nanotubes
suggests the use of a large number of contacts between
these tubes. Recent progress in technology has made it
possible to investigate experimentally the electron
transport through such contacts [1, 2]. Several theoreti-
cal models have been proposed [3–5] for studying the
physical properties of joint nanotubes. In particular, in
[5], the authors applied the tight-binding model to con-
sider the electron transport in a system consisting of
two single-wall nanotubes forming a cross-shaped
nanostructure.
However, it should be noted that the approach based
on the tight-binding method suggests performing long
and tedious computations, which do not always allow
one to Fnd out the physics behind the phenomenon
under investigation. Moreover, such an approach is
effective only for nanotubes of relatively small diame-
ters, whereas in [1] the authors experimentally investi-
gated nanotubes of diameters 25–30 nm. Therefore,
there is a need for a sufFciently simple model for study-
ing a contact between nanotubes, that would admit an
explicit analytic solution.
The aim of the present study is to investigate the
conductance of two crossed semiconducting carbon
nanotubes that have a point contact. The schematic of
the structure under investigation is shown in the inset of
±ig. 1. Each nanotube is modeled by a conducting cyl-
inder of radius
r
j
(
j
= 1, 2). The electron Hamiltonian
H
of the system represents a direct sum of the Hamilto-
nians of its parts,
HH
1
H
2
,
⊕
=
perturbed by the zero-radius potentials at the point of
contact. ±or each cylinder, it is convenient to introduce
its own cylindrical system of coordinates. Then, the
electron Hamiltonian in the
j
th nanotube can be
expressed as
(1)
where
m
* is the electron effective mass and
p
z
and
L
z
are the operators of the projections of the momentum
and the angular momentum onto the axis of a nanotube.