Molecular vibration sensor via transport measurements in carbon nanotubes
C. Ritter,
1
R. B. Muniz,
1
S. S. Makler,
1,2
and A. Latgé
1
1
Instituto de Física, Universidade Federal Fluminense, s/n, 24210-360 Niterói, RJ, Brazil
2
Departamento de Física, Universidade Federal de Juiz de Fora, 36035-330 Juiz de Fora, MG, Brazil
Received 15 June 2010; published 15 September 2010
When a molecule adsorbs to the surface of a carbon-based nanostructure the local binding potential and the
molecule mass determine the natural characteristic frequency with which it vibrates after being slightly per-
turbed from its equilibrium position. We perform phonon-assisted inelastic quantum transport calculations for
carbon nanotubes with a single molecule attached to its surface and show that the differential conductance
spectra may be used to identify the presence of the adsorbed molecule.
DOI: 10.1103/PhysRevB.82.113407 PACS numbers: 73.63.b, 72.10.Di, 72.80.r
The search for high-sensitive sensors capable of detecting
specific chemical and biological agents in real time and at
the lowest possible concentrations is presently a topical sub-
ject. The use of carbon-based nanostructures has been at-
tracting a great deal of interest for this purpose because their
properties may change considerably upon exposure to certain
agents. Various methods have been devised for developing
carbon-based molecule nanosensors.
1–5
However, the possi-
bilities of exploiting molecule vibrations for this aim has
been less investigated. Actually, the effects of intrinsic
electron-phonon e-ph interaction on the transport properties
of carbon nanotubes have been largely exploited.
6–9
In a re-
cent very interesting work, vibrational modes in a single
molecule were observed by measuring the differential con-
ductance as function of the applied bias voltage across the
molecular junction.
10
Here we propose a spectroscopic technique that may ef-
fectively detect the presence of a particular molecule down
to very low concentrations by exploring molecular-
vibrational features. The physical principle of detection is
rather simple, resembling inelastic electron tunneling spec-
troscopy techniques,
11
and is described as follows. Suppose
we wish to detect the presence of a specific molecule that
gets attached to the surface of a carbon-based nanostructure.
There is a characteristic angular frequency
0
with which the
attached molecule vibrates in the vicinity of its stable equi-
librium position that is determined by the local potential de-
scribing the connection between the molecule and the nano-
structure surface. The energies of the local mode are
quantized in multiples of
0
. We shall consider, as an ex-
ample, a sensor made of a single-wall carbon nanotube
CNT where electrical contacts are made to allow measure-
ments of the current-voltage I-V characteristic of the de-
vice. If one sweeps the applied voltage V through
0
/ e,
where e is the magnitude of the electron charge, when eV
reaches
0
a new channel opens up, by means of the
electron-phonon interaction, because the electron may inelas-
tically emit or absorb a vibrational quantum in the process.
As a consequence, the conductance varies when this occurs,
and one shall find very sharp features in the dI / dV and
d
2
I / dV
2
curves which distinctively identify the fingerprint of
the molecule presence.
It should be also possible to functionalize the carbon-
based surface to attract individual species of interest. In this
case, a considerable shift in
0
may be observed when the
desired molecule binds to the attractor, provided the mass of
the specific molecule we wish to detect is not relatively small
in comparison with the one employed in the functionaliza-
tion.
Our interest is in very low concentrations of molecules, a
regime where they may be approximately treated as nonin-
teracting. Therefore, we shall consider a single molecule
coupled to an infinite carbon nanotube. It is convenient to
label a CNT site by a pair of indices i , which specify the
CNT ring i to which it belongs and the position within this
ring where it is located. We assume that the single molecule
is attached to the CNT site labeled by 0,0. The electronic
structure is described by a single -band tight-binding
model, taking into account the electron interaction with a
local-vibrational mode. The Hamiltonian operator is written
as
H
ˆ
=
i
i
c
i
†
c
i
+
ij
t
ij
c
i
†
c
j
+
0
b
†
b + fc
00
†
c
00
b
†
+ b ,
1
where, c
i
†
and c
i
represent the electronic creation and anni-
hilation operators at the site i , , respectively;
i
describes
the on-site potential energy profile, including external poten-
tials, t
ij
denotes the electronic hopping integral between
sites i , and j , ; b
†
and b are the local-phonon creation
and annihilation operators, and f measures the strength of the
e-ph interaction that takes place at 0,0.
Following the approach developed in Refs. 12–14, we
choose a suitable basis set in =
1
n!
c
i
†
b
†
n
0 to construct
a matrix representation of H
ˆ
given by
H
i, j
n,m
=
i
+ n
0
ij
nm
+ t
ij
nm
+ f
i0
j0
0
0
m +1
nm+1
+
m
m-1n
, 2
where n, m are the number of phonons. In this representa-
tion, the problem is exactly mapped into a single-particle
one, though in a higher dimension which is specified by the
number of phonons considered, as schematically illustrated
in Fig. 1. At zero temperature, electrons enter the scattering
region via the zero-phonon channel only, and have a finite
probability of being transmitted to any of the outgoing leads.
In this case just phonon-emission processes are allowed. At
finite temperatures, however, a number n of phonons may be
PHYSICAL REVIEW B 82, 113407 2010
1098-0121/2010/8211/1134074 ©2010 The American Physical Society 113407-1