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FEATURE ARTICLE
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Understanding structures and electronic/spintronic properties of single
molecules, nanowires, nanotubes, and nanoribbons towards the design of
nanodevices
Woo Youn Kim, Young Cheol Choi and Kwang S. Kim*
Received 13th March 2008, Accepted 21st May 2008
First published as an Advance Article on the web 3rd July 2008
DOI: 10.1039/b804359k
Theoretical understanding of metal nanowires and molecular devices is described towards the design of
novel nanodevices. We focus our attention on structures, electronic, and spintronic properties of low
dimensional metallic/molecular nanostructures based mostly on our recent works. The discussion
includes (i) electric field induced molecular orbital control towards molecular electronic and spintronic
devices, (ii) conductances of carbon nanotubes and graphene nanoribbons, (iii) low dimensional
structures and properties, focusing on the stability, quantum conductance, and magnetic features of
metallic nanowires, and (iv) metal vs. carbon nanotube/graphene electrodes for negative differential
resistance in molecular electronics.
1. Introduction
Nanotechnology has settled as a prospective means to develop
novel nanodevices replacing conventional devices. It is now
possible to manipulate individual single atoms or molecules
which are building elements or blocks for fabrication of nanodevices in the bottom-up approach.1 The emergence of molecular
devices2–8 as well as intriguing molecules/materials such as
fullerenes,9 carbon nanotubes (CNTs),10 and graphenes11 has
further accelerated the research on the nanoscience field. Nonetheless, there are serious obstacles that we have to overcome in
order to utilize nanodevices for practical use. First of all, it
requires great effort to manipulate delicate nano-scale materials
in the fabrication processes. Furthermore, it is difficult to analyze
a fabricated nanodevice because of its small size. The functions of
Center for Superfunctional Materials, Department of Chemistry, Pohang
University of Science and Technology, San 31, Hyojadong, Namgu,
Pohang
790-784,
Korea.
E-mail:
[email protected];
Fax:
+82-54-279-8137; Tel: +82-54-279-2110
nanodevices are very sensitive to environmental perturbations.
Even an impurity of a single atom significantly influences the
electronic properties of a given nanodevice, so that the reproducibility has been seriously limited. The lack of understanding
of the underlying physics of the fabrication or operation process
hinders solving the complex problems of nanodevices.12
Since most nanodevices exhibit quantum phenomena, it is
necessary to understand them in an atomistic point of view.13
Theoretical studies of nanosystems have greatly progressed
because of the rapid growth of computing resources. Though it is
still difficult to handle large systems at the level of first principles
theory, accurate theoretical study on relatively small systems
ranging from an atomic scale to a few nanometres has been wellestablished. Since quantum features can hardly be understood by
intuition, quantum theoretical calculations help understand the
complex quantum phenomena of nanosystems14 as a powerful
complementary approach to experiments.
In this regard, we discuss here the theoretical understanding of
atomic/molecular clusters, atomic/molecular wires, and molecular electronic devices towards the design of novel devices. We
Woo Youn Kim is a PhD
candidate, working with K. S.
Kim at Pohang University of
Science and Technology. His
research interests include the
design of nanodevices such as
molecular
(spin-)electronic
devices and chemical sensors
using the non-equilibrium Green
function method.
Woo Youn Kim
4510 | J. Mater. Chem., 2008, 18, 4510–4521
Kwang S: Kim
Dr Kwang S. Kim received his
PhD degree from University of
California, Berkeley. He was
a postdoctoral fellow at IBM and
a visiting scientist at Rutgers
University, MIT, and Columbia
University. Currently, he is
a professor in the Department of
Chemistry and the director of the
Center for Superfunctional
Materials at Pohang University
of Science and Technology. His
research interests include investigations of nanomaterials and
molecular devices.
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begin with a brief discussion about theoretical backgrounds.
Then, we discuss (i) electric field induced molecular orbital
control towards molecular electronic/spintronic devices, (ii)
carbon nanotubes, graphene nanoribbons and their molecular
analogs, (iii) magic structures, electronic/spintronic properties,
and quantum conductance of metal nanowires, and (iv) metal vs.
CNT/graphene electrodes for molecular electronics. In particular, magic structures and fractional quantum conductance in
the thinning process of metal nanorods and the negative differential resistance in molecular electronics are discussed in detail.
2. Theoretical background
Electronic structures of molecules play a vital role in electronic,
magnetic, optical, and mechanical properties of nanodevices.15–17
Modern quantum chemistry approaches include various types of
theoretical methods to analyze such properties.18–20 On a molecular scale regime, the quantum phenomena are so dominant
that our discussion will focus on first principles methods which
fully take into account quantum effects. There are two fundamentally different schemes. One is based on the wavefunctions of
electrons, while the other, on the density of electrons. Wave
function theory (WFT) originates from Hartree–Fock (HF)
theory which uses mean field potential. Because the HF method
does not take into account electron correlations, various
methods have been developed to resolve the problem. The most
widely used theories are Møller–Plesset second-order perturbation (MP2), configurational interaction (CI), and coupled-cluster
theory with single, double, and perturbative triple excitations
[CCSD(T)]. In the case that the Gaussian-type basis sets are used,
the complete basis set limit values can be estimated by exploiting
the extrapolation scheme of the electron correlation energies.21,22
However, these state-of-the-art methods with large basis sets
require heavy computational resources and hence are not suitable
for calculations of large scale systems involving hundreds of
atoms. On the other hand, density functional theory (DFT) is
applicable to large systems because the fundamental variable,
electron density, depends only on three spatial degrees of freedom,
while variables in WFT are coordinates of all electrons for a given
system. Although in principle DFT pursues the exact description
of the Hamiltonian, in practical use, a single electron Hamiltonian, the so-called Kohn–Sham Hamiltonian, is also derived from
the mean field approximation like the HF method. Therefore, the
accuracy of the DFT calculations strongly depends on the
selection of the exchange–correlation functional which includes
all many-body effects of electron interactions. Local density
approximation (LDA) was developed as the first prototype of the
exchange–correlation functional. For a better description of the
electron–electron interaction, various types of generalized
gradient approximation (GGA) have been developed.23–25
Generally, both DFT and WFT give consistent results.
However, the DFT results depend on the given functionals, so it
is not clear whether the results are reliable unless they are well
tested for the given systems. In this regard, the CCSD(T) results
based on the complete basis set limit are often used as a guide to
test the reliability of the DFT results. Thus, it is important to
choose the most appropriate calculation method for the given
system. In contrast to MP2 or CCSD(T), DFT has serious
disadvantages in calculations of biomolecules or carbon-based
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systems involving p-stacking systems because it does not
properly take into account the dispersion energy. Recently, new
functionals to resolve such problems have been developed.
Excited states dynamics can be studied by using CI and complete
active space self-consistent theory (CASSCF),26 whereas DFT
can be applied mostly to the ground states. More recently, timedependent DFT (TDDFT) shows great potential for application
not only to the excited states spectrum but also to the excited
states dynamics.27 If the TDDFT method is further developed, it
would be widely used for studies of excited states because it can
deal with large systems.
To describe the transport phenomena of molecules, the
transmission probability or conductance needs to be calculated.
The non-equilibrium Green’s function (NEGF) method is the
most popular approach.28–31 While a few programs are available,29,30 we have developed a program package (POSTRANS32)
by implementing the NEGF method in DFT. Using this
software, we have studied the transport phenomena of spins as
well as charge carriers for both periodic and non-periodic
systems in the parallel computing mode.
3. Electronic devices
Twenty years after Aviram and Ratner2 suggested that a single
molecule could be used as an electronic device, such a device was
eventually fabricated in an elegant manner.3–8 A single molecular
device is contacted to the metallic electrodes with a molecular
scale junction and its transport properties are measured to
investigate its characteristics as an electronic device. Recently,
pure carbon-based materials such as carbon nanotubes and
graphenes have received considerable attention.33–39 Furthermore, molecular and metallic nanowires have shown broad
applicability as electronic devices. In this section, we discuss the
theoretical understanding of promising nanoelectronic devices
composed of single molecules, carbon-based materials, or
nanowires.
3.1 Electric field induced molecular orbital control towards
molecular electronic/spintronic devices
Various efforts have been devoted to finding appropriate
molecules for realizable electronic devices. Structures such as
molecular clusters can be changed in the presence of an electric
field.40 However, in monomeric molecules, the structures do not
change significantly unless a high electric field is applied. Phenyl
ring based molecules have been intensively studied as electronic
materials because of their good conductivity due to conjugated
p-orbitals and easy manipulation of the properties through
substitution of functional groups such as amide, nitride, etc.4,5,41–44
To understand how to utilize the p-orbitals of phenyl ring,
we investigated the electronic transport properties through
a benzene molecule.
In experiments, electric fields are often used as an important
means to control the transport properties externally. Thus, we
investigated the energy spectra and the conducting behavior
according to the change of molecular orbitals of the benzene in
the presence of an applied electric field.45 Fig. 1 shows the
direction of the applied electric field and the response of each
molecular energy level to the field. As the applied electric field
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Fig. 1 Change of the HOMO–LUMO energy gap and the frontier orbital energies of benzene as a function of the applied electric field (reproduced by
permission of American Institute of Physics [ref. 45]).
increases, the first and second lowest unoccupied molecular
orbital (LUMO) energies and the highest occupied molecular
orbital (HOMO) energies of the benzene do not change much,
while the third LUMO energy decreases. Therefore, the HOMO–
LUMO energy gap is reduced with increasing strength of the field.
There should be a threshold value of the applied field for the
crossing of the first and third LUMOs. Above the threshold field,
the third LUMO in the absence of field becomes the real LUMO.
This effect is closely related to the shape of the corresponding
Fig. 2 LUMOn of benzene depending on the applied electric fields
which are perpendicular (Et) and parallel (E||) (reproduced by permission of American Institute of Physics [ref. 45]).
4512 | J. Mater. Chem., 2008, 18, 4510–4521
orbitals. As shown in Fig. 2, each orbital has a different shape.
Some of them are diffusive, whereas others are localized. This
shape difference results in different polarizability which gives
a different response to an external electric field. The LUMO3
which is the most diffusive orbital, has the largest polarizability,
and hence its energy changes drastically as the applied field
increases, according to the second-order Stark effect:
Eel ¼ 1/2aEext
where Eel is the energy of the corresponding orbitals, a is the
anisotropic polarizability tensor, and Eext is the external electric
field. It is shown that the molecular orbitals and tuning parameters like the external field can play important roles in molecular devices. This concrete understanding in the atomistic point
of view is helpful for the design of electronic nanodevices.
Furthermore, we investigated the doping effects on the phenyl
ring in the presence of an external field. Many theoretical works
have shown that a doping or substitution to the phenyl ring
induces a substantial change of the electronic structure. One way
of doping is just to add a foreign atom to the benzene molecule.
Addition of two barium atoms on both sides of the phenyl ring
plane makes a conjugated system of high electron density for
which the electric field effect is intriguing.46 Indeed, it showed an
unexpected, novel phenomenon.47 As in the bare benzene molecule, each energy level responds differently under the external
field. However, in this case, the spin configuration changes as
shown in Fig. 3. The spin state of the ground state is a singlet in
the absence of external fields, while the energy of the triplet state
becomes lower than that of the singlet state above a certain
threshold electric field. This means that the spin state in a single
molecule can be controlled by means of external electric fields
which are easily realized in a laboratory. To utilize this property,
one may consider a single molecular magnetic switching device.
At the zero bias, the spin state is a singlet. However, under
a certain bias larger than the threshold field, the spin state
becomes a triplet, and hence the spin-dependent transmissions
would be controlled.
In this context, the benzene molecule doped with foreign
atoms can be used as a basic unit in molecular spin-based
electronics, so-called molecular spintronics which exploits the
spin states of electrons as well as their charge states. In fact, other
theoretical studies have shown that the assembly of several
phenyl rings with foreign atoms shown in Fig. 4 has an intriguing
electronic structure that can be used as a spin-valve device
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molecular spin of the fullerene.55 The entanglement between the
neighboring C60@A fullerenes could be utilized as a quantum
computing device with each C60@A as a qubit, according to
Kane’s suggestion.56 Exohedral fullerenes can also give unusual
magnetic properties, which could be utilized as a device.57
3.2 Conductances of carbon nanotubes and graphene
nanoribbons
Fig. 3 Stark effect on the relative energies of the singlet (,), triplet (B),
and quintet (6) electronic spin states in high electron density benzene. (a)
The electric field E|| is applied parallel to the benzene ring plane. (b) The
electric field Et is applied perpendicular to the benzene ring plane
(reproduced by permission of Wiley-VCH [ref. 47]).
Fig. 4 Assembly of high electron density phenyl rings (reproduced by
permission of Wiley-VCH [ref. 47]).
showing the highly spin-polarized transmission spectrum.48–50
Change of the spin configuration in the doped phenyl ring system
can also be found on CNTs which are regarded as a continuous
arrangement of phenyl rings with a given lattice periodicity.
CNTs become ferromagnetic conductors as they are doped by
transition metal wires inside cavities or on the surface of
CNTs.51–53 Especially, CNTs with vanadium or chromium
become half-metals which have a finite energy gap only for one
spin.52
Since molecular orbital energies can be manipulated by the
applied electric field, this promises that, using electric fields, one
may control spin states of a system as well as orbital energies in
a single molecular device.
Another option is to utilize doped molecular materials. A
simple example is the case with a spin in molecular systems such
as endohedral fullerenes C60@A, where A is N/P.54 In this case,
the spin in the N/P atom can be utilized as an isolated single
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Though germanium was the first material used in the fabrication
of a semiconducting device, silicon has led to a remarkable
success in semiconductor technology. Allotropes of carbon are
the undisputed uppermost material opening a new era of nanotechnology coming after silicon technology. Interestingly,
carbon, silicon, and germanium belong to the same group in the
periodic table. With the advance of technology, the main element
has moved from germanium to carbon. Thus, the emergence of
novel allotropes of carbon such as CNTs and graphenes may not
be due to accidental discoveries, but rather due to the natural
evolution of technology. The carbon-based materials have
received great attention as the next generation of electronic
devices because mechanically, they are very flexible and stable,
and electronically, they show the ballistic conductance, high
carrier mobility, and long spin-relaxation time.33,38,39 Here we
discuss theoretical approach towards the design of electronic
devices using CNTs and graphenes.
CNTs and graphenes are now well-studied materials for
electronic devices. While a CNT is 1-dimensional (1D), the
shortest CNTs are sort of organic beltenes.58 A short CNT shows
antiferromagnetic properties.59 A long CNT can be curved to
make a torus. Carbon tori also show interesting electronic
properties, which could be utilized as quantum solenoids.60 Ultralong CNTs show interesting electronic properties.34,35 While
a graphene sheet is 2-dimensional (2D), a graphene nanoribbon is
between 1D and 2D, showing antiferromagnetic ordering
between both edges.32,61 Here, we focus our attention on very long
CNTs and graphene nanoribbons.
3.2.1 Carbon nanotubes. In experiments, CNTs have been
used as a field effect transistors,62 resonators,63 biochemical
sensors,64 spin-valves,65,66 and so on. CNTs show ballistic
conductance. As doped with foreign atoms, the ballistic
conductance disappears, and the conductance changes drastically
depending on the doping atoms.32,67 Fig. 5 shows the conductance
and density of states (DOSs) of the armchair CNT(5,5) with N or
B dopants. For the pristine CNT(5,5), it shows quantized
conductance. However, with dopants, the conductance shows
fractional values especially around the localized states due to the
dopants. Boron plays a role as a dopant of a hole carrier so that
the localized state has a little negative value of EEF, while
nitrogen behaves in the opposite way. Therefore, the DOS around
EEF ¼ 1 eV of CNT(5,5) with the B dopant is larger than that
of the pristine one, but the conductance at the same E is smaller
than that of the pristine one. To utilize this intriguing property, an
external gate probe may be needed. If an external field is applied,
the energy of the localized states shifts according to the field
strength and direction. Then, the energy value for the fractional
conductance due to the localized states also shifts. This
phenomenon could be used as an electrically controllable
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dimensionality itself changes the electronic structure of systems
drastically. Graphene is a sole, natural, perfect two-dimensional
system and hence it shows its unique properties originated from
the dimensionality, such as the relativistic Dirac particle
behavior of an electron in the vicinity of the Fermi energy,77,78
which cannot be found in CNTs. In addition, a graphene sheet
can be more easily and specifically shaped using conventional
lithography compared to a CNT.39 Among many possible shapes
of graphene, the nano-strip with a certain edge structure, namely
graphene nanoribbon (GNR), has been well investigated. The
DFT calculation showed that GNRs with zigzag-shaped edges
have very unique spin configurations.79,80 Each spin state is
localized around each edge, and ferromagnetic ordering takes
place along the edge direction. Then, both edges show antiferromagnetic orientations as depicted in Fig. 6. If the spin
configuration is controlled using external electric fields, the
energy gap for one spin is closed beyond a certain threshold field,
so that the system becomes half-metallic.32,81–84 Fig. 7 shows band
structures of a GNR and the corresponding conductance curves.
In the absence of an electric field, there is a band gap, so that the
conductance around the Fermi energy is zero [Fig. 7(a) and (c)].
However, in the presence of a finite field (0.33 V Å1), the band
gap is closed for the down spin, so that the GNR indeed gives
completely spin-polarized conductance [Fig. 7(b) and (d)].
Fig. 5 (a) Conductance and (b) DOS for pristine and doped CNT(5,5).
G0 is the unit of the quantum conductance. The bottom figure represents
the structure of CNT(5,5) with dopants (N or B in black) (reproduced by
permission of Wiley [ref. 32]).
switching nanodevice.68 Similarly, a specific defect structure on
the CNTs generates spin-dependent conductance which is also
controllable by means of an external electric field.69 Various
defect structures which can be made in a fabrication process of
CNTs have been studied theoretically, and the defects could be
utilized for the design of novel nanodevices.70–73
On the other hand, since Kong et al. proposed that CNTs
were able to act as sensors to detect a small molecule such as
hydrogen, ammonia, and so on,74 CNTs have been studied on
diverse types of chemical sensors or biosensors in experiments.64
The ballistic conductance in CNTs is due to the delocalized
p-orbital of the CNTs. However, this ballistic conductance is
easily broken by an electronic perturbation induced from the
chemical doping on the surface as well as the substitution of
a carbon atom with foreign atoms as we discussed above. A
small portion of the chemical doping on the surface of CNTs
influences the conductance dramatically. Using this ultra-sensitivity, the detection of an individual single molecule is also
possible.75 Theoretical studies in this field focus mainly on the
modification of the CNTs in order to enhance their sensitivity
and selectivity. For example, some kinds of defects on the
surface of CNTs enhance the performance of CNTs as
sensors.71,72 It was known from ab initio conductance calculations that composites of CNTs and metal clusters show better
sensitivity than pristine CNTs.76
3.2.2 Graphenes. Graphenes show almost similar characteristics to armchair CNTs except for the dimensionality. The
4514 | J. Mater. Chem., 2008, 18, 4510–4521
Fig. 6 Spin density plot for the ground state of the GNR with zigzagshaped edges. The red and blue represent isosurfaces of spin up and down
density.
Fig. 7 Band structure of the GNR in the absence (a) or presence (b) of
an electric field (0.33 V Å1) and the corresponding conductance curves
(c, d) (reproduced by permission of Wiley [ref. 32]).
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Furthermore, Hod et al. showed theoretically that the doping to
the edge carbon atoms with certain chemical groups enhanced
the half-metallicity of GNRs.85 Other theoretical works investigated the variation of the energy gap in the vicinity of the Fermi
energy as a function of the width of GNRs which is useful
information for the study of semiconducting devices based on
GNRs.86,87 Their results show that the energy gap was inversely
proportional to the width and this was consistent with experimental work. In this case, doping or defects also play an
important role in determining the energy gap.88 Very recently, it
has been predicted that a spin-valve device based on GNRs gives
unrivaled large magnetoresistance values in comparison to the
conventional giant magnetoresistance devices.89
The conductance of a graphene sheet is extremely sensitive to
the electronic perturbation by adsorption of foreign species, since
transport properties at low energy regimes are governed by
p- and p*-orbitals like CNTs. In addition, the graphene is 2D so
that a Hall-conductivity can be measured. This makes it possible
to find out whether the adsorbed molecules or atoms are electron
donors or acceptors, because the Hall-conductivity gives
different signs depending on the carrier type. Schedin et al.
showed that individual single molecules can be detected by using
the graphene.90 Theoretical works verified the experimental
results by studying charge transfer and binding energy between
an adsorbed molecule and the graphene sheet.91,92 The research in
this field has recently received great attention.93 Both theory and
experiment complement each other for the realization of a sensor
device based on graphene.
3.3 Metallic nanowires: electronic/spintronic properties, magic
structures, and quantum conductance
3.3.1 Dimensional properties of metals: 0–3-dimensional
structures and electronic/magnetic properties. Dimensionality of
metal systems plays a vital role in electronic properties of
materials. As the dimension decreases from the bulk (3D) to
mono-layer films (2D) to linear atomic chains (1D) to nanoclusters or quantum dots (0D), the DOS changes drastically so
that their quantum features show the dimensional characteristics. In this regard, numerous studies have been carried out to
investigate metal clusters, nanowires/nanorods, ultra-thin films,
etc. Nano-size metal clusters behave like quantum dots. There
have been several reports on metal clusters such as silver, gold,
and silver–gold binary systems.94–97 The novel metal nanorods
can be utilized as sensors, and a special kind of nanorod/wire
composed of Sb and Bi which changes from semimetal to
semiconductor depending on the diameter would be utilized as
thermoelectric materials.98–101 Ultra-thin wires and atomic linear
chains102–109 show pure quantum characteristics. Dimensionality
is thus a very important issue in nanotechnology. Thus, we here
particularly focus our attention on metal nanowires, comparing
their properties with the 2D and 3D properties. Then, we discuss
how to make linear atomic chains and what kind of magic
structures are formed in linear wires.
Nanowires (NWs) hold great potential for application to the
design of nanodevices. Their 1D structure is a novel organization
of atoms. Intriguing characteristics appear because of the
quantum effects arising from the spatial confinement of electrons. Ultra-thin NWs including a monatomic chain have been
This journal is ª The Royal Society of Chemistry 2008
made by using the mechanically controllable break junction
(MCBJ) method.110 However, experimental characterization of
NWs is not a trivial task.
In this context, transition metal NWs have been systematically
investigated to understand how the dimensional effects change
the properties of NWs with respect to their bulk properties.111–114
In general, as dimensionality decreases, the ‘‘d’’ bands of
transition metals become sharper and their band edges rise
progressively, increasing the related DOS as shown in Fig. 8. As
a result, most 1D systems of transition metals are predicted to be
magnetic, despite that only Co, Fe, and Ni are magnetic in bulk
systems. Ugarte and coworkers verified experimentally that Pt
and Pd indeed formed magnetic NWs.115 In addition, the spin–
orbit interaction plays an important role in heavy atoms such as
5d-elements. This effect induces a significant change of quantum
conductance (or rarely a metal–insulator transition).113
Ultra-thin NWs are not stable so they exist transiently during
the thinning process in experiments.110,115,116 Therefore, stabilization of NWs is necessary to make practical use of their novel
properties. DFT calculations show that a certain NW can be
stabilized by alloying with particular species.117,118 In Fig. 9, 1D
Au has two energy minima, where the zigzag chain with
a bending angle of 60 has lower energy than that of 120 .
The zigzag chain readily changes into a higher dimension because
Au prefers more nearest neighbors. The injection of s-electrons
into the gold wire by zinc or magnesium lifts the Fermi level.117
The resulting s–d hybridization yields an energy minimum for the
linear structure. However, this system still is not a perfect linear
chain. To realize a perfect linear atomic chain, each atom in the
system should favor di-coordination. Alkali metals such as Na
and Cs have one valence s-electron, while noble metals such as
Au and Ag have one vacancy in the s-band. Therefore, the alloy
of the two elements by a one-to-one ratio would form a stable
di-coordinated atoms chain. Na and Cs have a zigzag structure
with a bending angle of 60 like Au as shown in Fig. 9.
However, when they form an alloy with Au, they have the lowest
energy for the perfect linear chain.118 In particular, the Cs–Au
alloy shows only one energy minimum so that it forms a stable
atomic chain. Our study explains that the stability is due to the
significant charge transfer from Cs to Au. The alternating
arrangement of the positive and negative charges along the linear
chain causes the same types of atoms to be apart in order to
minimize the repulsion between the same sign of charge as
depicted schematically in Fig. 10. Thus, apart from the effect of
the s–d hybridization due to the relativistic effects, it is the effect
of the charge separation due to the large difference of electron
affinity between Au and Cs that stabilizes the linear structure of
the Cs–Au alloy.
To sum up, owing to the effect of the dimensionality on NWs,
most transition metals have magnetic properties when they form
NWs, even though their bulk properties are non-magnetic. This
indicates that an atomic chain of transition metals can be utilized
for spintronic devices. Despite that linear atomic chains of metals
are hardly stabilized, the charge transfer driven stabilization of
doped NWs would be a useful approach for a realization of the
stable NWs.
3.3.2 Thinning process of metal nanorods: magic structures
and fractional quantum conductance. The stability of ultra-thin
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Fig. 9 Schematic diagram of a unit cell projected onto the yz plane
(circles are for atoms) (a), and plots of cohesive energies and bond angles
as a function of the chain length for pure Au/Na/Cs and binary Na/Cs–
Au atomic chains: (b) Au, (c) Na, (d) Cs, (e) Na–Au, and (f) Cs–Au
(where solid and open circles indicate cohesive energy and bond angle,
respectively) (reproduced by permission of American Physical Society
[ref. 118]).
Fig. 10 Schematic diagram of the electrostatic force on atoms constituting an infinitely long atomic chain, disfavoring the zigzag structure. A
circle denotes an atom with positive or negative charge, and the arrow
denotes the net electrostatic force on atom (reproduced by permission of
American Physical Society [ref. 118]).
Fig. 8 DOS (in states per cell, for non-magnetic cases, and in states per
cell per spin, for magnetic cases) for the 2D and 1D structures of the
transition metal elements of groups 8–10. The inset, indicating the
spin-polarization, shows an excess of majority and minority carriers for
magnetic cases. Fermi energy is at 0 eV. DOS (in the vertical axes) is
plotted with respect to energy (in the horizontal axes) (reproduced by
permission of American Physical Society [ref. 112]).
NWs is critical in nanosystems, as addressed earlier. NWs are
made in several ways. One of the simplest examples is the MCBJ
method.110 NWs adopted in the MCBJ method have been found
4516 | J. Mater. Chem., 2008, 18, 4510–4521
to undergo thinning on a time scale which allows snapshots.119,120
The conductance has also been studied to identify the structures
of very thin Ag NWs.121 However, identification of geometrical
structures for ultra-thin NWs is extremely difficult due to the
high signal-to-noise ratio in the experiments based on conventional experimental tools such as high-resolution transmission
electron microscopy.115 Theoretical calculations provide a useful
guide line for such an identification. As an example, we show our
recent study exploring the pathway of the thinning process for
transient [110] NWs of Ag associated with the ‘‘magic structures’’.122 By using the NEGF-DFT method, the quantum
conductance is obtained for various structures of NWs and
compared with the values observed in experiments. Then, the
one-to-one mapping between theoretical and experimental
results enables even the thinnest NWs to be identified.
Fig. 11(a) shows the energy profile for the average number of
atoms on each cross section (N/L) of NWs, where N is the
average number of atoms in a unit cell of a NW and L is the
length of the unit cell. The horizontal axis is given in the effective
radius (R) of the NW defined as [(N/L)sa/p]1/2 where sa is the
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Fig. 12 Simplified picture representing the extraction of a NW from the
bulk (reproduced by permission of American Physical Society [ref. 122]).
Fig. 11 Energy vs. O(N/L) (or effective radius, R) (a) and tension vs.
O(N/L) of [110] Ag NWs. The top view (the cross section of NW along
[110]) followed by two side views (along [-110] and [001]) is shown for the
well-favored (except 4/2 and 2/1) structures. The unlabeled structures
(from bottom to top) are 4/1, 3/4, 6/2, 2/6, 6/4, 8/3, 6/6, 5/8, 8/5 and 15/8.
The initial structure of various n/m NWs was built by alternate stacking
of (110) atomic planes, where n atoms are taken from one plane and m
from the other (reproduced by permission of American Physical Society
[ref. 122]).
atomic cross section, regardless of its shape. The energy profile
shows which structures are more stable for the given N. As N
decreases, the (slow/adiabatic) thinning process would take the
most stable structure among many possible NW conformations
for the given N. Thus, the thinning process follows the points
below the contour in Fig. 11(a) which correspond to the magic
structures based on the stability of isolated NWs. Fig. 11(b)
shows the magic structures when the NWs are extracted from the
bulk in the thinning process. This process is investigated from the
balance of strain [produced by stretching force (f)] vs. stress
[restoring force due to the surface tension (t ¼ gS) of NW, where
g is the surface tension per unit area of the NW and S is the
surface area per unit length of NW], since the NW stretched from
the bulk has the extra surface area (SL z 2pRL) with respect to
the bulk system [Fig. 12(a)].
In Fig. 12(b), the force f describing the generalized wire tension
in drawing a NW from length zero to L is f ¼ (E mbNw)/L,
where E is the wire free energy (this equals the total energy at
This journal is ª The Royal Society of Chemistry 2008
0 K), m/mb is the NW/bulk chemical potential, and Nw is the
number of atoms in the NW. Note that the bulk of atoms moved
out to form the NW. In a quasi-equilibrium, this force should be
balanced by the restoring force to reduce the surface tension: f ¼
gS (i.e., E can be considered as E ¼ mNw ¼ mbNw+ gSL). S may
be considered to be approximately proportional to the square
root of the cross section of the NW. If the cross section is close to
being circular, then f z g2pR. If it is far from the circular shape,
f>g2pR, because the circular cross section tends to have minimal
surface tension. In the thinning process, the NW becomes
thinner. As one atom is stripped off, the NW moves to the left
along the horizontal axis in Fig. 11 (i.e., smaller number of atoms
per cross section). It would be favorable to reduce the surface
tension, leading to the lowest f value (on the vertical axis) for the
given N (on the horizontal axis).
In the MCBJ experiments, the restoring process [from NW to
bulk in Fig. 12(b)] is the reverse direction to the thinning/pulling
process [from bulk to NW A to NW B in Fig. 12(a)]. NW B
appears by stripping the surface from NW A. The atoms
removed from the dotted hollow cylinder eventually move to the
surface of the bulk. Then, the original surface atoms are covered
by the atoms moved from the NW A, and thus become bulk
atoms because they are no longer surface atoms. Namely, the
atoms removed from NW A are diffused into the bulk. In this
way, we obtain the following equation which represents the
amount of energy change per unit length (i.e., restoring force)
during the thinning process (as NW B is stripped out from
NW A):
FA/B ¼
¼
DE
DL
ðEB mb NB Þ ðEA mb NA Þ
L
¼fB fA,
(1)
(2)
(3)
where
fx h
Ex mb Nx
L
(x ¼ A/B).
EA/EB and NA/NB are the energy and the number of atoms of
NW A/B with length L, respectively. The thinning process would
be favorable/unfavorable depending on the negative/positive sign
of fA / B. For the given NW A, when EB is the lowest among
many possible conformers of NW B, the string tension of NW B
(fB) will be the lowest, and so fA / Bwill be maximally decreased.
Namely, the most probable path is to maximally decrease the
value of fA / B for the given NA if there is not a large energy
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barrier. Consequently, the unique path is a line that connects the
lowest points on the smaller N {which should have a lower value
than that of the parent NW during the thinning process
[Fig. 11(a) and (b)]}. The relative stability of magic structures in
Fig. 11(b) is in good agreement with that in Fig. 11(a), but differs
only slightly because of the existence of the restoring force due to
the extraction of NWs from the bulk in Fig. 11(b) against the
isolated stability of NWs in Fig. 11(a). In this thinning process,
Fig. 11(b) would well reflect the real experimental process. It is
intriguing to note that Fig. 11(b) gives an almost straight line for
the points on the contour. The points above the line would be
hardly stable, while the points below the line would be more
stable, leading to magic structures. The fitted curve is useful to
gauge more stable structures. In this case, the slope of the curve
reflects the surface tension because f ¼ g2pR in the case of the
circular shape. This is why Fig. 11(b) gives an almost straight line
for the points on the contour. The smallest slope gives g ¼ 0.8 N
m1 for the 11/8 structure. The decrease in tension is the driving
force behind the thinning which takes place by depletion of
atoms from the NW to the tips. From Fig. 11, the ‘‘magic’’
structures indicate metastable states. For small cross sections
(1#N#15, or 1.5 Å<R<7.0 Å), the magic NWs are made of 11/8,
(9/8), 8/6, 5/4, (4/3), 2/2, (1/1), and 1/0 structures, as shown in
Fig. 13 (with only slightly favored structures in parentheses).
This is consistent with the experimental data available.121
To get a better insight into the thinning process vis-à-vis
experimental results,121 the conductance (G) for the NWs was
investigated using NEGF-DFT and the Landauer formula with
a single zeta polarization basis set. In the Landauer formula, G
can be approximated by the transmission function near the
Fermi energy, EF. The G value for the 4/3, 4/2, 4/1, 2/2, 2/1, 1/1,
and 1/0 structures at/around EF is integral being 6, 5, 4, 3, 3, 2,
and 1 G0, respectively. However, the experimental global
histogram121 shows peaks at 1, 2.4, and 4 + G0. Since thinning is
a transient process, a new structure might evolve before the old
structure has actually fully faded away, i.e. mixed structures may
exist.
Fig. 14(a) shows one of the mixed structures which corresponds to 5/4 4–4/3 3–2/2 3. The 5/4 3 of both ends were
used as left and right electrodes and the remaining 5/4 1
structure was included in the central part. Fig. 14(b) shows the
conductance change according to the evolution of NWs from
4/3 1 to 4/3 3–2/2 2–1/1 3 for two kinds of leads; one is the
5/4 4 structure (solid line), and the other is the planar surface in
the Ag [110] direction (dashed line). The pure 4/3 structure has G
as 6 G0, while the conductance of the mixed 5/4 4–4/3 N
structure (N: integer) reduces to 5 Go. When N changes from
1 to 3, the conductance is slightly reduced and fluctuates around
5 G0. After the 2/2 structure appears in the further evolving
Fig. 13 Pathway (showing up the top view) of the thinning process for
[110] Ag NWs. The value in parentheses are the energies per atom in eV
(reproduced by permission of American Physical Society [ref. 122]).
4518 | J. Mater. Chem., 2008, 18, 4510–4521
Fig. 14 (a) An example of a mixed structure. The 4/3 3–2/2 3
structure as a device part is located between both leads comprised of 5/4
4 structures. (b) Change of conductance during the evolution of each
structure, 4/3 L (L ¼ 1–8), 4/3 3–2/2 M (M ¼ 1–4) and 4/3 3–2/2
2–1/1 N (N ¼ 1–3), between two 5/4 leads or between two infinite
planar surfaces (110). Indices L, M, and N denote the units of each
structure during evolution as in (a) (reproduced by permission of
American Physical Society [ref. 122]).
process, the G value reduces abruptly below 3 G0. During
evolution of the 2/2 structure, G remains almost constant. The
planar surface makes the G value further reduced. The G value of
4/3 drops to 4.5 G0 and that of 2/2 to 2.7 G0. In this case, the
conductance curve fluctuates more because of the larger selfenergy term for the semi-infinite surface. This lowering trend is
also observed for all mixed structures in Fig. 14(b). The 4/3 (or
4/2), which has 6 G0 (5 G0) for the pure structure, could be 4 + G0
in mixed structures, while 2/2 and 2/1 (with 3 G0 for the pure)
could be 2.4 G0, as observed in the experiment.121 To conclude, the
magic structures during the thinning of [110] Ag NWs are 11/8,
8/6, 5/4, (4/3), 2/2, (1/1), and (1/0) NWs which appear more stable.
The structure of the electrodes is found to have a profound effect
on the G value; the mixed structure gives the smaller G value.
3.4 CNT/graphene electrodes for molecular electronics
3.4.1 Metal vs CNT/graphene electrodes. Realizing molecular
electronic devices primarily depends upon material properties of
basic units in the given circuit: electrodes, molecules, and linkages between an electrode and a molecule, as depicted in Fig. 15.
Along this line, many works have focused only on revealing the
role of molecules as an independent device rather than as
a component in an assembly with other units.1,23 However, these
units should not be standing alone because all units in the nanoscale device are in the quantum interference regime, so that the
transport phenomena through the circuit are determined in the
Fig. 15 Schematic illustration for the components of a molecular
electronic device.
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final stage as their combination rather than individual properties
of units. Transition metals with the sulfur linkage are the most
widely used material as an electrode. However, it has been
revealed that serious problems such as irreproducibility of the
measured currents due to the ill-defined chemical bond between
a molecule and transition metals exist. To avoid this problem,
there have been several reports focused on the importance of
electrodes and their linkages.42–44,123,124 Recently, the transport
through a molecule between CNTs has been measured experimentally,125,126 while the unique properties of CNTs as electrodes
have not been well understood.
CNTs/graphenes satisfy a precondition for an optimal
electrode because of the following advantages: (i) it is easy to
form a robust and reproducible covalent bond with organic
molecules through well-established chemistry,127 (ii) it is possible
to utilize metallic properties of CNTs/graphenes, and (iii) CNTs/
graphenes have quasi-one/two-dimensional structures useful to
integrate many individual devices.128
3.4.2. Negative differential resistance in molecular electronics.
The current–voltage (I–V) characteristics for CNT–molecule–
CNT systems have been investigated with several feasible
linkages (Fig. 16).129 The I–V characteristics highly depend on
the bias-dependent transmission. Each linkage gives a different
transmission curve, consequently showing distinctive I–V characteristics. First of all, for amide linkage, the I–V characteristics
showed consistent results with experiment within a low bias
regime where the experiment was performed. Each linkage connected to the same molecule generates different coupling effects
between the molecule and electrodes. Among the four linkages,
the imide produces the smallest HOMO–LUMO energy gap for
a given molecule, because the imide linkage maintains a better
conjugation between a molecule and a CNT. The ester and amide
linkages show similar properties to the imide. In contrast, the
ether linkage has the largest HOMO–LUMO energy gap among
them and shows a considerably different behavior. In another
study, Ke et al. showed that contacts through a five-membered
ring between CNTs and a molecule like the imide linkage gave
full conjugation, resulting in transparent transmissions.130
Fig. 17 shows the I–V curves of two different molecules for
four different linkages. In contrast to the phenyl-ethynyl (PE)
molecule where only the ester linkage shows negative differential
resistance (NDR), the case of the pyrrollo-pyrrole (PP) molecule
shows the NDR for the amide, ester, and imide linkages within
the bias below 3.0 V. This emphasizes the role of linkage properties. The NDR originates from an asymmetric potential drop
in the junction at both contacts. The asymmetric potential is
attributed to the unique electronic structure of CNTs. Although
all the linkages give rise to an asymmetric potential drop, the
shapes of the potential contours through the molecule are
different from each other. Because of this difference, the ether
linkage does not show NDR.
In order to design a molecular device having a specific function, we must understand not only the properties of materials
themselves but also the effects of their combination. In this way,
it is evident that theoretical studies provide experimentalists with
insights to guide the experimental design of molecular electronic
devices.
4. Concluding remarks
Fig. 16 Structure of the CNT–molecule–CNT system with various
linkages (bottom) (reproduced by permission of American Physical
Society [ref. 129]).
We have discussed structures and electronic/spintronic properties of low dimensional nanostructures (single molecules,
nanowires, nanotubes, and nanoribbons). This theoretical
understanding would help in the design novel nanodevices. As
Fig. 17 I–V curves for CNT–molecule–CNT systems for PE (left) and PP (right) molecules (reproduced by permission of American Physical Society
[ref. 129]).
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electric fields can control molecular orbital energy levels, the spin
states of molecules can be changed, which would be useful for
molecular spintronic devices. As carbon nanotubes, graphene
nanoribbons and their molecular analogs show unusual characteristic features in electronic and magnetic properties, they would
be widely used for novel electronic/spintronic devices. Low
dimensional metallic nanowires also show characteristic stability,
quantum conductance, and unusual electronic and magnetic
properties. The ferromagnetic properties of atomic chains and
metallic nanowires could be utilized for spintronic devices.
Carbon nanotube and graphene electrodes have similar electronic
properties to carbon-based molecules, so the molecular orbitals
of these electrodes can couple with those of the electronic
molecules between the electrodes, giving intriguing electronic
features. In addition, the negative differential resistance
phenomena in molecular electronics with carbon nanotube/
graphene electrodes could be utilized for novel electronic
nanodevices.
References
1 F. Chen, J. Hihath, Z. F. Huang, X. L. Li and N. J. Tao, Annu. Rev.
Phys. Chem., 2007, 58, 535.
2 A. Aviram and M. A. Ratner, Chem. Phys. Lett., 1974, 29, 277.
3 C. Joachim, J. K. Gimzewski, R. R. Schlittler and C. Chavy,
Phys. Rev. Lett., 1995, 74, 2102.
4 M. A. Reed, C. Zhou, C. J. Muller, T. P. Burgin and J. M. Tour,
Science, 1997, 278, 252.
5 J. Chen, M. A. Reed, A. M. Rawlett and J. M. Tour, Science, 1999,
286, 1550.
6 C. Joachim, J. K. Gimzewski and A. Aviram, Nature, 2000, 408, 541.
7 A. H. Flood, J. F. Stoddart, D. W. Steuerman and J. R. Heath,
Science, 2004, 306, 2055.
8 N. J. Tao, Nat. Nanotechnol., 2006, 1, 173.
9 H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl and
R. E. Smalley, Nature, 1985, 318, 162.
10 S. Iijima, Nature, 1991, 354, 56.
11 K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang,
S. V. Dubonos, I. V. Grigorieva and A. A. Firsov, Science, 2004,
306, 666.
12 A. Nitzan and M. A. Ratner, Science, 2003, 300, 1384.
13 N. J. Singh, E. C. Lee, Y. C. Choi, H. M. Lee and K. S. Kim, Bull.
Chem. Soc. Jpn., 2007, 80, 1437.
14 N. J. Singh, H. M. Lee, S. B. Suh and K. S. Kim, Pure Appl. Chem.,
2007, 79, 1057.
15 K. S. Kim, Bull. Korean Chem. Soc., 2003, 24, 757.
16 D. Majumdar, H. M. Lee, J. Kim and K. S. Kim, J. Chem. Phys.,
1999, 111, 5866.
17 H. G. Kim, C.-W. Lee, S. Yun, B. H. Hong, Y.-O. Kim, D. Kim,
H. Ihm, J. W. Lee, E. C. Lee, P. Tarakeshwar, S.-M. Park and
K. S. Kim, Org. Lett., 2002, 4, 3971.
18 Theory and Applications of Computational Chemistry: The First 40
Years, ed. C. E. Dykstra, G. Frenking, K. S. Kim, and G. E.
Scuseria, Elsevier, Amsterdam, 2005.
19 A. Szabo and N. S. Ostlund, Modern Quantum Chemistry, McGrawHill, New York, 1989.
20 R. G. Parr and W. Yang, Density-Functional Theory of Atoms and
Molecules, Oxford University Press, New York, 1989.
21 S. K. Min, E. C. Lee, H. M. Lee, D. Y. Kim, D. Kim and K. S. Kim,
J. Comput. Chem., 2008, 29, 1208.
22 T. Helgaker, T. A. Ruden, P. Jorgensen, J. Olsen and W. Klopper,
J. Phys. Org. Chem., 2004, 17, 913.
23 J. Heyd, G. E. Scuseria and M. Ernzerhof, J. Chem. Phys., 2003, 118,
8207.
24 V. N. Staroverov, G. E. Scuseria, J. Tao and J. P. Perdew, J. Chem.
Phys., 2003, 119, 12129.
25 V. N. Staroverov, G. E. Scuseria, J. Tao and J. P. Perdew, Phys. Rev.
B, 2004, 69, 075102.
4520 | J. Mater. Chem., 2008, 18, 4510–4521
26 M. Ko1aski, H. M. Lee, C. Pak and K. S. Kim, J. Am. Chem. Soc.,
2008, 130, 103.
27 A. L. Marques, C. A. Ullrih, F. Nogueira, A. Rubio, K. Burke and
E. K. U. Gross, Time-Dependent Density Functional Theory,
Springer, Berlin, Heidelberg, 2006.
28 S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge
University Press, Cambridge, England, 1995.
29 A. R. Rocha, V. M. Garcia-Suarez, S. W. Bailey, C. J. Lambert,
J. Ferrer and S. Sanvito, Nat. Mater., 2005, 4, 335.
30 M. Brandbyge, J. L. Mozos, P. Ordejon, J. Taylor and K. Stokbro,
Phys. Rev. B, 2002, 65, 165401.
31 J. Taylor, H. Guo and J. Wang, Phys. Rev. B, 2001, 63, 121104.
32 W. Y. Kim and K. S. Kim, J. Comput. Chem., 2008, 29, 1073.
33 R. H. Baughman, A. A. Zakhidov and W. A. de Heer, Science, 2002,
297, 787.
34 B. H. Hong, J. P. Small, M. S. Purewal, A. Mullokandov,
M. Y. Sfeir, F. Wang, J. Y. Lee, T. F. Heinz, L. E. Brus, P. Kim
and K. S. Kim, Proc. Natl. Acad. Sci. U. S. A., 2005, 102, 14155.
35 B. H. Hong, J. Y. Lee, T. Beetz, Y. Zhu, P. Kim and K. S. Kim,
J. Am. Chem. Soc., 2005, 127, 15336.
36 Y. Zhang, Y.-W. Tan, H. L. Stormer and P. Kim, Nature, 2005, 438,
201.
37 K. S. Novoselov, Z. Jiang, Y. Zhang, S. V. Morozov, H. L. Stormer,
U. Zeitler, J. C. Maan, G. S. Boebinger, P. Kim and A. K. Geim,
Science, 2007, 315, 1379.
38 P. Avouris, Z. H. Chen and V. Perebeinos, Nat. Nanotechnol., 2007,
2, 605.
39 L. A. Ponomarenko, F. Schedin, M. I. Katsnelson, R. Yang,
E. W. Hill, K. S. Novoselov and A. K. Geim, Science, 2008, 320, 356.
40 Y. C. Choi, C. Pak and K. S. Kim, J. Chem. Phys., 2006, 124,
094308.
41 T. Dadosh, Y. Gordin, R. Krahne, I. Khivrich, D. Mahalu,
V. Frydman, J. Sperling, A. Yacoby and I. Bar-Joseph, Nature,
2005, 436, 677.
42 L. Venkataraman, J. E. Klare, C. Nuckolls, M. S. Hybertsen and
M. L. Steigerwald, Nature, 2006, 442, 904.
43 P. G. Piva, G. A. DiLabio, J. L. Pitters, J. Zikovsky, M. Rezeq,
S. Dogel, W. A. Hofer and R. A. Wolkow, Nature, 2005, 435, 658.
44 X. F. Guo, J. P. Small, J. E. Klare, Y. L. Wang, M. S. Purewal,
I. W. Tam, B. H. Hong, R. Caldwell, L. M. Huang, S. O’Brien,
J. M. Yan, R. Breslow, S. J. Wind, J. Hone, P. Kim and
C. Nuckolls, Science, 2006, 311, 356.
45 Y. C. Choi, W. Y. Kim, K. S. Park, P. Tarakeshwar, K. S. Kim,
T. S. Kim and J. Y. Lee, J. Chem. Phys., 2005, 122, 094706.
46 M. Diefenbach and H. Schwarz, Chem.–Eur. J., 2005, 11, 3058.
47 M. Diefenbach and K. S. Kim, Angew. Chem., Int. Ed., 2007, 46,
7640; M. Diefenbach and K. S. Kim, Angew. Chem., 2007, 119, 7784.
48 J. L. Wang, P. H. Acioli and J. Jellinek, J. Am. Chem. Soc., 2005,
127, 2812.
49 V. V. Maslyuk, A. Bagrets, V. Meded, A. Arnold, F. Evers,
M. Brandbyge, T. Bredow and I. Mertig, Phys. Rev. Lett., 2006,
97, 097201.
50 M. Koleini, M. Paulsson and M. Brandbyge, Phys. Rev. Lett., 2007,
98, 197202.
51 E. Durgun, S. Dag, V. M. K. Bagci, O. Gulseren, T. Yildirim and
S. Ciraci, Phys. Rev. B, 2003, 67, 201401.
52 C. K. Yang, J. J. Zhao and J. P. Lu, Nano Lett., 2004, 4, 561.
53 E. Durgun and S. Ciraci, Phys. Rev. B, 2006, 74, 125404.
54 T. A. Murphy, Th. Pawlik, A. Weidinger, M. Höhne, R. Alcala and
J. Spaeth, Phys. Rev. Lett., 1996, 77, 1075.
55 J. M. Park, P. Tarakeshwar, K. S. Kim and Tim Clark, J. Chem.
Phys., 2002, 116, 10684.
56 E. Kane, Nature, 1998, 393, 133.
57 K. S. Kim, J. M. Park, J. Kim, S. B. Suh, P. Tarakeshwar, K. H. Lee
and S. S. Park, Phys. Rev. Lett., 2000, 84, 2425.
58 H. S. Choi and K. S. Kim, Angew. Chem., Int. Ed., 1999, 38, 2256;
H. S. Choi and K. S. Kim, Angew. Chem., 1999, 111, 2400.
59 Z. Chen, D. Jiang, X. Lu, H. F. Bettinger, S. Dai, P. R. Schleyer and
K. N. Houk, Org. Lett., 2007, 9, 5449.
60 D.-H. Oh, J. M. Park and K. S. Kim, Phys. Rev. B, 2000, 62, 1600.
61 Y. W. Son, M. L. Cohen and S. G. Louie, Nature, 2006, 444, 347.
62 S. J. Tans, A. R. M. Verschueren and C. Dekker, Nature, 1998, 393,
49.
63 V. Sazonova, Y. Yaish, H. Ustunel, D. Roundy, T. A. Arias and
P. L. McEuen, Nature, 2004, 431, 284.
This journal is ª The Royal Society of Chemistry 2008
Published on 03 July 2008. Downloaded by Pohang University of Science and Technology on 30/05/2015 15:06:17.
View Article Online
64 B. L. Allen, P. D. Kichambare and A. Star, Adv. Mater., 2007, 19,
1439.
65 K. Tsukagoshi, B. W. Alphenaar and H. Ago, Nature, 1999, 401,
572–574.
66 L. E. Hueso, J. M. Pruneda, V. Ferrari, G. Burnell, J. P. ValdesHerrera, B. D. Simons, P. B. Littlewood, E. Artacho, A. Fert and
N. D. Mathur, Nature, 2007, 445, 410.
67 H. J. Choi, J. Ihm, S. G. Louie and M. L. Cohen, Phys. Rev. Lett.,
2000, 84, 2917.
68 Y. W. Son, J. Ihm, M. L. Cohen, S. G. Louie and H. J. Choi, Phys.
Rev. Lett., 2005, 95, 216602.
69 Y. W. Son, M. L. Cohen and S. G. Louie, Nano Lett., 2007, 7, 3518.
70 Y. S. Lee, M. B. Nardelli and N. Marzari, Phys. Rev. Lett., 2005, 95,
076804.
71 Y. S. Lee and N. Marzari, Phys. Rev. Lett., 2006, 97, 116801.
72 H. Park, J. J. Zhao and J. P. Lu, Nano Lett., 2006, 6, 916.
73 R. G. Amorim, A. Fazzio, A. Antonelli, F. D. Novaes and
A. J. R. da Silva, Nano Lett., 2007, 7, 2459.
74 J. Kong, N. R. Franklin, C. W. Zhou, M. G. Chapline, S. Peng,
K. J. Cho and H. J. Dai, Science, 2000, 287, 622.
75 B. R. Goldsmith, J. G. Coroneus, V. R. Khalap, A. A. Kane,
G. A. Weiss and P. G. Collins, Science, 2007, 315, 77.
76 Q. Zhao, M. B. Nardelli, W. Lu and J. Bernholc, Nano Lett., 2005, 5,
847.
77 K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang,
M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos and
A. A. Firsov, Nature, 2005, 438, 197.
78 Y. B. Zhang, Y. W. Tan, H. L. Stormer and P. Kim, Nature, 2005,
438, 201.
79 M. Fujita, K. Wakabayashi, K. Nakada and K. Kusakabe, J. Phys.
Soc. Jpn., 1996, 65, 1920.
80 S. Okada and A. Oshiyama, Phys. Rev. Lett., 2001, 87, 146803.
81 Y. W. Son, M. L. Cohen and S. G. Louie, Nature, 2006, 444, 347.
82 L. Pisani, J. A. Chan, B. Montanari and N. M. Harrison, Phys. Rev.
B, 2007, 75, 235126.
83 O. Hod, V. Barone and G. E. Scuseria, Phys. Rev. B, 2008, 77,
035411.
84 O. Hod, J. E. Peralta and G. E. Scuseria, Phys. Rev. B, 2007, 76,
233401.
85 O. Hod, V. Barone, J. E. Peralta and G. E. Scuseria, Nano Lett.,
2007, 7, 2295.
86 Y. W. Son, M. L. Cohen and S. G. Louie, Phys. Rev. Lett., 2006, 97,
216803.
87 V. Barone, O. Hod and G. E. Scuseria, Nano Lett., 2006, 6, 2748.
88 M. Y. Han, B. Ozyilmaz, Y. B. Zhang and P. Kim, Phys. Rev. Lett.,
2007, 98, 206805.
89 W. Y. Kim and K. S. Kim, Nat. Nanotechnol., 2008, 3, 408–412.
90 F. Schedin, A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake,
M. I. Katsnelson and K. S. Novoselov, Nat. Mater., 2007, 6, 652.
91 I. Zanella, S. Guerini, S. B. Fagan, J. M. Filho and A. G. S. Filho,
http://arXiv.org/abs/0711.1131, 2007.
92 O. Leenaerts, B. Partoens and F. M. Peeters, http://arXiv.org/abs/
0710.1757, 2007.
93 T. O. Wehling, K. S. Novoselov, S. V. Morozov, E. E. Vdovin,
M. I. Katsnelson, A. K. Geim and A. I. Lichtenstein, Nano Lett.,
2008, 8, 173.
94 J. Yoon, K. S. Kim and K. K. Baeck, J. Chem. Phys., 2000, 112,
9335.
95 H. M. Lee, M. Ge, B. R. Sahu, P. Tarakeshwar and K. S. Kim,
J. Phys. Chem. B, 2003, 107, 9994.
96 M. Diefenbach and K. S. Kim, J. Phys. Chem. B, 2006, 110, 21639.
97 U. Landman, W. D. Luedtke, B. E. Salisbury and R. L. Whetten,
Phys. Rev. Lett., 1996, 77, 1362.
This journal is ª The Royal Society of Chemistry 2008
98 Y. Wang, J. Y. Lee, J.-S. Kim, G. H. Kim and K. S. Kim, Chem.
Mater., 2007, 19, 3912.
99 Y. W. Wang, J. S. Kim, G. H. Kim and K. S. Kim, Appl. Phys. Lett.,
2006, 88, 143106.
100 Y. W. Wang, B. H. Hong and K. S. Kim, J. Phys. Chem. B, 2005,
109, 7067.
101 Y. W. Wang, B. H. Hong, J. Y. Lee, J.-S. Kim, G. H. Kim and
K. S. Kim, J. Phys. Chem. B, 2004, 108, 16723.
102 H.-B. Yi, M. Diefenbach, Y. C. Choi, E. C. Lee, H. M. Lee,
B. H. Hong and K. S. Kim, Chem.–Eur. J., 2006, 12, 4885.
103 A. Bala, T. Nautyal and K. S. Kim, Phys. Rev. B, 2006, 74,
174429.
104 S. B. Suh, B. H. Hong, P. Tarakeshwar, S. J. Youn, S. Jeong and
K. S. Kim, Phys. Rev. B, 2003, 67, 241402(R).
105 K. S. Kim, Curr. Appl. Phys., 2002, 2, 65.
106 B. H. Hong, S. C. Bae, C.-W. Lee, S. Jeong and K. S. Kim, Science,
2001, 294, 348.
107 J.-H. Cho, D.-H. Oh, K. S. Kim and K. Leonard, Phys. Rev. B, 2001,
64, 235302.
108 R. N. Barnett and U. Landman, Nature, 1997, 387, 788.
109 E. Tosatti, S. Prestipino, S. Kostlmeier, A. Dal Corso and F. D. Di
Tolla, Science, 2001, 291, 288.
110 A. I. Yanson, G. R. Bollinger, H. E. van den Brom, N. Agrait and
J. M. van Ruitenbeek, Nature, 1998, 395, 783.
111 T. Nautiyal, S. J. Youn and K. S. Kim, Phys. Rev. B, 2003, 68,
033407.
112 T. Nautiyal, T. H. Rho and K. S. Kim, Phys. Rev. B, 2004, 69,
193404.
113 W. Y. Kim, T. Nautiyal, S. J. Youn and K. S. Kim, Phys. Rev. B,
2005, 71, 113104.
114 A. Bala, T. Nautiyal and K. S. Kim, Phys. Rev. B, 2006, 74,
174419.
115 V. Rodrigues, J. Bettini, P. C. Silva and D. Ugarte, Phys. Rev. Lett.,
2003, 91, 096801.
116 J. Burki, C. A. Stafford and D. L. Stein, Phys. Rev. Lett., 2005, 95,
090601.
117 W. T. Geng and K. S. Kim, Phys. Rev. B, 2003, 67, 233404.
118 Y. C. Choi, H. M. Lee, W. Y. Kim, S. K. Kwon, T. Nautiyal,
D. Y. Cheng, K. Vishwanathan and K. S. Kim, Phys. Rev. Lett.,
2007, 98, 076101.
119 V. Rodrigues, T. Fuhrer and D. Ugarte, Phys. Rev. Lett., 2000, 85,
4124.
120 J. C. González, V. Rodrigues, J. Bettini, L. G. C. Rego, A. R. Rocha,
P. Z. Coura, S. O. Dantas, F. Sato, D. S. Galvão and D. Ugarte,
Phys. Rev. Lett., 2004, 93, 126103.
121 V. Rodrigues, J. Bettini, A. R. Rocha, L. G. C. Rego and D. Ugarte,
Phys. Rev. B, 2002, 65, 153402.
122 D. Cheng, W. Y. Kim, S. K. Min, T. Nautiyal and K. S. Kim, Phys.
Rev. Lett., 2006, 96, 096104.
123 S.-H. Ke, J. Am. Chem. Soc., 2004, 126, 15897.
124 G. S. Tulevski, M. B. Myers, M. S. Hybertsen, M. L. Steigerwald
and C. Nuckolls, Science, 2005, 309, 591.
125 X. F. Guo, A. Whalley, J. E. Klare, L. M. Huang, S. O’Brien,
M. Steigerwald and C. Nuckolls, Nano Lett., 2007, 7, 1119.
126 A. C. Whalley, M. L. Steigerwald, X. Guo and C. Nuckolls, J. Am.
Chem. Soc., 2007, 129, 12590.
127 S. Niyogi, M. A. Hamon, H. Hu, B. Zhao, P. Bhowmik, R. Sen,
M. E. Itkis and R. C. Haddon, Acc. Chem. Res., 2002, 35, 1105.
128 H. J. Dai, Acc. Chem. Res., 2002, 35, 1035.
129 W. Y. Kim, S. K. Kwon and K. S. Kim, Phys. Rev. B, 2007, 76,
033415.
130 S. H. Ke, H. U. Baranger and W. T. Yang, Phys. Rev. Lett., 2007, 99,
146802.
J. Mater. Chem., 2008, 18, 4510–4521 | 4521