Chapter 4 Epoch Making Simulation

Large Scale Simulations for Carbon Nanotubes
Project Representative

Kazuo Minami

Research Organization for Information Science & TechnologyAuthors

Syogo Tejima 1, Kazuo Minami 1, Satoshi Nakamura 1, Kohji Makino 1,Yoshiyuki Miyamoto 2, Mari Ohfuti 3, Mamoru Sakaue 3 and Hisashi Nakamura 1
1 Research Organization for Information Science &Technology (RIST)
2 Fundamental and Environmental Research Laboratories, NEC Corporation
3 Nanotechnology Research Center, Fujitsu Laboratories Ltd.
CARBON NANOTUBE RESARCH GROUPE

Morinobu Endo, Eiji Osawa, Atushi Oshiyama, Yasumasa Kanada, Susumu Saito,
Riichiro Saito, Hisanori Shinohara, David Tomanek, Tsuneo Hirano, Shigeo Maruyama,Kazuyuki Watanabe, Takahisa Ohno, Yoshiyuki Miyamoto, Hisashi Nakamura

Nano carbon materials as nanotubes (CNTs) and fullerenes in nanotechnology have a lot of potential for industrial applications. On the efforts of developing applications, it has been recognized that computational simulations are powerful and efficient tools to find and create new materials from nano scale.
Aiming at realistic simulations for nonmaterial, we have developed a large-scale computation technique utilizing tightbinding molecular dynamic method, ab initio density functional theory (DFT), and time-dependent DFT method.
We have studies various physical properties of nano-carbon and applications e.g., (1) Ultra-fast carrier dynamics in carbon
nanotubeshot carrier dynamics, (2) High-energy and Highly charged ion-collision to graphite and subsequent structuralchange, (3) Atomic and Electronic Structures of CNT-Metal Contacts, (4) Generation of new atomic structure using GSW
rearrangement, (5) Superconducting transition temperatures of hole-doped diamonds. In addition to nano carbon as nanotube,
diamond and graphite of traditional carbon material came into limelight.
Along these works, we have realized that the Earth Simulator is a very powerful tool for large-scale material simulations.
Keywords: Large scale simulation, TB theory, ab initio theory, DFT, Carbon Nanotube, Fullerenes

1. INTRODUCTION

mary objectives with this work: (1) design of innovative nonmaterial with certain desired properties; (2) obtaining fundamental properties in nano-scale matter, and (3) nano-applications. Our purpose is to give the clear explanation of properties and phenomena of nano-scale events and deduce guiding
principle to design new materials for applications from nanostructures using super-computers.

Carbon materials have been expected to make a breakthrough in material science and nanotechnology. A lot of
potential applications of nanotubes and fullerenes e.g., electronic field emitter and electronic devices have attracted scientific community. In the investigation and utilizing theirmaterial properties, numerical simulation using supercomputer has turned to be a very efficient tool. A recent developmentin nanotechnology has required a more efficient supercomputing capable of a large-scale simulation of up to 104 atoms.
Aiming large-scale simulations utilizing Earth Simulator,
we have developed computational package based on ab initio
DFT theory and parameterized tight-binding (TB) method.
The TB code we have developed is shown to be suitable forthe very large systems even though the lack of symmetricalarrangement. We have carried out some subjects in this work,
which are described in the next section. There are three pri-

2. PHYSICAL STUDIES ON NANOMATERIALS
2.1 Ultra-fast carrier dynamics in carbon nanotubes
Last year, we demonstrated rapid reduction of electronhole energy gap in the (3, 3) nanotube and the temperaturedependence of carrier decay, which manifested an existenceof electron-electron and electron-phonon time domains in the(3, 3) nanotube. These findings give important knowledge on
application to high-speed optical and electronic devices. The
computational method is a combination of the time-depend167

Annual Report of the Earth Simulator Center April 2005 - March 2006

ent density functional theory (TDDFT) being coupled withthe molecular dynamics (MD), which enables us to simultaneously treat electron-dynamics and ion dynamics.
This year, we have found that the decay dynamics
depends on nanotube chi rarity. The figure 1 shows timeevolution of electron and hole energy levels for (3, 3) nanotube (left) and the (7, 0) nanotube (right). One can clearly
notice significant reduction of the electron-hole energy gap
in the (3, 0) nanotube while such reduction is not the case inthe (7, 0) nanotube. This fact suggests an efficient light radiation only from semiconducting nanotubes. Although theexcited electron-hole pair is stable in the (7, 0) nanotube, we
expect that presence of defect or impurity may cause rapid
reduction of the energy gap because of induction of defector impurity-induced energy levels near the Fermi level. Thisis our near-future plan of investigation.

conventional graphite by smashing highly-charged ions.
Possibility of graphite-diamond conversion by irradiating
Ar+8 ions was reported by Meguro et al. [See, Appl. Phys.
Lett. 79. 3866 (2001).] Motivated by this experiment, weinvestigated the high-energy Ar+8 ion collision on the surfaceof graphite. Our computational model consists of four-layer
graphite sheets in the AB stacking. We smashed a center of aC-C- bond on the first layer by an Ar+8 ion with kinetic energy of 400 eV.
Figure 2 shows the snapshots of atomic geometry andcharge density upon collision of an Ar+8 ion. Two major
events are rapid charge transfer from graphite to the ion
before collision and formation of sp3-like bond formation
later the collision. These two events were monitored by theTDDFT-MD simulation. Surprisingly, the incident Ar+8,
which was almost neutralized after the collision, werestopped in between the first and second layer despite its
heavy mass (more than twice of that of C atom) and highkinetic energy. The structural change is expected to be sensitive to the incident energy which is now under investigation.

2.2 High-energy and Highly charged ion-collision tographite and subsequent structural change
We explore the possibility of changing the structure of(3, 3) Metallic tube
Rapid relaxation(7, 0) Semiconducting tube
Slow relaxation

42.0

1.0

Energy (eV)Energy (eV)200.0

–2–1.0–40100200300–2.0050Time (fs)

100 150 200Time (fs)250300Fig. 1 Time-evolution of excited electron-hole pairs in (left) (3, 3) nanotube and (right) (7, 0) nanotubes. The insets are atomic geometries of the nanotubes.

Ar+8Ar

4.06 fs

Ar28.26 fs

52.47 fs

Fig. 2 Snapshots of collision of an Ar+8 ion on graphene layers. The contour lines are valence charge density
showing rapid charge transfer from graphene sheet to the Ar ion prior to the collision. The right-most column shows appearance of sp3-like bonds, which may indicate formation of nano-diamond.

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2.3 Atomic and Electronic Structures of CNT-MetalContacts
Carbon nanotubes (CNTs) have shown potential properties for electronic devices. The contacts with the metal, however, have not been understood enough. The atomic andelectronic structures of CNT-metal contacts have been studied by using ab-initio molecular dynamics. We have examined titanium (Ti) and molybdenum (Mo) as possible contact
materials. When the unit length of the model is 2 nm (90 carbon atoms and 96 metal atoms in a unit cell), the optimization is unable to keep the interface for both of the metals.
The contacts show the clear difference between the metals
by enlarging the model to 4 nm (170 carbon atoms and 216
metal atoms in a unit cell). For CNT-Ti, only metal atoms in
the outermost layer move by optimization from the initial
simple contact. For CNT-Mo, all metal atoms show remarkable change in their positions. We can obtain the local densities of states near the Fermi level accounting for electricconductance. This suggests that Ti is better as a contact
material and that we need larger-scale calculations than theforecast to discuss the properties of nano-contact structures.

rearrangement until the generation should be stored in adatabase. Searching for all the paths, with the help of capability the large-scale parallel computer, is executed along
master/slave type parallel program in which a processor
operates as master and the other processors as slave. The
slave calculates the energy of new structure generated by
GSW rearrangement and the master gathers all of data calculated by slaves and classifies them. In accordance with gathering data, next GSW rearrangement's structures being calculated is send to slaves. We achieved the high performancecomputing through the processors of 512 nodes.
Figure 4 illustrates snapshots of isomerization from (8, 1)
CNT to (5, 4) CNT and (10, 3) CNT, and Figure 5 shows thecorresponding energy of each step. It is confirmed that the (8,1) CNT can isomerize to two types of CNT with a different
chirality and radius. We guess that the intermediate structure(for example, B and D in Fig. 4) change to CNTs (for example, C and F in Fig. 4) by self-organization because the energy of intermediate structure is higher than one of CNTs.
One-dimensional problem such as CNT has been dealt
with in the simulation. As a next target, we are challenging
to three-dimensional problem in Fig. 6. It is a simulation
whether the path from the structure connected by C60 tothree-dimensional Mackay structure exists or not. In thissimulation the objective nano particle is assumed to be consists of hexagon and heptagon. Figure 6 exhibits snapshotsof the intermediate generation process. The future work willanalyze the process to generate Mackay structure that has
been predicted to be stable but not been produced yet.

2.4 Generation of new atomic structure using GSW
rearrangement
The purpose of this research is to find out more energetically stable and useful structure from a certain given initialstate (including fullerene, CNT and nano particle) by using
only Generalized Stone-Wales (GSW) rearrangement. In thesimulation, the initial structure generates a huge number of
topologically different or new ones by means of GSW

CNT-Ti

CNT-Ti0.25

0.25

SimpleStableSimple
Stable0.20

0.15

DOSDOS

0.20

0.10

0.15
0.10
0.05

0.05

0.00

0.00
012304123

Coordinate (nm)Coordinate (nm)SimpleSimpleStableStableTiMo

CNT
(a)

4CNT
(b)

Fig. 3 Simple and stable structures of CNT-Ti (a) and CNT-Mo (b) contact and local density ofstates accounting for electric conductance.

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2.5 Superconducting transition temperatures of hole-doped
diamonds
The development of the room temperature superconductor
would be a key for human to solve human race's energy problems. The conventional superconductivity can be understoodby the electron-phonon pairing mechanism. Recently the spin
fluctuation mechanism for the superconductivity has attracted
attention as a promising mechanism for the high temperature
superconductivity of cuprates. However, the recent experimental results indicate that the charge fluctuation is surprisingly large and may be possibly responsible for the pairing
mechanism. From the point, Tachiki et.al. have proposed a
new mechanism of superconductivity due to charge fluctuation. The central concept of their theory is that electron-electron interaction via strong charge fluctuation mediated byphonon can result in attractive force between electrons. We
propose here that the charge fluctuation mechanism is applicable to hole-doped diamond superconductor which is currently attracting considerable attention. Hole-doped diamondhas the strong electron-phonon interaction and is considered
to be highly correlated electron system as expected from theinsulation of pure diamond. Therefore, according to thecharge fluctuation mechanism, hole-doped diamond is astrong candidate for a high temperature superconductor.
Diamond, when it is heavily doped with boron, becomessuperconducting with reports as high as 12 K. However,
impurities such as boron are known to suppress Tc due toAbrikosov-Gor'kov pair breaking. Our aim is to study bysimulation experiment that at what temperature hole-doped
diamond becomes superconducting if holes are doped into
diamond without using impurities.
To this end, we have simulated the time evolution of displacement δ u(t) of the C atoms relative to the equilibrium
position by using tight-binding molecular dynamics code forlarge scale simulation. In the present simulation, the numberof C atoms in the diamond is 512 and the simulation of δ u(t)is performed up to 4ps with 8,000 time steps. Using thetime-series date of δ u(t), we can obtain the dielectric function through the linear-response theory. Figure 1 shows anexample of the frequency dependence of the dielectric function for q = (0.25, 0, 0)π/a, a being the lattice constant. Onecan note that the dielectric function becomes negative in thewide range around ω = 0. The longitudinal optical phononchanges the transfer integrals for electrons, since the phonon
amplitude in diamond is very large, and also holes weaken
the bond strength between carbons. Especially, when (q, ω)
component of the dielectric function is near the longitudinalphonon dispersion curve, the electron-motion is resonantly
modified and the dielectric function becomes negative due tothe overscreening effect.
The Fourier component of the effective interaction Veff (q, ω)is written as 4πe2/[q2ε (q, ω)]., where ε (q, ω) is the dielectric

Initial (8, 1) CNT(A)GSW: 4 timesGSW: 10 times

GSW: 6 times(B)

GSW: 10 times(D)(5, 4) CNT(C)(10, 3) CNT(E)

Energy(computed by the Huckel method)

Fig. 4 Snapshots of isomerization from (8, 1) CNT to (5, 4) CNT and(10, 3) CNT.

DB
ACE

0

10
The number of GSW rearrangements

20Fig. 5 Energy of each step.

Initial structure (C60 × 8)

GSW: 7 times

GSW: 6 times

GSW: 12 times

The structure consist ofhexagon and heptagon

Fig. 6 Snapshot of the generation process.

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Chapter 4 Epoch Making Simulation

showed that the computation on the Earth Simulator could
give an exceptional performance and enables us morechance for large-scale and realistic simulations. Our large
scale simulations can provide the nanotechnology industries
valuable information on novel nano material properties andon nano electrical designs for application.

400Re1(q, )20–20

References

–40
00.05

0.1

0.15

0.2

[1] Y. Miyamoto, Simulation of excited state dynamics in
nanotubes with use of the Earth Simulator,
Computational Challenges and Tools for Nanotubes, 26JUN 2005, Chalmers University of Technology,
Göteborg, Sweden.
[2] S. Tejima, Large-scale simulations for nanocarbons,
Computational Challenges and Tools for Nanotubes, 26
JUN 2005, Chalmers University of Technology,Göteborg, Sweden.
[3] Y. Miyamoto, Ultra-fast Dynamics in Carbon Nanotubes
Explored by the Earth Simulator, The 3rd NanoSimulation Technology Workshop, Nov 24 2005, Mita,Tokyo, Japan.
[4] S. Tejima, Large-Scale Nano Carbon Simulation, The
3rd Nano-Simulation Technology Workshop, Nov 242005, Mita, Tokyo, Japan.
[5] S. Tejima, K. Minami, M. Iizuka and H. Nakamura,
Large-scale simulation on Carbon Nanotubes, The Japan
Society of Applied Physics, Vol.74, No.8, p.1045–1051(2005).
[6] M. Tachiki and S. Nakamura, International Workshop on
Superconductivity in Diamond and Related Materials, 08
DEC 2005, NIMS, Tsukuba, Japan.

(eV)Fig. 7 Real part of dielectric function versus ω for q = (0.25, 0, 0) π/a.

function. From the above result Veff(q, ω) becomes negative
and the strong attractive force appears between electrons. Tc isdetermined as the temperature below which the linearized gap
equation for the anormalous Green's function has a nontrivial
solution. By solving the linearized gap equation with Veff(q, ω)
numerically, we obtained that Tc is about 260 K for diamondwith 0.2 holes per carbon atom. While in our calculation theBrillouin zone is divided into 4 × 4 × 2 equal cubes and thenumber of samplings of data is 4, they are not large enough to
get statistically meaningful ensemble average for temperature.
However, our result suggests that hole-doping to pure diamonds makes them high temperature superconductors.
Henceforth, in addition to improving the precision of ournumerical computation, we will incorporate the effect of selfenergy for the single-particle Green's function.

3. SUMMARY
The large-scale simulations on nonmaterial have been carried out by ab initio density functional method and the parameterized tight-binding calculations. The optimized codes

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113

1

1

12

3

12 NEC

CNT

3

1.
CNT

2.
H14

H15 H16
13, 3-22GSW
512
CNT10, 3 CNT-CNT

8, 1 CNT
C60Ar
sp34,

172

GSW
5, 4 CNT