電子結構計算的基礎與應用研究

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行政院國家科學委員會專題研究計畫成果報告

電子結構計算的基礎與應用研究(第 3 年)

研究成果報告(完整版)

計畫類別：個別型

計畫編號： NSC 98-2112-M-004-003-MY3

執行期間： 100 年 08 月 01 日至 101 年 07 月 31 日

執行單位：國立政治大學應用物理研究所

計畫主持人：楊志開

共同主持人：吳璧如

計畫參與人員：碩士班研究生-兼任助理人員：王瑞騰

博士後研究：李啟玄

報告附件：出席國際會議研究心得報告及發表論文

公開資訊：本計畫可公開查詢

中華民國 101 年 10 月 26 日

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中文摘要：在以密度泛涵計算研究置於奈米硼化氮管內的一些生化分子

的電子結構後，發現生化分子與奈米硼化氮管並無鍵結或化

學吸收，顯示可將奈米硼化氮管作為輸送生化分子的管道。

石墨烯氫化後有可能留下空缺，這些空缺也有可能為其它不

同原子所佔據，以密度泛涵計算研究這些可能的結構後，可

得到複雜電子能帶，包括種種空缺態，雜質態，及各種形成

能量，結合能，及磁性等，可供以石墨烯為基礎之奈米電子

學設計參考。

中文關鍵詞：奈米硼化氮管，生化分子，胺基酸，核苷酸，密度泛涵理

論，石墨烯，氫空缺，過渡金屬，缺陷態，雜質態，線性傳

導

英文摘要： We study the interaction between boron nitride

nanotubes (BNNTs) and a variety of biological

molecules using density functional theory. Some amino

acids and nitrogenous bases that are parts of

nucleotides are inserted inside the cavity of the

BNNT and the overall electronic structure calculated.

We conclude that there is no bonding or chemical

adsorption between the wide band-gap BNNT and the

biological molecules considered. This suggests that

BNNTs can be used as a smooth nanoscale channel for

transporting biological molecules.

Graphane has a large band gap around 3.5 eV. In the

situation of a vacant hydrogen atom,

defect states appear in the energy gap, according to

density functional calculation, and a

local magnetic moment of 1 Bohr magneton is

generated. Furthermore, if the vacancy is

occupied by an atom from the transition-metals, not

only do impurity levels make their

presence in and out of the gap region but larger

moment can also occur as a result. The calculation

also shows that the doped structures are robust and

the choice of dopant can

change the electrical conduction and magnetism

greatly. We investigate the electronic structure of

graphane with hydrogen vacancies, which are supposed

to occur in the process of hydrogenation of graphene.

A variety of configurations is considered and defect

states are derived by density functional calculation.

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We find that a continuous chain-like distribution of

hydrogen vacancies will result in conduction of

linear dispersion, much like the transport on a

superhighway cutting through the jungle of hydrogen.

The same conduction also occurs for chain-like

vacancies in an otherwise fully fluorine-adsorbed

graphene. These results should be very useful in the

design of graphene-based electronic circuits.

英文關鍵詞： Boron nitride nanotubes, biochemical molecules, amino

acids, nucleotides, density functional theory,

graphene, hydrogen vacancies, transition-metals,

defect states, impurity levels, linear conduction

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Computer Physics Communications 182 (2011) 39–42 Contents lists available atScienceDirect

Computer Physics Communications

www.elsevier.com/locate/cpc

Exploring the interaction between the boron nitride nanotube and biological

molecules

Chih-Kai Yang

Graduate Institute of Applied Physics, National Chengchi University, Taipei 11605, Taiwan, ROC

a r t i c l e

i n f o

a b s t r a c t

Article history:

Received 26 January 2010

Received in revised form 17 July 2010 Accepted 28 July 2010

Available online 10 August 2010

Keywords:

Boron nitride nanotubes Biological molecules Encapsulation Electronic structure

We study the interaction between boron nitride nanotubes (BNNTs) and a variety of biological molecules using density functional theory. Some amino acids and nitrogenous bases that are parts of nucleotides are inserted inside the cavity of the BNNT and the overall electronic structure calculated. We conclude that there is no bonding or chemical adsorption between the wide band-gap BNNT and the biological molecules considered. This suggests that BNNTs can be used as a smooth nanoscale channel for transporting biological molecules.

1. Introduction

Because of their small sizes and unique physical properties nanotubes have been used extensively in many novel physical and chemical applications. There is also great expectation of their mak-ing an impact on biomedical sciences. A properly handled nano-tube, for example, is ideally suited to target a cell at pinpoint accuracy. Recently, a functionalized multi-walled carbon nanotube (CNT) attached to an atomic force microscope was used as a tip to penetrate cell membranes and deliver “cargo” to the interior of the cell [1]. The successful operation raises hope of using the “nanoneedle” or “nanoinjector” as a high-precession delivering ve-hicle for transporting biological molecules to a variety of cells and may eventually contribute to the treatment of diseases.

Compared with CNTs, boron nitride nanotubes (BNNTs)[2]have similar tubular structure and mechanical properties and are thus an equally capable alternative for the precision transport of bi-ological molecules through cell membranes. In electric property, however, BNNTs have a large band gap around 5.5 eV, slightly de-pending on the diameter and helicity[3], which is quite different from the case of CNTs. BNNTs are also chemically inert and resis-tant to oxidation and corrosion[4]. Such qualities suggest that the biological “cargo” can pass safely through the cavity under the pro-tection of the BNNT coating. Furthermore, it has been conﬁrmed experimentally that CNTs are pernicious to the survival of cells

[5,6]. A less reactive conduit such as BNNT may be less harmful to the biological molecules it carries and the cell at which it is targeted.

E-mail address:[email protected].

In this article we report the investigation of the interaction be-tween BNNTs and some typical biological molecules. We choose three among the 20 amino acids, glycine, serine, and cysteine, and all members of the two families of the nitrogenous bases, pyrim-idines and purines, which are vital parts of the nucleotides. Each is placed inside a BNNT and the whole structure calculated by using density functional theory.

2. Calculation method

The calculation employs both ultrasoft and projector augment-ed-wave (PAW) pseudopotentials as implemented in the VASP code

[7,8]. A cutoff energy close to 300 eV is chosen and the self-consistent cycles are stopped when the variation of the total en-ergy per unit cell and band structure enen-ergy are both less than 10−4 eV, which is quite stringent for a unit cell with more than 150 atoms. One-dimensional periodicity is imposed by using a large unit cell. Take, for example, the case of a

(

12

,

0

)

BNNT en-capsulating a glycine molecule. The size of the unit cell is about 17

×

17

×

13 in Å, where the last number is the length of the BNNT segment along the tube axis. Larger unit cells are used for bigger tubes to ensure the isolation of the combined structure. Multiple k points sampling in the ﬁrst Brillouin zone is also taken for struc-tural relaxation and band structure calculation. In particular 31 k points are used for all calculations involving the electronic struc-ture. For exchange–correlation functionals, we try both general gra-dient approximation (GGA) and local density approximation (LDA). GGA is known to underestimate the interaction among molecules where long-range dispersion force such as van der Waals inter-action is concerned, while LDA tends to overcompensate for the lack of binding [9]. This description is quite consistent with our

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40 C.-K. Yang / Computer Physics Communications 182 (2011) 39–42

Fig. 1. Distribution of binding energies for the encapsulation of glycine by a series of BNNTs ranging from(7,0)to(14,0). The nearest distance between glycine and BNNT increases with the size of the tube.

calculations. It is also found that different versions of GGA pro-duce slightly different results. However, the general trend and con-clusion of our results are not affected by any speciﬁc choice of exchange–correlation functional, as is discussed in the next sec-tion.

3. Results and discussion

We ﬁrst investigate how the molecule glycine interacts with BNNTs. The molecule is initially placed in an arbitrary position close to the tube’s inner wall. Different initial positions can be ob-tained by varying the distance between one atom of the molecule and that of the wall or by translation of the whole molecule. The whole structure is then relaxed, using PAW pseudopotentials and the exchange–correlation functionals of Perdew, Burke and Ernzer-hof[10] under GGA, by allowing each atom to move to minimize the total energy. By subtracting both the total energy of the iso-lated tube and the energy of the molecule from the total energy of the combined structure after optimization we obtain the bind-ing energy for the interactbind-ing system. The calculation is repeated for different initial positions of glycine and a series of tubes of dif-ferent sizes ranging from

(

7

,

0

)

to

(

14

,

0

)

and one typical result is plotted inFig. 1.

Each point on the plot indicates the binding energy and the corresponding nearest distance between the tube and glycine. It shows clearly that the interaction between the two gets repulsive

rapidly once the distance is shorter than 2.2 Å. Weak attractive interaction exists for larger tubes and the minimum binding en-ergy

(

−

0

.

098 eV

)

occurs at the

(

12

,

0

)

tube. Overall the picture conﬁrms the inert and non-reactive quality of BNNTs in their en-capsulation of glycine.

Take the most energetically favorable conﬁguration for a more detailed discussion. The glycine molecule is at ﬁrst placed close to the inner wall of the

(

12

,

0

)

tube. Thorough relaxation process, however, pushes the molecule away to a position with nearest distance of 3.21 Å, as is shown in Fig. 2A. Calculated electronic density of states (DOS) for this optimized position is presented in the bottom panel of Fig. 3. Shown in the top and middle panel of the same ﬁgure represent the DOS for a pristine

(

12

,

0

)

BNNT and DOS for an isolated glycine molecule respectively, aligned to the same Fermi level as that of the bottom panel. It is obvious that the bottom panel is almost a superposition of the top and the middle, with some scaling in the height of DOS and slight shift of energy levels of glycine taken into account. That means the elec-tronic structure of each of the two components of the combined structure is essentially intact despite the encapsulation. We also perform calculation for local density of states and partial waves for each atom of the encapsulated glycine. Inside each designated atomic sphere of the molecule there is hybridization of orbitals from other atoms of the molecule. But almost no contribution from the BNNT can be found. Fig. 2B is the calculated charge density on a plane penetrating the tube and the molecule. It shows that there is no appreciable overlap of electronic charge between the two constituents.

The same relaxation and electronic structure calculation are also applied to the series of BNNTs encapsulating glycine using exchange–correlation functionals under LDA, which, as has been stated earlier, produce higher attractions for the glycine and tend to overcompensate for the lack of the van der Waals interaction. We nonetheless obtain similar distribution of binding energy ver-sus distance and the same non-interacting nature from the DOS and charge density.

We next expand our research to include two more amino acids, serine and cysteine, and all members of pyrimidines and purines, which are indispensable parts of genetic materials. Each of the molecules is now placed in the

(

13

,

0

)

BNNT and the encapsula-tion goes through relaxaencapsula-tion and electronic structure calculaencapsula-tion. This time we try ultrasoft pseudopotentials and the exchange– correlation functionals of the Perdew–Wang 1991 version[11]. In

Table 1 we list the calculated binding energy for each

molecu-Fig. 2. A) Conﬁguration of the encapsulation of glycine by BN(12,0)nanotube. B) Charge density on a plane passing through the tube and molecule.

Table 1

Binding energies for the encapsulation of serine, cysteine, cytosine, thymine, uracil, adenine, and guanine by BN(13,0)nanotube. Conﬁgurations are shown inFig. 4.

BN tube+molecule Serine Cysteine Cytosine Thymine Uracil Adenine Guanine

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C.-K. Yang / Computer Physics Communications 182 (2011) 39–42 41

Fig. 3. DOS for a pristine(12,0)BNNT (top panel), an isolated glycine molecule (middle panel), and their combined structure (bottom panel) as shown inFig. 2A, all aligned to the same Fermi level. The unit of all three panels is 1/eV/unit cell. The unit cell for the bottom two panels is three times as large as that of the top panel.

lar encapsulation. Conﬁgurations are shown inFigs. 4A to 4G. We observe that for the same tube smaller molecules such as ser-ine and cysteser-ine are weakly attractive to the BNNT while larger molecules tend to push up the binding energy, indicating stronger repulsion. The relaxation process not only forces the encapsu-lated molecule to reposition itself but can distort the BN tube, in the case of a large molecule, in the process of minimizing the strain.

Whatever the ﬁnal conﬁguration the encapsulation assumes, there is no chemical adsorption or bonding occurring between the molecules and the tube, under the different pseudopotentials and exchange–correlation functionals. In Fig. 5 we illustrate the DOS for guanine encapsulation. The top and middle panels again rep-resent those of the isolated tube and molecule respectively. The bottom panel, which represents the encapsulation, is basically the superposition of the energy levels of the top two panels from en-ergy deep below the Fermi level all the way to those over it. There is negligible hybridization of orbitals from the molecule and those from the tube and inertness of the BNNT is again in dis-play.

Fig. 4. Conﬁguration of a(13,0)BNNT encapsulating A) serine, B) cysteine, C) cytosine, D) thymine, E) uracil, F) adenine, and G) guanine. Colors for elements are grey (carbon), white (hydrogen), blue (nitrogen), red (oxygen), and yellow (sulfur). (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)

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42 C.-K. Yang / Computer Physics Communications 182 (2011) 39–42

Fig. 5. DOS for a pristine(13,0)BNNT (top panel), an isolated guanine molecule (middle panel), and their combined structure (bottom panel) as shown inFig. 4G. 4. Conclusion

Based on our calculations it can be reasonably inferred that the weak binding energy between a biological molecule and a BNNT of proper size should present only limited kinetic barrier to the movement of the molecule under room temperature. The small size and sturdy constitution of BNNTs are on a par with CNTs. And the non-reacting nature not only protects the “cargo” from outside interferences but also makes the molecular movement less

hindered in passage. There are other methods for delivering bio-chemical molecules, using functionalized nanoparticles or quantum dots, for example. However, none is comparable in achieving the pinpoint accuracy a nanotube has to offer. Experiments involving drug dispensation in particular is a very useful application in this direction.

Acknowledgements

This work has been ﬁnanced by the National Science Council of the Republic of China under grant number NSC 98-2112-M-182-002-MY3. We are also grateful for supports provided by the National Center for Theoretical Sciences and National Center for High-performance Computing of the ROC.

References

[1] X. Chen, A. Kis, A. Zettl, C.R. Bertozzi, Proc. Natl. Acad. Sci. 104 (2007) 8218. [2] N.G. Chopra, R.J. Luyken, K. Cherrey, V.H. Crespi, M.L. Cohen, S.G. Louie, A. Zettl,

Science 269 (1995) 966.

[3] A. Rubio, J.L. Corkill, M.L. Cohen, Phys. Rev. B 49 (1994) 5081.

[4] Y. Chen, J. Zhou, S.J. Campbell, G.L. Caer, Appl. Phys. Lett. 84 (2004) 2430. [5] C.A. Poland, R. Duﬃn, I. Kinloch, A. Maynard, W.A.H. Wallace, A. Seaton, V.

Stone, S. Brown, W. MacNee, K. Donaldson, Nature Nanotechnol. 3 (2008) 423. [6] S.K. Manna, S. Sarkar, J. Barr, K. Wise, E.V. Barrera, O. Jejelowo, A.C. Rice-Ficht,

G.T. Ramesh, Nano Lett. 5 (2005) 1676. [7] G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) R558. [8] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169.

[9] P. Sony, P. Puschnig, D. Nabok, C. Ambrosch-Draxl, Phys. Rev. Lett. 99 (2007) 176401.

[10] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865.

[11] J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C. Fiolhais, Phys. Rev. B 46 (1992) 6671.

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Graphane with defect or transition-metal impurity

Chih-Kai Yang

*

Graduate Institute of Applied Physics, National Chengchi University, Taipei 11605, Taiwan, ROC

A R T I C L E I N F O

Article history:

Received 13 January 2010 Accepted 25 June 2010 Available online 30 June 2010

A B S T R A C T

Graphane has a large band gap around 3.5 eV. In the situation of a vacant hydrogen atom, defect states appear in the energy gap, according to density functional calculation, and a local magnetic moment of 1 Bohr magneton is generated. Furthermore, if the vacancy is occupied by an atom from the transition-metals, not only do impurity levels make their presence in and out of the gap region but larger moment can also occur as a result. The cal-culation also shows that the doped structures are robust and the choice of dopant can change the electrical conduction and magnetism greatly.

1. Introduction

Since its successful synthesis, graphene [1–3] has been eagerly explored for its potential as a next-generation nanoelectronic device, which would replace current metal-oxide-semiconductor field effect transistors. Graphene has some attractive properties, such as high mobility and ballistic transport over long distances, for making high-quality electronic devices. However, a pristine graphene sheet is a zero-gap semiconductor, hardly suitable for making a useful electronic device without some sort of band gap engineering. To introduce an energy gap, one can resort to carving a nano-ribbon out of a larger graphene sheet or doping graphene with impurities.

In the latter practice, hydrogenation of a graphene sheet has been successfully achieved, and the hydrocarbon often referred as ‘‘graphane’’[4,5]. Predicted by density functional calculation (DFT) to have a large band gap around 3.5 eV[6], each C atom in graphane is bonded to a hydrogen atom alter-nately on either side of the graphene sheet. And each C in this conformation is pulled out of the plane by the hydrogen by a small distance, forming a crumpled two-dimensional struc-ture. The large band gap produced by hydrogenation is quite exceptional, considering that if H is replaced by lithium for adsorption on the graphene the whole structure becomes a conductor[7].

Experimentally it is likely and perhaps highly controllable to have a few isolated H vacancies during the synthesis of gra-phane, which involves an exposure to hydrogen plasma. The defect states as a result of the H vacancies would greatly af-fect the conduction. Since transition-metals (TM) are associ-ated with magnetism, and there is already DFT calculation showing that embedded TM atoms in single or double vacan-cies in graphene can produce quite unexpected magnetism [8], it would be only natural and worthwhile to consider the scenario in which the vacancies are filled with one of these impurities. This may be achieved through, for example, a sec-ond exposure to the gas of individual TM atoms or the moving tip of a scanning tunneling microscope guiding the adsorbed TM atom to the right place[9]. Graphane thus doped has an additional benefit in that the H-terminated structure is less reactive to other atoms and molecules whether it is deposited on a substrate or freestanding itself and thus makes a stable structure both chemically and electronically. Its electronic structure and magnetism, which largely determine its useful-ness in electronics, are what we are going to discuss next in the article.

2. Calculation method

Our first step is to calculate the electronic structure of a pure graphane using DFT. It employs the projector augmented

* Fax: +886 2 29387769.

E-mail address:[email protected]

C A R B O N 4 8 ( 2 0 1 0 ) 3 9 0 1– 3 9 0 5

a v a i l a b l e a t w w w . s c i e n c e d i r e c t . c o m

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wave potentials as implemented in the VASP code[10,11]. The exchange–correlation functional is provided by the version of Perdew et al.[12]and energy cutoff set at 400 eV. The unit cell consists of a total of four atoms with two from each species (C2H2). It also has a vacuum space with the fixed length of

12 A˚ to accommodate displacement of atoms along the sur-face normal during the relaxation process. Under a 9 · 9 · 1 Monkhorst–Pack k point mesh, the system is allowed to change not only the lattice constant of the unit cell along the other two lateral directions but the relative positions of the individual atoms in order to minimize the total energy. Di-pole corrections[13]for potential and total energy are also provided to address the errors caused by the repeated super-cells. The result essentially reproduces what is called ‘‘chair’’ conformation in Ref.[6]. Optimal lattice constant is 2.545 A˚ and the C–C and C–H bond length are 1.54 and 1.11 A˚ , respec-tively. The calculated energy gap is 3.59 eV, also quite close to that mentioned in Reference 6.

3. Results and discussion

Using the optimal C2H2as a basis, we expand the lattice four

times to accommodate an isolated defect, i.e., a missing H, and, later, a TM impurity atom taking its place. The lattice constant is now 10.18 A˚ and the unit cell contains 32 C and 31 H. Relaxation of atomic positions is always included in the calculation either for defect or doping. Band structure cal-culation for the optimal structure of C32H31 yields Fig. 1,

which is divided into six panels. The right three panels corre-spond to the majority spin and the left three to the minority spin. All k points in the figure are sampled from the three directions of symmetry in the irreducible Brillouin zone. Two essentially dispersionless defect levels stand out in the energy gap. One is 0.62 eV below the Fermi level and thus be-longs to the majority spin. Another is 1.20 eV above the Fermi level, corresponding to the minority spin. Density of states (DOS) of C32H31, calculated from all k points, also identifies

the two defect levels with two peaks inFig. 2a, with the other parts of the spectrum showing no appreciable difference be-tween the two spins.

The spin-polarized distribution of energy levels results in a magnetic moment of 1.0 lBper unit cell. Obviously, this

mag-netism has its origin in the missing hydrogen. Adsorption of hydrogen turns the sp2_{hybridization of orbitals in graphene}

into sp3 _{in graphane. A missing H therefore leaves an}

un-paired electron in the lone dangling bond connecting the C. A calculation of local density of states (LDOS) of the C uncon-nected to H confirms that the two spin-polarized defect levels are almost entirely pZorbital in nature, as is shown inFig. 2b.

LDOS for other C atoms, on the other hand, all have electronic structures typical of a C in pure graphane, indicating that the magnetic moment is localized. Spin polarized charge distribu-tions are illustrated inFig. 3a and b, where charge density for each spin on a plane passing through the vacancy and some of the C–H atoms is shown. Besides the easily recognizable C-H bonds it also clearly indicates that the difference in charge density between the majority (a) and minority spin (b) occurs only in the vacancy.

In further testing the localized moment theory, we also calculate the electronic structure of the same unit cell with two hydrogen vacancies separated by 5.09 A˚ . The result indi-cates a net magnetic moment of only 0.020 lBfor the unit cell.

In fact two localized anti-parallel spins pair off each other al-most completely in the unit cell.

We then turn our attention to the doping of graphane by a TM atom. Using the same unit cell consisting of 32 C and 31 H,

-6 -4 -2 0 2 4 K M Γ Γ

E

_F

E (eV)

K M K

Fig. 1 – Band structure of C32H31. The right three panels are

for the majority spin, the left three for the minority spin.

-15 -10 -5 0 5 30 20 10 0 10 20 30 Majority spin Minority spin

E

_F DOS

E (eV)

0 1 2 3 4 -20 -15 -10 -5 0 5 4 3 2 1 0 E_F LDOS s px+py pz dxy+dx2_-y2 dxz+dyz dz2

E (eV)

a

b

Fig. 2 – (a) DOS of C32H31. (b) LDOS of the C atom not

connected to hydrogen. Top (bottom) panel is for the majority (minority) spin. Inset is the conformation of C32H31.

3902

C A R B O N4 8 ( 2 0 1 0 ) 3 9 0 1– 3 9 0 5

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the vacancy is now filled with one of the TMs running from scandium to zinc. The first concern is binding energy, which is defined as the difference between the total energy of C32H31TM and the sum of total energies of the two

constitu-ents, C32H31and the single TM atom. Result of the calculation,

listed inTable 1, reveals that, with the exception of zinc, each of the other TM atoms in the series is bonded to the hydrocar-bon quite strongly, with binding energy ranging from –2.67 to –1.22 eV. Even for Zn, adsorption to the hydrocarbon is still an exothermic reaction, with a relatively smaller binding energy

of –0.30 eV. This indicates that graphane doped with an iso-lated TM atom is a robust structure.

Fig. 3 – Charge density for (a) the majority spin and (b) the minority spin on a plane passing through the vacancy and some of the C and H atoms of C32H31.

Table 1 – Binding energy (EB) for the adsorption of a transition-metal atom taking place of the missing hydrogen. Also listed are the magnetic moment and bond length between the metal and C.

C32H31TM Sc Ti V Cr Mn Fe Co Ni Cu Zn EB(eV) 2.67 2.39 1.94 1.58 1.22 1.53 2.14 2.33 2.18 0.30 Bond length (A˚ ) 2.26 2.18 2.14 2.12 2.14 2.03 1.99 1.95 1.96 2.18 Moment (lB) 1.95 3.00 4.00 5.00 5.87 3.00 2.00 1.00 0.00 1.00 -6 -4 -2 0 2 4 K M K

M

K

E

F M

E (eV)

Γ Γ

Fig. 4 – Band structure of C32H31Ti.

-20 -15 -10 -5 0 5 -30 -20 -10 0 10 20 30 E_F DOS E (eV) Majority spin Minority spin 0 2 4 6 8 10 -4 -3 -2 -1 0 1 2 3 10 8 6 4 2 0 E_F LDOS s px+py p_Z dxy+dx2_-y2 d_xz+d_yz dz2 E (eV)

a

b

Fig. 5 – (a) DOS of C32H31Ti. (b) LDOS of the impurity Ti. Inset

is the conformation of C32H31Ti.

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Also shown in Table 1 are magnetic moments for TM atoms for the unit cell of C32H31TM, with the highest going

to C32H31Mn and none for C32H31Cu. The calculated

magne-tism is very consistent with the Hund’s rules. Taking, for example, the case of C32H31Cu, the only 4s electron of Cu is

paired off with the electron in the lone dangling bond of the C and the 3d subshells are closed with 10 electrons, making a non-magnetic structure. While for C32H31Mn, exchange

interaction favors as many electrons having the same spin direction as possible, resulting in a very high moment of 5.87 lB.

Rich electronic structures also arise from the doping of TM atoms. As an example we discuss the adsorption of titanium, which is often used to build contacts with CNTs. Band struc-ture, as shown in Fig. 4, reveals numerous spin-polarized impurity levels as a result of the doping. Four distinct and well-separated impurity levels appear in the band gap for the majority spin (the right three panels), the middle two of them being twofold degenerate. They are located at -0.72,

-0.37, 0.37, and 0.96 eV. Three impurity levels, corresponding to the minority spin, are also found in the gap region. One is 1.94 eV below the Fermi level, the other two being located at 0.56 and 1.43 eV above the Fermi level. The middle one shows slight dispersion due to the finite size of the unit cell and the last one is doubly degenerate. There are other impu-rity levels mingled with the bulk of the hydrocarbon as are shown inFigs. 4 and 5a.The latter not only gives positions of the impurity levels but also indicates their degeneracy through the height of the peaks.

LDOS offers more details of the impurity levels. Top panel ofFig. 5b, which represents states of the majority spin, reveals that the level at 0.72 is made of 3d2_Zand s orbitals, a sure sign of s–d hybridization. Both degenerate levels at 0.37 and 0.37 eV are comprised of the other d orbitals. For the energy levels of the minority spin in the bottom panel, the two at 1.94 and 0.56 eV come from the hybridization of s and d2Z

and that at 1.43 eV from the other degenerate d orbitals. Charge density shown inFig. 6a and b once again confirms the localized nature of spin polarization.

Since it is an energy level of the majority spin ( 0.37 eV) that is closest to the Fermi level, conduction of the Ti-doped graphane is greatly influenced by the excitation of the elec-tron occupying that impurity level. This preference of major-ity spin is reversed in the iron-doped graphane. Shown in Fig. 7 is the band structure for C32H31Fe, where a doubly

degenerate impurity level for the minority spin is just 0.092 eV below the Fermi level. Electron occupying this level can be promoted to the impurity levels above the Fermi level and the conduction bands most easily. Spin transport thus depends on the choice of TM dopant. And if more vacancies and thus more TM dopants are present in the unit cell con-duction will be enhanced by more available charge carriers and hopping.

4. Conclusion

Our calculations show that graphane with a missing hydro-gen atom has two spin-polarized defect levels within the band gap, producing a local magnetic moment of one Bohr magneton. A TM atom filling the vacancy generally forms a Fig. 6 – Charge density for (a) the majority spin and (b) the minority spin on a plane passing through the Ti impurity in C32H31Ti. -6 -4 -2 0 2 4 M K K K

E (eV)

M E_F Γ Γ

Fig. 7 – Band structure of C32H31Fe.

(12)

robust structure and produces magnetism essentially follow-ing the Hund’s rules. Rich electronic structure also arises from the adsorption of the impurity, providing much varied electri-cal conduction and potentially useful optielectri-cal properties. Most importantly, synthesis of doped graphane is an extension of currently available technique and can be verified readily by a variety of methods[14,15]. This should make it useful both as a platform for scientific inquiry and a building block for devices for nanoelectronics and spintronics.

Acknowledgements

This work was supported by the National Science Council of the Republic of China under contract number NSC 98-2112-M-182-002-MY3. Supports from the National Centers for The-oretical Sciences and High-performance Computing of the ROC are also gratefully acknowledged.

R E F E R E N C E S

[1] Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, et al. Electric field effect in atomically thin carbon films. Science 2004;306:666–9.

[2] Geim AK, Novoselov KS. The rise of graphene. Nature Mater 2007;6:183–91. and references therein.

[3] Castro Neto AH, Guinea F, Peres NMR, Novoselov KS, Geim AK. The electronic properties of graphene. Rev Mod Phys 2009;81:109–62. and references therein.

[4] Elias DC, Nair RR, Mohiuddin TMG, Morozov SV, Blake P, Halsall MP, et al. Control of graphene’s properties by reversible hydrogenation: Evidence for graphane. Science 2009;323:610–3.

[5] Savchenko A. Transforming grapheme. Science 2009;323:589–90.

[6] Sofo JO, Chaudhari AS, Barber GD. Graphane: a two-dimensional hydrocarbon. Phys Rev B 2007;75:153401-1–4. [7] Yang CK. A metallic graphene layer adsorbed with lithium.

Appl Phys Lett 2009;94:163115-1–3.

[8] Krasheninnikov AV, Lehitnen PO, Foster AS, Pyykko¨ P, Nieminen RM. Embedding transition-metal atoms in graphene: structure, bonding, and magnetism. Phys Rev Lett 2009;102:126807-1–4.

[9] Hirjibehedin CF, Lin CY, Otte AF, Ternes M, Lutz CP, Jones BA, et al. Large magnetic anisotropy of a single atomic spin embedded in a surface molecular network. Science 2007;317:1199–203.

[10] Kresse G, Hafner J. Ab initio molecular dynamics for liquid metals. Phys Rev B 1993;47:R558–561.

[11] Kresse G, Furthmu¨ller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 1996;54:11169–86.

[12] Perdew JP, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys Rev Lett 1996;77:3865–8. [13] Makov G, Payne MC. Periodic boundary conditions in ab initio

calculations. Phys Rev B 1995;51:4014–22.

[14] Krause S, Berbil-Bautista L, Herzog G, Bode M, Wiesendanger R. Current-induced magnetization switching with a spin-polarized scanning tunneling microscope. Science 2007;317:1537–40.

[15] Meier F, Zhou L, Wiebe J, Wiesendanger R. Revealing magnetic interactions from single-atom magnetization curves. Science 2008;320:82–6.

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Electronic structures of graphane with vacancies and graphene adsorbed

with fluorine atoms

Bi-Ru Wu

and

Chih-Kai Yang

Citation:

AIP Advances

2, 012173 (2012); doi: 10.1063/1.3696883

View online:

http://dx.doi.org/10.1063/1.3696883

View Table of Contents:

http://aipadvances.aip.org/resource/1/AAIDBI/v2/i1

Published by the

American Institute of Physics.

Transport properties of hybrid graphene/graphane nanoribbons

Appl. Phys. Lett. 100, 103109 (2012)

Lateral in-plane coupling between graphene nanoribbons: A density functional study

J. Appl. Phys. 111, 043714 (2012)

Single-particle tunneling in doped graphene-insulator-graphene junctions

J. Appl. Phys. 111, 043711 (2012)

Electronic structures of an epitaxial graphene monolayer on SiC(0001) after metal intercalation (metal=Al, Ag,

Au, Pt, and Pd): A first-principles study

Appl. Phys. Lett. 100, 063115 (2012)

Electronic states in heterostructures with piece-wise uniform Dirac cones

J. Appl. Phys. 111, 033706 (2012)

Additional information on AIP Advances

Journal Homepage:

http://aipadvances.aip.org

Journal Information:

http://aipadvances.aip.org/about/journal

Top downloads:

http://aipadvances.aip.org/most_downloaded

(14)

AIP ADVANCES 2, 012173 (2012)

Electronic structures of graphane with vacancies and

graphene adsorbed with fluorine atoms

Bi-Ru Wu

1

and Chih-Kai Yang

2,a

1

_{Center for General Education, Chang Gung University, Kueishan, Taiwan}

2

_{Graduate Institute of Applied Physics, National Chengchi University, Taipei 11605, Taiwan}

(Received 16 November 2011; accepted 22 February 2012; published online 13 March 2012)

We investigate the electronic structure of graphane with hydrogen vacancies, which

are supposed to occur in the process of hydrogenation of graphene. A variety of

configurations is considered and defect states are derived by density functional

cal-culation. We find that a continuous chain-like distribution of hydrogen vacancies will

result in conduction of linear dispersion, much like the transport on a

superhigh-way cutting through the jungle of hydrogen. The same conduction also occurs for

chain-like vacancies in an otherwise fully fluorine-adsorbed graphene. These results

should be very useful in the design of graphene-based electronic circuits. Copyright

2012 Author(s). This article is distributed under a Creative Commons Attribution 3.0

Unported License. [

http://dx.doi.org/10.1063/1.3696883

]

Graphane

1,2

_{is a single sheet of graphene fully adsorbed with hydrogen atoms, with each carbon}

atom bonded to an H atom alternately on either side of the layer. Graphane is known to have a

large band gap

3

_{around 3.5 eV and is more chemically inert compared with the pristine graphene.}

However, it is always possible that a small amount of H vacancies remains after a hydrogenation

process or occurs by means of physical or chemical desorption. Magnetism caused by vacancies in

graphane attracts much interest.

4–7

In addition, such a distribution of vacancies has the potential to

alter the conduction property drastically and find application in the growing field of graphene-based

nanoelectronics.

7–11

Fluorine atoms are also known to bond to graphene strongly. A graphene layer fully adsorbed

with F atoms

12

_{is also a semiconductor with a large band gap, making the composite chemically}

stable but difficult for application in nanoelectronic circuits. It is thus a natural extension to explore

what roles F vacancies may play in F-adsorbed graphene.

13,14

_{In this paper we report our systematic}

investigation of various distributions of vacancies on both H and F-adsorbed graphene and how they

affect the overall physical properties.

We use density functional calculation as the main tool for the research. The calculation is based

on the projector augmented wave potentials implemented in the ab initio VASP code

15–18

_with

generalized gradient approximation. For exchange-correlation functional, the version of Perdew,

Burke and Ernzerhof

19

_{is adopted. Energy cutoff is set at 500 eV. A 9× 9× 1 Monkhorst-Pack}

k-point mesh is used for the sampling of k points in the Brillouin zone. By allowing relaxation of

the size of the unit cell as well as relative positions of atoms, we derive an optimal lattice constant of

2.545 Å for pure graphane and 2.578 Å for graphene fully adsorbed with F atoms. To accommodate

vacancies a unit cell consisting of 32 C atoms and 32 adsorbed impurities is adopted. For bigger

vacancy clusters, an even larger unit cell with 50 atoms for each species is used. Adjacent to the

atomic layer is added a vacuum slab with thickness of 15 Å, which, after repeated tests with much

larger lengths, proves sufficient for the relaxation of adsorbed atoms and avoids the interaction

between neighboring atomic layers. All configurations are subject to relaxation until the force acting

on each atom is less than 0.05 eV/Å.

a_{Electronic mail:}_{[email protected]}

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012173-2 B. Wu and C. Yang AIP Advances 2, 012173 (2012)

FIG. 1. Configurations of chains, lines, and clusters considered in the calculation. Circles represent positions of vacancies or adsorbed F atoms. Red (dark) and green (gray) circles denote F atoms adsorbed on different sides. Single vacancy and adsorbed F are shown in the left and right side of (a) respectively.

Fig.

1 gives a depiction of many of the configurations included in our calculation. A single H

vacancy and an adsorbed F atom filling the place are considered (Fig.

1(a)

). For vacancy numbers

larger than two we use chains, lines and clusters to describe the configurations. A zigzag distribution

of H vacancies is called a vacancy chain and their filling by F atoms called F chain (Fig.

1(b)

). The

latter has F atoms connected to C atoms alternately on either side of graphene. Linear distribution of

H vacancies or adsorbed F atoms filling the same H vacancies is called a line (Fig.

1(c)

). An F line

has all its F atoms present on one side of the graphene. Finally, clusters are all compact aggregations

of H vacancies or adsorbed F except in the case of three vacancies (F atoms) (Fig.

1(d)

). Neighboring

F atoms in a cluster appear alternately on either side of the carbon layer. There are two cluster types

in the case of four vacancies or adsorbed F, a ring and a triangle.

Formation energies for lines, chains, and clusters of H vacancies are plotted in Fig.

2(a)

.

Formation energy of an H vacancy is calculated by Ef

= [Etot(graphane with Nvac

H

vacancies)-Etot(pure graphane)+Nvac×Etot(one free H atom)]/Nvac, where Nvac

is the number of H vacancies

and Etot

is the total energy of the configuration enclosed in the parenthesis. As is clearly shown in

the figure, it is much easier to form H vacancies in clusters or chains than in lines. The difference is

usually more than 1 eV per vacancy. There is also a slight advantage for forming a cluster in closed

ring (such as N

= 6) than a chain. We expand the unit cell to accommodate a larger cluster or chain

in some cases and the trend remains. Since the distance between two nearest vacancies in a line is

much larger than that between two nearest vacancies in a chain or cluster, it clearly indicates that

a patch of neighboring vacancies is favored over disconnected ones. Formation energy for the ring

type of N

= 4 is lower than the triangle type by 0.35 eV/vacancy.

For F atoms taking H vacancies the trend is completely reversed. Shown in Fig.

2(b)

is a plot of

adsorption energy per F atom against the number of adsorbed F atoms. Adsorption energy of an F

atom taking place of an H vacancy is E

ad

= [Etot

(graphane adsorbed with N

F

F atoms)-E

tot

(graphane

with N

vac

H vacancies)-N

F×Etot

(one free F atom)]/N

F

, where N

F

is the number of adsorbed F atoms.

F atoms in clusters and chains, which are crammed into tighter space and hence more repulsive to

each other, tend to be more difficult to be adsorbed than those in a line. For example, adsorption

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0

2

4

6

8 Number of defects

2.5

3

3.5

4

4.5

5 E

f

(eV/vacancy)

Line

Chain

Cluster

Triangle

Vacancy

0

2

4

6

8 Number of defects

-5.5

-5

-4.5

-4

-3.5

-3

E

ad

(eV/F atom)

F atom

(a)

(b)

triangle-1

traingle-2

triangle-1

traingle-2

FIG. 2. (a) Formation energies for chains, lines, and clusters of H vacancies in graphane. (b) Adsoption energy per F atom taking the same H vacancies.

energy for the ring type of N=4 is higher than that of the triangle type. The more so the more

adsorbed F atoms. But the relatively large absolute values of adsorption energies in all cases confirm

strong bonding between C and F atoms.

Next we turn to the electronic structure of the calculation. An isolated H vacancy represents an

unpaired electron in the dangling bond extending from the C, thus producing a magnetic moment of

1 μ

B.20

This is the common starting point of all subsequent calculations on configurations related to

H vacancies. For odd numbers of nearest-neighbor vacancies, such as those in chains and clusters,

there is always one unpaired electron and a total magnetic moment of 1

μ

B

per unit cell. For unit cells

containing even number of nearest-neighbor vacancies, complete pairing of electrons produces no

net moment except in lines of vacancies. However, the triangle type consisting of four H vacancies

shows different behavior. Because three of the H vacancies are not adjacent to one another, only one

pairing of electrons is possible and a total magnetic moment of 2

μ

B

is produced in the unit cell.

As to the line configuration shown in Fig.

1 , H vacancies in lines are not adjacent to each other and

therefore contribute parallel magnetic moments proportional to the number of vacancies in the unit

cell. For the same reason, the unit cell containing 3 triangular vacancies also possesses a moment

of 3

μ

B.

As typical examples we illustrate in Fig.

3 and

4 band structure, density of states (DOS) and

local density of states (LDOS) of vacancies for an odd (N

= 3) and even number (N = 4) of vacancies

respectively. Spin polarized impurity states can be identified in all three configurations in Fig.

3(a)

.

For the chain configuration two almost dispersionless defect states are found within 1 eV below and

above the Fermi level, corresponding to the majority and minority spin respectively. For the other

two configurations, spin-polarized defect states are also found on either side of the Fermi level. But

only in the three vacancies in line can one find slight dispersion in the defect states. Although there

is a distinct possibility of optical transition between defect states on either side of the Fermi level,

there is virtually no electric transport possible for graphane with isolated H vacancies. Fig.

3(b)

provides spin-polarized DOS and LDOS for defects of the three configurations. In Fig.

4(a)

defect

states are spin-polarized for the triangle and line configurations. The chain and cluster display no

magnetism and produce more separated defect states. DOS and LDOS of the four configurations are

depicted in Fig.

4(b)

.

When H vacancies are occupied by fluorine atoms, as are shown in the configurations related

to F in Fig.

1 , impurity states caused by F atoms are generally deep below or well above the Fermi

level and thus play no part in the transport property. A typical example of F adsorption is provided

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FIG. 3. (a) Band structure for configurations with a chain, line, and triangle of three H vacancies. (b) DOS and LDOS for the same H vacancies.

by Fig.

5 , where impurity states of the three F atoms in a chain, line, and triangle are shown. Most

are well below -2 eV and graphene valence bands or close to 4 eV above the Fermi level. There is

even an increase of band gap as a result of the adsorption of F atoms. This is in agreement with the

large adsorption energy and chemical inertness associated with F.

One surprise comes from the configuration of a continuous chain of H vacancies. For the

continuous chain we also try a rectangular supercell and allow it to relax in size in the lateral

direction. The results are similar to the unrelaxed supercell, including the electronic structure in the

low energy region and magnetic property. Found in the band structure (Fig.

6(a)

) are crossing bands

centered on

point, with linear valence and conduction bands converged at the Fermi level. The

crossing bands are mainly populated by the p orbitals (88 % at

point) of the continuous carbon

chain not bonded to H. This is in sharp contrast to pure graphene, whose Dirac points are at K and

K

. Thus graphane with a continuous chain of H vacancies is a conductor providing linear transport

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FIG. 4. (a) Band structure for configurations with four H vacancies. (b) DOS and LDOS for the same H vacancies.

through the jungle of H atoms. However, if the vacancies are filled with F atoms, the whole structure

relapses into a high band-gap (4.230 eV) semiconductor.

Similar linear dispersion also occurs for a chain of vacancies in a graphene layer that is otherwise

adsorbed with F atoms, as is shown in Fig.

6(b)

. Interestingly, if the chain of vacancies is in graphene

adsorbed with H on one side and F on the other, a small energy gap of 0.106 eV is generated,

separating the valence bands from the conduction bands (Fig.

6(c)

). Apparently the gap is caused

by symmetry breaking as a result of the heterogeneous adsorption.

Finally we consider configurations in which two continuous chains of vacancies come across

each other, as is shown in Fig.

7 . Calculation shows that a gap developed as a result of defect bands

repelling each other. For crossing chains in graphane the gap (0.231 eV) is the smallest compared

with that of graphene with one side adsorbed with H and another with F (0.442 eV) or graphene

with both sides adsorbed with F (0.379 eV).

In conclusion, H vacancies in graphane produce defect states that appear in the graphane band

gap. Magnetic moments can also be generated depending on whether there are unpaired electrons

in the configuration. H vacancies filled with F atoms, however, generate deep impurity states. A

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Μ Γ Κ Μ

-4

-2

0

2

4 E-E

F

(eV)

Chain

Μ Γ Κ Μ

3 adsorbed F atoms

Line

Μ Γ Κ Μ

Triangle-2

FIG. 5. Impurity states for three F atoms filling the H vacancies.

FIG. 6. Linear crossing bands are formed at point for a continuous chain of H vacancies in a graphene layer otherwise adsorbed with H (a) or F (b) atoms. If the layer is adsorbed with H on one side and F on the other, the chain of vacancy will result in a small gap (c).

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FIG. 7. Band structure for two continuous chains of vacancies crossing each other in a layer adsorbed with H (a), F (b) atoms, and (c) H on one side and F on the other.

continuous chain of vacancies in H or F adsorbed graphene turns the structure into a conductor

of linear dispersion. These results should be useful in designing nanoelectronic circuits based on

graphene.

ACKNOWLEDGMENTS

This work was supported by the National Science Council of the Republic of China under

contract number NSC 98-2112-M-004-003-MY3. Supports from the National Centers for Theoretical

Sciences and High-performance Computing of the ROC are also gratefully acknowledged.

1_{D. C. Elias, R. R. Nair, T. M. G. Mohiuddin, S. V. Morozov, P. Blake, M. P. Halsall, A. C. Ferrari, D. W. Boukhvalov,}

M. I. Katsnelson, A. K. Geim, and K. S. Novoselov,Science323, 610 (2009).

2_{A. Savchenko,}_Science_{323, 589 (2009).}

3_{J. O. Sofo, A. S. Chaudhari, and G. D. Barber,}_{Phys. Rev. B}_{75, 153401 (2007).} 4_{H. S¸ahin, C. Ataca, and S. Ciraci,}_{Appl. Phys. Lett.}_{95, 222510 (2009).} 5_{J. Berashevich and T. Chakraborty,}_{Nanotechnology}_{21, 355201 (2010).}

6_{J. Zhou, Q. Wang, Q. Sun, X. S. Chen, Y. Kawazoe, and P. Jena,}_{Nano Lett.}_{9, 3867 (2009).} 7_{J. Berashevich and T. Chakraborty,}_{Phys. Rev. B}_{82, 134415 (2010).}

8_{A. K. Singh, E. S. Penev, and B. I. Yakobson,}_{ACS Nano}_{4, 3510 (2010).}

9_{Y. Wang, X. Xu, J. Lu, M. Lin, Q. Bao, B. ¨}_{Ozyilmaz, and K. P. Loh,}_{ACS Nano}_{4, 6146 (2010).}

10_{D. Haberer, D. V. Vyalikh, S. Taioli, B. Dora, M. Farjam, J. Fink, D. Marchenko, T. Pichler, K. Ziegler, S. Simonucci,}

M. S. Dresselhaus, M. Knupfer, B. B¨uchner, and A. Gr¨uneis,Nano Lett.10, 3360 (2010).

11_{R. Balog, B. Jørgensen, L. Nilsson, M. Andersen, E. Rienks, M. Bianchi, M. Fanetti, E, Lægsgaard, A. Baraldi, S. Lizzit,}

Z. Sljivancanin, F. Besenbacher, B. Hammer, T. G. Pedersen, P. Hofmann, and L. Hornekær,Nat. Matter.9, 315 (2010).

12_{P. V. C. Medeiros, A. J. S. Mascarenhas, F. de Brito Mota, and C. M. C. de Castilho,}_{Nanotechnology}_{21, 485701 (2010).} 13_{J. T. Robinson, J. S. Burgess, C. E. Junkermeier, S. C. Badescu, T. L. Reinecke, F. K. Perkins, M. K. Zalalutdniov,}

J. W. Baldwin, J. C. Culbertson, P. E. Sheehan, and E. S. Snow,Nano Lett.10, 3001 (2010).

14_{J. O. Sofo, A. M. Suarez, G. Usaj, P. S. Cornaglia, A. D. Hern´andez-Nieves, and C. A. Balseiro,}_{Phys. Rev. B}_{83, 081411}

(2011).

15_{G. Kresse and J. Hafner,}_{Phys. Rev. B}_{47, 558 (1993).} 16_{G. Kresse and J. Hafner,}_{Phys. Rev. B}_{49, 14251 (1994).} 17_{G. Kresse and J. Furthm¨uller,}_{Phys. Rev. B}_{54, 11169 (1996).} 18_{G. Kresse and J. Furthm¨uller,}_{Comput. Mater. Sci.}_{6, 15 (1996).}

19_{J. P. Perdew, K. Burke, and M. Ernzerhof,}_{Phys. Rev. Lett.}_{77, 3865 (1996).} 20_{Chih-Kai Yang,}_Carbon_{48, 3901 (2010).}

(21)

2012 年美國物理學會三月全會

楊志開

國立政治大學應用物理研究所

一、參加會議經過

The 2012 March Meeting of the American Physical Society was held in the

Convention Center of Boston, Massachusetts, from February 27 to March 2. I took

China Airlines flight CI0008 on February 25 to Los Angeles and connected to

American Airlines flight AA 192 nonstop to Boston, arriving at the Logan

International Airport in the morning of the 26

th

, February. I went to the Convention

Center and registered for the meeting that afternoon and began to attend sessions next

day.

A talk to be presented by my postdoctoral associate, Chi-Hsuan Lee, was

scheduled for Session L 7 on Tuesday, February 28, presided by Mohan Rao of

Clemson University. The paper was about the composite structure and electronic

property of a carbon nanotube deposited on a graphene nanoribbon. The combined

structure is greatly enhanced in structural stability by the adsorption of a transition

metal wire. Interesting magnetism and electrical conduction are presented by Dr. Lee

in the session.

二、

與會心得

One of the sessions beginning on 8 am on the first day of meeting was

concerned with excitonic and correlation effects in single-layer graphene. It was an

invited session with five speakers of theorists and experimentalists. Their

presentations clearly showed that graphene, composed of light atoms as simple as

carbon, have strong electronic screening for the electrons. Any optical properties

(22)

concerning graphene, therefore, have much to do with excitons which cannot be

explained by any theory based on independent electron approximation. Even

density-functional calculation with random phase approximation is not enough to

predict correct optical properties. As was shown by Steven Louie of Berkeley and

Tony Heinz of Columbia, only by using Bethe-Salpeter equation that takes into

account the attractive interaction between electrons and holes can reasonable results

come out that match the experiment to theory. This comes out as no surprise since the

fractional quantum Hall effect detected on graphene clearly indicated that some

strongly-correlated interaction is at work within this system. It is clear from this

interesting session and numerous others that graphene, besides its much touted

application as the next “building block” of nanoelectronics, will continue to attract the

attention of physicists more interested in its fundamental aspects.

Another hot topic for this meeting is the ever-glowing field of topological

insulators. One notable success was presented by Yoichi Ando of the Institute of

Scientific and Industrial Research in Osaka University, Japan, who, with his

coworkers, has come a long way to confirm the predicted electronic properties of

topological insulators. Researches on the transport in topological insulators by other

groups have also illuminated the transition from weak localization to weak

antilocalization. It is still too early to predict any practical use of the novel materials.

But its connection to quantum Hall and spin Hall effects has prompted speculation

about the use in quantum computing. In any case, its major interests are still on the

side of the fundamentals. So-called topological superconductors are an apparent

extension of the concept.

I also sampled talks on Fe-based and copper oxide superconductivity. People are

getting more familiar with phase diagrams of the unconventional superconductivity,

but the exact mechanism is still hotly debated and a convincing theory still nowhere in

(23)

sight. I also notice the increased number of sessions devoted to energy research,

reflecting part of the latest funding trend and priority of research institutes. Research

related to lithium batteries, solar cells, high storage memories, and rare earth materials

are on the rising.

I left Boston on Friday afternoon, March 2, taking AA 145 and CI 0007 back to

Taiwan, and landed on the Taoyuan International Airport on Sunday, March 4.

三、

攜回資料

(24)

You are cordially invited to attend the 2012 March Meeting of the American Physical

Society (APS) to be held February 27-March 2, 2012 in Boston, Massachusetts, USA.

The APS March Meeting is the largest and most prestigious meeting of physicists in the

world. More than 7,500 papers will be presented by eminent scientists in the field of

physics, including condensed matter physics, materials physics, biological physics,

chemical physics, polymer physics and computational physics.

For more information, please visit the conference website:

http://www.aps.org/meetings/march/index.cfm

We look forward to seeing you in Boston in 2012.

Sincerely,

Terri Gaier

Director of Meetings and Conventions

American Physical Society

One Physics Ellipse • College Park, MD 20740-3844 • www.aps.org

TO:

Chih-Kai Yang

Chang Gung Univ

Graduate Institute of Applied Physics

National Chengchi University

64 ZhiNan Road, Section 2

Taipei, 11605

Taiwan R.O.C.

FROM:

Terri Gaier

Director of Meetings and Conventions

DATE:

January 06, 2012

SUBJECT:

Letter of Invitation to Attend the Annual March Meeting of the

American Physical Society

(25)

Abstract Submitted

for the MAR12 Meeting of

The American Physical Society

Coupling of carbon nanotubes and graphene nanoribbons by the

titanium and vanadium nanowires: First-principles study

1

_CHI-HSUAN

LEE, CHIH-KAI YANG, Graduate Institute of Applied Physics, National Chengchi

University — We investigate the combined structure of a carbon nanotube (CNT)

and graphene nanoribbon (GNR) through the adsorption of a titanium or vanadium

nanowire (NW), using first-principles calculations. The binding energy depends

upon the stacked configuration and is much larger than that between the two

sub-systems without the nanowire. The band structure reveals strong hybridization

between $d$ orbitals of the transition metal and $p$ orbitals of the carbon atoms.

Furthermore, if the CNT is deposited near the border of GNR, structural stability is

enhanced and magnetic moments of the edge atoms are reduced. The result points

to possible application for synthesizing nanowires in nanoelectronic devices.

1

_{This work was supported in part by the National Center for High-performance}

Computing, the National Center for Theoretical Sciences, and the National Science

Council of Taiwan, the Republic of China under Grant number NSC

98-2112-M-004-003-MY3

Chi-Hsuan Lee

Graduate Institute of Applied Physics, National Chengchi University

(26)

國科會補助計畫衍生研發成果推廣資料表

日期:2012/10/16

國科會補助計畫

計畫名稱: 電子結構計算的基礎與應用研究

計畫主持人: 楊志開

計畫編號: 98-2112-M-004-003-MY3

學門領域: 表面物理－理論

無研發成果推廣資料

(27)

98 年度專題研究計畫研究成果彙整表

計畫主持人：

楊志開

計畫編號：

98-2112-M-004-003-MY3

計畫名稱：