Tunable MoS2 bandgap in MoS2-graphene heterostructuresAbbas Ebnonnasir, Badri Narayanan, Suneel Kodambaka, and Cristian V. Ciobanu

Citation: Applied Physics Letters 105, 031603 (2014); doi: 10.1063/1.4891430 View online: http://dx.doi.org/10.1063/1.4891430 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/105/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Toward epitaxially grown two-dimensional crystal hetero-structures: Single and double MoS2/graphene hetero-structures by chemical vapor depositions Appl. Phys. Lett. 105, 073501 (2014); 10.1063/1.4893448 Mechanical properties of MoS2/graphene heterostructures Appl. Phys. Lett. 105, 033108 (2014); 10.1063/1.4891342 Indirect-direct band gap transition through electric tuning in bilayer MoS2 J. Chem. Phys. 140, 174707 (2014); 10.1063/1.4873406 Density functional theory study of chemical sensing on surfaces of single-layer MoS2 and graphene J. Appl. Phys. 115, 164302 (2014); 10.1063/1.4871687 Hydrogenation-induced edge magnetization in armchair MoS2 nanoribbon and electric field effects Appl. Phys. Lett. 104, 071901 (2014); 10.1063/1.4865902

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Tunable MoS2 bandgap in MoS2-graphene heterostructures

Abbas Ebnonnasir,1,2 Badri Narayanan,1 Suneel Kodambaka,2,a) and Cristian V. Ciobanu1,a)

1Department of Mechanical Engineering and Materials Science Program, Colorado School of Mines, Golden,Colorado 80401, USA2Department of Materials Science and Engineering, University of California Los Angeles, Los Angeles,California 90095, USA

(Received 10 April 2014; accepted 15 July 2014; published online 25 July 2014)

Using density functional theory calculations with van der Waals corrections, we investigated how

the interlayer orientation affects the structure and electronic properties of MoS2-graphene bilayer

heterostructures. Changing the orientation of graphene with respect to MoS2 strongly influences the

type and the value of the electronic bandgap in MoS2, while not significantly altering the binding

energy between the layers or the interlayer spacing. We show that the physical origin of this

tunable bandgap arises from variations in the S–S interplanar distance (MoS2 thickness) with the

interlayer orientation, variations which are caused by electron transfer away from the Mo–S bonds.VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4891430]

Two-dimensional (2-D) materials can vary in terms of

their electronic properties (e.g., graphene is metallic,

hexagonal-BN (hBN) is insulating, and MoS2 is semicon-

ducting) and, hence, are attractive, often in combinations, for

technological applications. Among this class of materials,

many studies have focused on molybdenum disulfide, which

exhibits a number of interesting properties such as bandgap

variation with the number of layers,1,2 high carrier

mobility,3,4 high Seebeck coefficient,5 photoconductivity,6,7

large excitonic effects,8 environmental sensitivity,9,10 and

high mechanical strength,11—properties which make this

material promising for next-generation optoelectronic and

nanoelectronic devices.12,13 Recent efforts have focused on

taking advantage of the individual properties of different 2-D

materials by fabricating heterostructures,14 which are verti-

cal stacks of 2-D layers of dissimilar materials held together

by van der Waals (vdW) forces. Such heterostructures not

only can lead to opening of a bandgap in graphene (e.g., in

graphene-hBN bilayers)15 without impairing its electronic

mobility but can also develop direct bandgaps in multilayer

heterostructures16 or improve the on/off current ratios drasti-

cally (�104 in graphene-MoS2).12,17,18

Motivation for the present study stems from the fact that

interlayer orientation can affect the electronic properties of

monolayers on their growth substrate,19,20 as well in multi-

layered structures of the same material.21 In this Letter, we

investigate the use of interlayer orientation between two dif-

ferent 2-D materials as a tuning parameter for the electronic

properties of the bilayer heterostructure. We present results

from vdW-corrected density functional theory (DFT) calcu-

lations on the effect of interlayer orientation on the elec-

tronic structure of the MoS2-graphene bilayers. We find that

the relative orientation of graphene with respect to the MoS2

layer strongly influences the value and type of the bandgap

in MoS2, while having little effect on both the interlayer

spacing and the binding energy. The physical origin of this

strong orientation dependence stems from particular atomic

registries in which carbon atoms of graphene can effectively

weaken a significant number the MoS2 bonds, thus changing

both the thickness and the bandstructure of MoS2. Using a

tight-binding approach to rationalize the results of DFT cal-

culations, we show that it is valence band edge at the C point

that is the most sensitive to the variations in MoS2 thickness,

sensitivity which gives rise to the computed changes in

MoS2 bandgap with graphene orientation. These results are

relevant for heterostructures as potential photovoltaic devi-

ces in which exciton pairs could be created in MoS2 and col-

lected by graphene electrodes,22 and furthermore, provide

perspective on previous related works23–25 showing the tuna-

bility of the bandgap in single-layer MoS2 via tensile strain.

To study the effect that graphene has on the electronic

structure of the MoS2 monolayer, we constructed commensu-

rate moir�e patterns of graphene on MoS2 for two interlayer

orientations with large spatial periodicities (refer to Fig. 1).

The DFT calculations were performed using the SIESTA

Package26 with Troullier-Martins pseudopotentials,27 vdW

exchange-correlation functional of Klime�s et al. (optB88-

vdW version),28 and double-f basis set with polarization

functions. This basis set is sufficient, since the use of larger

sets did not lead to significant changes in the structural and

electronic properties.29 We have validated our computational

approach by reproducing the structural and electronic prop-

erties of MoS2 single-layers and bulk crystals; the validation

for graphene was performed in our earlier works20,21,30 on

epitaxial graphene. We have ensured commensurability of

the graphene and MoS2 layers by applying small biaxial

strains to graphene while keeping the lattice constant of

MoS2 at the relaxed equilibrium value of 3.204 A. This value

for single-layer MoS2 is close to those reported from X-ray

diffraction experiments,31,32 and consistent with values from

other DFT approaches.33,34 Our use of the equilibrium value

for the lattice constant of MoS2 ensures that we do not intro-

duce spurious strains that might obfuscate the effects of

interlayer orientation that we seek to reveal. For atomic

relaxations and bandstructure calculations, we used

Monkhorst-Pack C-centered 10� 10� 1 and 24� 24� 1

grids, respectively. The structural optimization was carried

a)Authors to whom correspondence should be addressed. Electronic

addresses: cciobanu@mines.edu and kodambaka@ucla.edu

0003-6951/2014/105(3)/031603/5/$30.00 VC 2014 AIP Publishing LLC105, 031603-1

APPLIED PHYSICS LETTERS 105, 031603 (2014)

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out until the residual forces fell below 0.01 eV/A. The elec-

tronic convergence tolerance was set to 10�6 eV. For all cal-

culations, an energy cutoff of 250 Ry was chosen for the

integration mesh.

Our results on interlayer binding energies and structural

properties of the heterostructures35 shown in Fig. 1 are sum-

marized in Table I. The strains in graphene are sufficiently

small that they do not unduly influence our conclusions

regarding the electronic properties of the MoS2 layer. The

binding energies and interlayer distance, measured between

graphene and the closest S atomic plane, do not change sig-

nificantly with the graphene orientation. The atomic-scale

corrugations of MoS2 and graphene are practically inexis-

tent. Large 2-D crystals undergo the formation of spontane-

ous long-range ripples, whose effect on the bandstructure is

presently not fully understood;36–40 by studying virtually flat

bilayers (i.e., without significant corrugation, Table I), we

ensure that the effects reported here are strictly due to inter-

layer orientation. The S–S interplanar spacing—i.e., the

thickness of the MoS2 layer—varies little with the orientation

(Table I); however, these small variations in thickness largely

control the electronic properties of the MoS2 layer.

As seen in the table, the binding energies are small,

since the two layers of the bilayer heterostructures are physi-

cally bonded. The binding energy is virtually the same for

the two structures (Table I), and, by itself, it does not affect

their electronic properties. The fact that there are no signifi-

cant changes in the (weak) binding implies that many differ-

ent graphene-MoS2 interlayer orientations would likely be

encountered in experiments, a situation which is typical for

weakly bonded 2-D systems;19,21,41 our models in Fig. 1 are

representative of two orientations. The properties of the het-

erostructure, as we shall see, are controlled by the interlayer

orientation. At a given interlayer orientation in a large-

period moir�e pattern, the in-plane sliding of the layers does

not change their binding or the electronic properties.42

Figure 2 shows the bandstructures and orbital-decomposed

densities of states for the structures studied (Fig. 1). Graphene

retains its semi-metallic character, as there is no distinguishable

bandgap in the pz states. However, the bandgap in MoS2 varies:

1.674 eV for the 4:5z supercell, and 1.561 eV for 4:3a. As seen

in Fig. 2, the nature of the bandgap is different for the two

systems (Fig. 1): the gap is direct at the K point for the 4:5z

structure, and indirect (from K to C) for 4:3a. Although the

assignment of a bandgap type (direct versus indirect) when

using supercells that consist of multiple primitive cells is

affected by the well-known Brillouin zone folding effect,43 the

variations in badgap values and type are physically significant

for cells of the same size (4:5z and 4:3a) for which the folding

across the Brillouin zone is identical. Next, we will focus on

understanding why the orientation of graphene affects the

bandstructure of MoS2.

Figures 2(b) and 2(c) show that the MoS2 bandgap is

direct for the 4:5z configuration, but indirect for 4:3a. Since

both systems have the same 4� 4 MoS2 cell, we focus on the

Table I information pertaining to MoS2 that can be influ-

enced by the proximity of graphene. This key information is

the MoS2 thickness t, which changes from 3.227 A to

3.174 A. To understand how the thickness of MoS2 can affect

its bandstructure, we first study the bandgap as a function of

thickness using 1� 1 unit cells—which ensures the removal

of zone folding artifacts. Our results for MoS2 1� 1 are

shown in Figs. 3(a) and 3(b); in these calculations, the

atomic positions are kept fixed, and the bandgap is computed

for different values of t. At equilibrium (t¼ 3.21 A), the

bandgap is direct, while a slight decrease in the thickness

makes the bandgap indirect. As seen in Fig. 3(b), the

bandgap can be tuned over a span of �0.6 eV by varying the

MoS2 thickness over a span of only �0.2 A—which is con-

sistent with other reports.24,25 The reason for this high

FIG. 1. Surface unit cells of the MoS2-graphene bilayer heterostructures

considered in this work: (a) 4:5z, denoting a 4� 4 MoS2 cell and a 5� 5 gra-

phene cell, oriented so as the ½2�1�10� crystallographic directions of the two

layers in the heterostructure are parallel to one another, and (b) 4:3a, denot-

ing a 4� 4 MoS2 cell matched to a 3ffiffiffi3p� 3

ffiffiffi3p

graphene unit cell, in which

the armchair graphene direction is parallel to MoS2 ½2�1�10� axis.

TABLE I. Calculated properties of the MoS2-graphene systems: binding energy, corrugation of graphene, average spacing between graphene and MoS2, strain

imposed for commensurability, thickness, and corrugation of MoS2.

Binding Energy Graphene Corrugation Interlayer DistanceStrain %

MoS2 Thickness Corrugation

System eV/A2 A A MoS2 Gr A A

4:5z 0.051 0.086 3.110 0.0 þ3.0 3.227 0.001

4:3a 0.051 0.014 3.131 0.0 �0.7 3.174 0.002

031603-2 Ebnonnasir et al. Appl. Phys. Lett. 105, 031603 (2014)

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sensitivity of the bandgap is that the small variations in t(e.g., 0.05 A) amount to changing the length of the Mo–S

bonds by �1%: Since these bonds are strong and covalent, a

bondlength variation of �1% will significantly affect the

bandstructure.23,24

Fig. 3(a) shows that a small decrease in the thickness tresults in a large increase in energy of the valence band at C,

while the energy values of both the valence and conduction

edges at the K point remain largely unchanged. This disparity

in the thickness-dependence of the energies at the valence

band maxima at C and K causes the direct-indirect band gap

transition in the MoS2 layer [Fig. 3]. To understand the physi-

cal origin of such a disparity, we turn to a tight-binding (TB)

model that describes the band structure of MoS2 in terms of

electronic hopping processes associated with the 4d Mo and

3p S orbitals.44,45 In this description, the energy of the

valence edge Ej (j¼C, K) at C or K points is expressed as:45

Ej ¼ hj1 þ hj

2

2

� �þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffihj

1 � hj2

2

� �2

þ 2 hj3

� �2

s; (1)

where hji are hopping terms related to different types of

atom-pairs. The terms hj1 and hj

2 describe electronic Mo–Mo

hopping and S–S hopping, respectively, while hj3 is associ-

ated with Mo–S nearest-neighbor pairs.

In general, hopping terms hji (i¼ 1, 2, 3; j¼C, K) in

Eq. (1) are influenced by the variation in the distances

between relevant atom pairs.44 However, in the range of

thickness values considered here (i.e., 3 A–3.3 A), the h1 and

h2 parameters should not be affected by t. This is because

they depend primarily only on the in-plane S–S and Mo–Mo

distances, which do not change. Therefore, the variations in

band edges at K and C (Eq. (1)) are mostly governed by

changes in hK3 and hC

3 , respectively, which do vary signifi-

cantly with t because the Mo–S bonds are directly affected

by thickness variations. Figures 4(a) and 4(b) show the

thickness-dependence of the hK;C3 parameters and the corre-

sponding valence band edges at K and C. The calculations

were performed35 using the parameters in Ref. 45. As seen in

Fig. 4, the variations of hC3 and EC are more pronounced than

their counterparts at the K point, which leads to significant

thickness-dependence of the valence band energy at C and to

the direct-to-indirect bandgap transition upon decreasing

layer thickness below its equilibrium value.

Last, we discuss the reason why the in-plane rotation of

graphene affects the MoS2 thickness, which, as we have

seen, leads to changes in the bandgap (Fig. 3). To this end,

we have determined the electronic transfer that occurs when

the two layers (graphene and MoS2) are brought together.

For the larger supercells, 4:5z and 4:3a, this electron transfer

is shown in Figs. 5(a) and 5(b). Focusing on Fig. 5(a), we

note that nine out of the 48 Mo–S bonds on the graphene

side (the three-lobed areas identified for clarity in Fig. 5(a)),

lose electronic density, meaning that they become weaker

and slightly longer (by 0.25%). In turn, the thickness tincreases beyond the equilibrium value of 3.22 A and the

bandgap is direct according to Fig. 3. On the other hand, in

Fig. 5(b) where graphene is rotated by 30�, the three-lobed

clusters are not present because graphene has a different

registry with respect to the S atoms in MoS2. Consequently,

there is no electronic loss in the Mo–S bonds. Instead, we

find a weak and directional increase in the charge associated

with these bonds, which makes them slightly shorter; conse-

quently, the S–S interlayer spacing t becomes smaller than

its equilibrium value, and the bandgap becomes smaller and

indirect.

FIG. 3. Bandgap variation for 1� 1 MoS2 layer with respect to its thickness.

The direct bandgap is measured from the K point on valence band to the K

point on conduction band. The indirect bandgap is from the C point on the

valence band to the K point on conduction band.

FIG. 4. Effect of thickness on the MoS2 valence band, calculated via the

tight-binding model of Ref. 45. (a) Hopping terms hC3 and hK

3 as functions of

thickness. (b) Energies of the valence band edges EC and EK at C and K

points, respectively, as functions of thickness. For clarity, we plot the varia-

tion of the quantities with respect to their corresponding equilibrium values

(e.g., DhC3 ¼ hC

3 � hC3;eq and DEC ¼ EC � EC

eq). The inset shows a part of the

MoS2 structure (Mo: red, S: yellow) and defines the geometric parameters t,rMo�S; rS�S, and h.

FIG. 2. Bandstructure and projected density of states for the bilayer hetero-

structures shown in Fig. 1. The pz, dxy=dx2�y2 , and dz2 characters of the bands

are indicated in black, green, and blue, respectively.

031603-3 Ebnonnasir et al. Appl. Phys. Lett. 105, 031603 (2014)

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In conclusion, we have shown that the orientation of

graphene in MoS2 heterostructures affects the bandgap of

MoS2, and have traced the physical origin of this result to

the highly sensitive dependence of the bandgap value on the

thickness of the MoS2 layer. Changes in registry between

graphene and MoS2 are accompanied by interfacial elec-

tronic transfer, which affects the Mo–S bondlengths and

hence the bandstructure. This suggests that graphene-MoS2

heterostructures are suitable for photovoltaic devices, in

which the exciton pair could be created in MoS2 and col-

lected at graphene layers situated on either side of the MoS2

layer. Furthermore, our results provide another perspective

on previous works23,24 which showed tunability of the

bandgap via tensile strain in the MoS2 layer, and contributes

to an increasing body of work that exploits different stacking

registries for discovering useful electronic properties (e.g.,

Ref. 46).

The authors thank Dr. E. Cappelluti for discussions

regarding the tight-binding parametrization published in Ref.

45. The authors gratefully acknowledge funding from

National Science Foundation (A.E., B.N., and C.V.C.)

through Grant No. CMMI-0846858, and from the Office of

Naval Research (A.E. and S.K.), ONR Award No. N00014-

12-1-0518 (Dr. Chagaan Baatar). Supercomputer time for

this project was provided by the Golden Energy Computing

Organization at Colorado School of Mines.

1K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Phys. Rev. Lett. 105,

136805 (2010).2C. Lee, H. Yan, L. E. Brus, T. F. Heinz, J. Hone, and S. Ryu, ACS Nano 4,

2695 (2010).

3Y. Zhang, J. Ye, Y. Matsuhashi, and Y. Iwasa, Nano Lett. 12, 1136

(2012).4B. Radislajevic, A. Radenovic, J. Brivio, V. Giacometti, and A. Kis, Nat.

Nanotechnol. 6, 147 (2011).5M. Buscema, M. Barkelid, V. Zwiller, H. S. van der Zant, G. A. Steele,

and A. Castellanos-Gomez, Nano Lett.13, 358 (2013).6H. S. Lee, S. W. Min, Y. G. Chang, M. K. Park, T. Nam, H. Kim, J. H.

Kim, S. Ryu, and S. Im, Nano Lett. 12, 3695 (2012).7Z. Y. Yin, H. Li, L. Jiang, Y. M. Shi, Y. H. Sun, G. Lu, Q. Zhang, X. D.

Chen, and H. Zhang, ACS Nano 6, 74 (2012).8A. Ramasubramaniam, Phys. Rev. B 86, 115409 (2012).9H. Qui, L. J. Pan, Z. N. Yao, J. J. Li, Y. Shi, and X. R. Wang, Appl. Phys.

Lett. 100, 123104 (2012).10D. J. Late, B. Liu, H. S. S. R. Matte, V. P. David, and C. N. R. Rao, ACS

Nano 6, 5635 (2012).11R. C. Cooper, C. Lee, C. A. Marianetti, X. D. Wei, J. Hone, and J. W.

Kysar, Phys. Rev. B 87, 035423 (2013).12L. Britnell, R. V. Gorbachev, R. Jalil, B. D. Belle, F. Schedin, A.

Mishchenko, T. Georgiou, M. I. Katsnelson, L. Eaves, S. V. Morozov,

et al., Science 335, 947 (2012).13W. J. Yu, Z. Li, H. Zhou, Y. Chen, Y. Wang, Y. Huang, and X. Duan, Nat.

Mater. 12, 246 (2012).14A. K. Geim and I. V. Grigorieva, Nature (London) 499, 419 (2013).15G. Giovannetti, P. A. Khomyakov, G. Brocks, P. J. Kelly, and J. van den

Brink, Phys. Rev. B. 76, 073103 (2007).16H. Terrones, F. L�opez-Ur�ıas, and M. Terrones, Sci. Rep. 3, 1549 (2013).17N. Myoung, K. Seo, S. J. Lee, and G. Ihm, ACS Nano 7, 7021 (2013).18G.-H. Lee, Y.-J. Yu, X. Cui, N. Petrone, C.-H. Lee, M. S. Choi, D.-Y. Lee,

C. Lee, W. J. Yoo, K. Watanabe et al., ACS Nano 7, 7931 (2013).19Y. Murata, E. Starodub, B. B. Kappes, C. V. Ciobanu, N. C. Bartelt, K. F.

McCarty, and S. Kodambaka, Appl. Phys. Lett. 97, 143114 (2010).20B. B. Kappes, A. Ebnonnasir, S. Kodambaka, and C. V. Ciobanu, Appl.

Phys. Lett. 102, 051606 (2013).21Y. Murata, S. Nie, A. Ebnonnasir, E. Starodub, B. B. Kappes, K. F.

McCarty, C. V. Ciobanu, and S. Kodambaka, Phys. Rev. B 85, 205443

(2012).22K. Roy, M. Padmananabham, S. Goswami, T. P. Sai, S. Kaushal, and A.

Ghosh, Solid State Commun. 175–176, 35 (2013).23E. Scalise, M. Houssa, G. Pourtois, V. Afanase, and A. Stesmans, Nano

Res. 5, 43 (2011).24W. S. Yun, S. W. Han, S. C. Hong, I. G. Kim, and J. D. Lee, Phys. Rev. B

85, 033305 (2012).25M. Ghorbani-Asl, S. Borini, A. Kuc, and T. Heine, Phys. Rev. B 87,

235434 (2013).26J. M. Soler, E. Artacho, J. D. Gale, A. Garcia, J. Junquera, P. Ordej�on, and

D. S. S�anchez-Portal, J. Phys.: Condens. Matter 14, 2745 (2002).27N. Troullier and J. L. Martins, Phys. Rev. B 43, 8861 (1991).28J. Klime�s, D. R. Bowler, and A. Michaelides, Phys. Rev. B 83, 195131

(2011).29A. Kumar and P. K. Ahluwalia, Modell. Simul. Mater. Sci. Eng. 21,

065015 (2013).30H. S. Mok, A. Ebnonnasir, Y. Murata, S. Nie, K. F. McCarty, C. V.

Ciobanu, and S. Kodambaka, Appl. Phys. Lett. 104, 101606 (2014).31P. Joensen, E. D. Crozier, N. Alberding, and R. F. Frindt, J. Phys. C: Solid

State Phys. 20, 4043 (1987).32D. Yang, S. J. Sandoval, W. M. R. Divigalpitiya, J. C. Irwin, and R. F.

Frindt, Phys. Rev. B 43, 12053 (1991).33H.-P. Komsa and A. V. Krasheninnikov, Phys. Rev. B 88, 085318 (2013).34A. Molina-S�anchez and L. Wirtz, Phys. Rev. B 84, 155413 (2011).35See supplementary material at http://dx.doi.org/10.1063/1.4891430 for the

atomic coordinates associated with each structure shown in Fig. 1, and for

a detailed description of the tight-binding calculations.36J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth,

and S. Roth, Nature (London) 446, 60 (2007).37J. Brivio, D. T. L. Alexander, and A. Kis, Nano Lett. 11, 5148 (2011).38S. Y. Zhou, G. H. Gweon, J. Graf, A. V. Fedorov, C. D. Spataru, R. D.

Diehl, Y. Kopelevich, D. H. Lee, S. G. Louie, and A. Lanzara, Nat. Phys.

2, 595 (2006).39W. Jin, P. Yeh, N. Zaki, D. Zhang, J. T. Sadowski, A. Al-Mahboob, A. M.

van der Zande, D. A. Chenet, J. I. Dadap, I. P. Herman, P. Sutter, J. Hone,

and R. M. Osgood, Jr., Phys. Rev. Lett. 111, 106801 (2013).40P. Miro, M. Ghorbani-Asl, and T. Heine, Adv. Mater. 25, 5473 (2013).41Z. Yan, Y. Liu, L. Ju, Z. Peng, J. Lin, G. Wang, H. Zhou, C. Xiang, E. L.

G. Samuel, C. Kittrell, V. I. Artyukhov, F. Wang, B. I. Yakobson, and J.

M. Tour, Angew. Chem. Int. Ed. 53, 1565 (2014).

FIG. 5. Electronic charge transfer between the MoS2 and graphene layers

for two different relative orientations present in (a) the 4:5z and (b) the 4:3a

structures. The insets are side views for the normal cross-sections shown as

dashed lines in the main (top) views. The three-lobed contours in panel (a)

show the specific local registries that cause the weakening of Mo–S bonds.

031603-4 Ebnonnasir et al. Appl. Phys. Lett. 105, 031603 (2014)

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 130.39.62.90

On: Sun, 24 Aug 2014 09:07:12

42Y. Ma, Y. Dai, M. Guo, C. Niu, and B. Huang, Nanoscale 3, 3883 (2011).43C. Hamaguchi, Basic Semiconductor Physics, 2nd ed. (Springer, 2010), p. 388.44A. Castellanos-Gomez, R. Roldan, E. Cappelluti, M. Buscema, F. Guinea,

H. S. J. van der Zant, and G. A. Steele, Nano Lett. 13, 5361 (2013).

45E. Cappelluti, R. Roldan, J. A. Silva-Guillen, P. Ordej�on, and F. Guinea,

Phys. Rev. B 88, 075409 (2013).46A. Shmeliov, M. Shannon, P. Wang, J. S. Kim, E. Okunishi, P. D. Nellist,

K. Dolui, S. Sanvito, and V. Nicolosi, ACS Nano 8, 3690 (2014).

031603-5 Ebnonnasir et al. Appl. Phys. Lett. 105, 031603 (2014)

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