Interlayer Interactions in van der Waals Heterostructures: Electronand Phonon PropertiesNam B. Le,†,‡ Tran Doan Huan,§ and Lilia M. Woods*,†

†Department of Physics, University of South Florida, Tampa, Florida 33620, United States‡Institute of Engineering Physics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi, Vietnam§Department of Materials Science & Engineering and Institute of Materials Science, University of Connecticut, 97 North EaglevilleRd., Storrs, Connecticut 06269-3136, United States

*S Supporting Information

ABSTRACT: Artificial van der Waals heterostructures constitute an emerging field thatpromises to design systems with properties on demand. Stacking patterns and theutilization of different types of chemically inert layers can deliver novel materials anddevices. Despite the relatively weak van der Waals interaction, which does not affect theelectronic properties around the Fermi level, our first-principles calculations showsignificant changes in the higher conduction and deeper valence regions in the consideredgraphene/silicene, graphene/MoS2, and silicene/MoS2 systems. Such changes are linkedto strong out-of-plane hybridization effects and van der Waals interactions. We also findthat the interface coupling significantly affects the vibrational properties of theheterostructures when compared to the individual constituents. Specifically, the vander Waals coupling is found to be a major factor for the stability of the system. Theemergence of shear and breathing modes, as well as the transformation of flexural modes,are also found.

KEYWORDS: van der Waals interactions and heterostructures, band structure and unfolding, interface phonons

■ INTRODUCTION

The discovery of graphene,1 an atomically thin layer ofhoneycomb C atoms, has inspired much interest not only inits basic and applied aspects, but also into finding other two-dimensional (2D) materials with various chemical composi-tions. This flourishing field has become a new realm forfundamental and device physics. Besides graphene, there areother 2D systems with hexagonally arranged atoms, such assilicene (composed of Si atoms) and germanene (composed ofGe atoms).2−5 Although these layers exhibit many commonproperties, the strong spin−orbit coupling and staggered latticedistinguish silicene and germanene as unique structurescompared to graphene.6−8 Single-layer transition metaldichalcogenides, such MoS2 and WSe2, for example, areanother class of 2D materials, in which the d-electronsinteractions give rise to interesting phenomena related tonovel spin, valley, and optoelectronic effects.9,10 Novelsynthesis techniques11 based on chemical methods ormechanical transfer have contributed toward numerousapplications of such materials in electronics, optics, and sensorsamong others.12

A new area of research utilizing layers of different kinds of2D materials has also emerged.13 Vertically stacking thesechemically inert systems, similar to toy building bricks,promises to achieve desired properties by design. While strongchemical bonds are responsible for the in-plane stability of eachlayer, the relatively weak van der Waals (vdW) interaction

holds the heterostructure (HS) stack together. Several two-layered HSs have already been synthesized showing thatexperimental advances of different stacking patterns can beused to achieve a system with an array of differentcharacteristics.14−18 Recent computational studies of 2D vdWHSs have also been reported.19−22 These investigations aretypically concerned with the energetic stability of the systemand mainly with the electronic band structures around theFermi level, where the energy bands are additive. Theoreticalstudies uncovering the evolution of the higher conduction andlower valence regions are lacking, however. The influence ofinterlayer hybridization in vdW HSs is of much interest notonly from a fundamental point of view, but also for practicalapplications in view of control and design of desired properties.Furthermore, interlayer optical coupling involving 2D

transition metal dichalcogenides has been demonstratedalready.23 Such interactions are inevitably connected with theunderstanding of changes in the electronic structure due to theinterlayer coupling. Thus, addressing the roles of the dispersivevdW interactions and the orbital overlap is necessary in order toprovide effective ways of tuning capabilities. Along these lines,determining universal and material specific hybridizationfeatures would be much desirable. The vibrational properties

Received: January 8, 2016Accepted: February 17, 2016Published: February 17, 2016

Research Article

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© 2016 American Chemical Society 6286 DOI: 10.1021/acsami.6b00285ACS Appl. Mater. Interfaces 2016, 8, 6286−6292

of vdW HSs are also of great interest. Studies of phononexcitations of homogeneous vdW systems (composed ofgraphenes only or MoX2 layers only, where X is the chalcogenatom) as a function of number of layers have shown there is adelicate balance between surface vs bulk effects.24−27 Theevolution of acoustic and other low-frequency modes, such asshear and breathing modes, for a given 2D vdW HS can hardlybe overestimated as such issues are of primary relevance tothermal conduction.In this study, using first-principles simulations, we investigate

the interface properties of the following 2D HSs: graphene/silicene (GR/SIL), graphene/MoS2 (GR/MoS2), and silicene/MoS2 (SIL/MoS2). It turns out that the vdW interaction is ofprimary importance for the electronic and vibrational propertiesof the studied systems. On one hand, the vdW interactiontogether with the orbital overlap leads to nontrivial changes inthe deeper valence and higher conduction regions in terms ofhybridization energy gaps. On the other hand, the vdWcoupling is found to be necessary for the vibrational stability ofthe HS, meaning that real phonon dispersion relations areachieved. The calculations are performed by constructingsupercells with periodic boundary conditions. For this purpose,several unit cells from each constituent are utilized, which,however, leads to artificially folded bands in the bandstructure.28 Such artificial folding inhibits the discovery ofimportant features in the electronic properties and makes thecomparison with experimental data difficult. Here we presentthe unfolded band structures for each HS projected on theindividual primitive Brillouin zones (BZ). We find that thereare emerging energy gaps in the conduction and valenceregions, which are explained in terms of interlayer hybridization

and vdW effects. The interface phonon properties are alsoinvestigated with acoustic, shear and breathing modes analyzedin terms of the interlayer interactions and comparisons with thephonon properties of the individual constituents.

■ RESULTS AND DISCUSSIONSThe calculations are performed using periodic boundaryconditions by constructing a supercell for each consideredsystem. Because the layered constituents have different bondlengths and lattice parameters, the supercells consist of severalunit cells of the individual layer. Specifically, the GR/SILstructure is formed by 9 graphene (18 atoms) and 4 silicene (8atoms) unit cells, the GR/MoS2 is formed by 25 graphene (50atoms) and 16 MoS2 (48 atoms) unit cells, and the SIL/MoS2is formed by 16 silicene (32 atoms) and 25 MoS2 (75 atoms)unit cells. The particular stacking configurations after relaxationwith respect to the atomic positions and lattice parameters areshown in Figure 1.The formation of each vdW HS introduces slight strains in

the 2D layers when compared with the individual, free-standingconstituent. These relative lattice strains are calculated via (aHS− a)/a, where aHS is the lattice constant of each layer in the HS(Table 1) and a is the lattice constant of the correspondinglayer with and without the vdW interaction, which is taken intoaccount via the DF2 functional as discussed in the Computa-tional Methods. For example, the graphene layer in the GR/SILstructure is expanded by 0.8%, while the silicene is shrunk by3.5% when compared with their free-standing counterparts. IfDF2 is included in the simulations, we find that after relaxationthe graphene expansion is slightly higher (1.0%), while thesilicene shrink is slightly less (−3.8%). The respective values for

Figure 1. Atomic representation for the (a) GR/SIL (9-GR; 4-SIL unit cells); (b) GR/MoS2 (25-GR; 16-MoS2 unit cells); (c) SIL/MoS2 (16-SIL,25-MoS2 unit cells) supercells; and (d) BZ and its characteristic points for GR/SIL. The interlayer separation is denoted as d.

Table 1. Structural Parameters Obtained after Relaxationa

HS GR/SIL GR/MoS2 SIL/MoS2

strain (%) no vdW +0.8/−3.5 +1.0/−2.1 +1.8/−1.0DF2 +1.0/−3.8 +1.9/−4.0 +3.5/−1.6

aHS (Å) no vdW 2.49/3.73 2.49/3.12 3.94/3.15DF2 2.50/3.75 2.52/3.15 4.04/3.23

d (Å) no vdW 4.28 4.32 3.98DF2 3.73 3.54 3.53

ΔE (meV) no vdW −1.28 −0.82 −2.43DF2 −28.07 −24.67 −34.57

charge transfer (e) no vdW 0.016 0.014 0.276DF2 0.034 0.046 0.755

aStrain values correspond to lattice expansion (+) or shrinking (−) with respect to the corresponding free layers. ΔE = EHS − (E1 + E2) is theenergy/atom (EHS, total energy for the HS; E1,2, total energy for each layer). The lattice structure constant aHS for each layer from the HS, theinterlayer spacing d, and the charge transfer are also shown.

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the other two HSs can also be found in Table 1. The latticechanges occurring in each HS can further be quantified bycomparing the nearest neighbor bond lengths, which are givenin Table 2. For example, the C−C distance of 1.425 Å in agraphene monolayer becomes 1.437 Å when graphene is in theGR/SIL HS and no vdW interaction is taken into account. Thiscorresponds to an overall 0.8% stretching denoted by the strainin Table 1. The other bond lengths are also shown in Table 2.We note that slight straining in order to achieve a compositestructure with different individual lattices is found in othersystems, such as graphene on Au, Ag, and SiC substrates.29−31

Our subsequent calculations indicate that comparing theproperties of the slightly strained individual layers with theproperties of the fully relaxed ones does not show significantdifferences, therefore one concludes that such small latticeparameters modifications have little effect on the vdW HScharacteristics.It is further found that the separation between the layers is

affected significantly by the vdW interactions. This distance isreduced upon taking into account the DF2 functional; thelargest reduction of 0.078 nm occurs for the GR/MoS2 system.The buckling of silicene as well as the thickness of MoS2 are notonly affected by the vdW interaction, but also by the specificHS, as can be seen from the thickness, H, of each layer inFigure S1 and Table S1 in the Supporting Information). TheDF2 correction generally enhances the silicene buckling andthe MoS2 thickness. Graphene also makes a big difference in Hwhen forming the particular HS, such that H of silicene isincreased by 0.112 Å, while H for MoS2 is increased by 0.086 Åwhen compared with their free counterparts (DF2 included inboth cases). Interestingly, the buckling of silicene in its HS withMoS2 is reduced by 0.036 Å. The role of the vdW interaction isalso significant when considering the energetic stability of eachstructure. Our results in Table 1 show that each vdW HS ismuch more stable upon the inclusion of the DF2 functional asthe corresponding energy is increased by at least an order ofmagnitude. The case of SIL/MoS2 is particularly noteworthy.The calculations indicate that the vdW interaction resultsenergetic stability that is 32.14 meV higher as compared to thecase of no DF2. We conclude that such long-range correctionsplay an important role for the stability of the layered HS andmust be included in the subsequent analysis.Our calculations also show there is charge transfer between

the layers in each HS, as can be seen in Table 1, which displaysthese values in units of the electron charge (e). Specifically, asmall amount of 0.016 (e) is transferred from graphene tosilicene, which is doubled if the vdW interaction is included.Graphene donates similar charge amount (0.014 (e)) to MoS2,which is increased to 0.046 (e) with DF2. In the case of SIL/MoS2, however, the MoS2 layer transfers 0.276 (e) charge tothe silicene layer, which is increased to 0.755 (e) uponincluding DF2.The electronic structure properties of the different HSs are

also calculated. The different number of unit cells for each layerused to construct the supercell result in two BZs with different

sizes, as shown in Figure 1d for GR/SIL. The resultingartificially folded bands are untangled and projected on theprimitive BZs of the individual components. The unfoldingprocedure is described in the Computational Methods sectionand the results are shown in Figure 2. Considering Figure 2a,

we see distinct Dirac-like bands crossing the Fermi level, suchthat the linear bands at the K-points belong to silicene, whilethe linear bands at the M-point belong to graphene. Anotherset of linear bands for graphene crossing at the Γ-point (barelyvisible in the graph) is also present. Comparing with the densityof states results in Figure 3a,b, it is determined that theelectronic structure around EF is essentially a superposition ofthe graphene and silicene individual contributions (SupportingInformation) from their out-of-plane π orbitals. Thus, the Diraccones for each layer are intact with well-preserved characteristiclinear dispersion.The electronic structure, however, is significantly altered in

the deeper valence and higher conduction regions. First, onenotes that while the vdW interaction does not affect theproperties close to the Fermi level, its role away from it is muchmore pronounced. The inclusion of DF2 results in shifting ofseveral of the characteristic peaks including those around −4,−2, and 2 eV regions (Figure 3a). In addition, the bandstructure projected on the primitive silicene cell (Figure 2a)shows that there are several energy gaps of rather significantmagnitude, opened in the conduction region around or below 2eV. These energy gaps, which are on the order of 0.3−0.05 eV,occur when strong hybridization between the π-states of C andSi happens, as evident in Figure 3b. Similar hybridization occursin the −2 and −4 eV regions, although the energy gaps aresmaller and they are visible on the GR/SIL band structure

Table 2. Nearest Neighbor Distances in Each Layer

monolayer GR/SIL GR/MoS2 SIL/MoS2

distance (Å) no vdW DF2 no vdW DF2 no vdW DF2 no vdW DF2

C−C 1.425 1.430 1.437 1.444 1.439 1.456Si−Si 2.278 2.306 2.234 2.249 2.310 2.378Mo−S 2.413 2.487 2.399 2.441 2.408 2.458

Figure 2. Band structures for (a) GR/SIL projected on the SIL BZ;(b) GR/MoS2 projected on the GR BZ; (c) GR/MoS2 projected onthe MoS2 BZ; (d) SIL/MoS2 projected on the MoS2 BZ. The openingof some energy gaps due to interlayer hybridization are circled in red.

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projected on the primitive cell of the graphene BZ (SupportingInformation).The electronic structure of the other two HSs exhibits similar

features. Figure 2b−d and Figure 3c−f show that again theenergy bands and DOS are a superposition of the contributionsfrom the graphene (silicene) and MoS2. While the correspond-ing Dirac bands cross EF, MoS2 is a conventional semi-conductor with parabolic dispersion and no states around EF.We find that the MoS2 in the GR/MoS2 HS is an indirect gapsemiconductor with a gap of 1.6 eV along the K−Γ path. MoS2from SIL/MoS2 has a direct gap of the same magnitude at theK-point. Although the magnitude of the energy gap of the freeMoS2 layer (a direct gap semiconductor) is not affected due tothe particular HS (Supporting Information), it is concludedthat the role of the graphene is more prominent as compared tosilicene. Specifically GR/MoS2 resembles the situation of two-

layer MoS2 system, which also exhibits similar transition to anindirect semiconductor when compared to the individuallayer.10

The vdW interaction is also important for the GR/MoS2 andSIL/MoS2 systems. The inclusion of the DF2 function leads toshifting of the DOS peaks toward the Fermi level whencompared to the DOS peaks with no DF2 corrections (Figure3c,e). These shifts are more pronounced for the deeper valenceand higher conduction regions. Further inspection of theelectronic structure shows that significant hybridization due tothe out-of-plane overlapping orbitals leads to strong mod-ifications farther away from EF. Figure 2b−d show the openingof several energy gaps as large as 0.3 eV along several directionsof the graphene and silicene bands in the (−4,−2) eV region.Similar situation is observed for the conduction range aroundor below 2 eV. These effects are due to hybridization of the p-orbitals (graphene or silicene) and the d-orbitals (MoS2) asindicated from the DOS results (Figure 3d,f). The strong out-of-plane character is quite prominent in these HSs similar tothe case of GR/SIL. It is interesting to note that recentexperimental studies32 have investigated the energy bandstructure of GR/MoS2, where ARPES measurements revealthat indeed the DOS for the individual constituents around theFermi level is preserved, while energy gaps due to orbitalhybridization occur deeper in the valence region, similar to thesimulations results found here.Understanding the vibrational properties is also important in

building a complete picture of the unique interface character-istics of the vdW heterostructures. Recent studies haveinvestigated graphene/h-BN systems, stacked 2D transitionmetal dichalcogenides, and few layer graphene structures.33−37

Much of the emphasis in these reports has been on the layerbreathing modes, since such vibrations are specific to astructure with two or more stacked layers. It has been shownthat breathing mode vibrations have relatively low frequenciesand they can be Raman or Infrared active.34,35 Characteristicenergetic shifts of these breathing modes in terms of number oflayers comprising the system have also been reported.34

In this study, we focus on the vibrational properties of GR/SIL and GR/MoS2 structures. Figure 4 summarizes our resultsfor the phonon bands and associated total and atomicallyresolved phonon DOS for each case. It turns out that the vdWinteraction is quite prominent here. Specifically, without takinginto account the DF2 functional, there are imaginary frequencybranches which indicate that the GR/SIL and GR/MoS2systems are unstable. Taking into account the vdW coupling

Figure 3. (a) Total DOS for free graphene, free silicene, GR/SIL withand without DF2. (b) Projected DOS for the p and pz orbitals forgraphene and silicene in the HS. (c) Total DOS for free graphene, freeMoS2, GR/MoS2 with and without DF2. (d) Projected DOS for the pand d orbitals for graphene and MoS2 in the HS. (e) Total DOS forfree silicene, free MoS2, and SIL/MoS2 with and without DF2. (f)Projected DOS for the p and d orbitals for silicene and MoS2 in theHS.

Figure 4. Phonon dispersion and density of states (total and atomically resolved) for (a) GR/SIL and (b) GR/MoS2. Schematics of the shear andbreathing modes are also given.

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leads to removing the imaginary frequency branches (Figure 4)stabilizing each HS.The three lowest frequency modes starting at the Γ-point

constitute the acoustic branches, which are compared to thecorresponding acoustic branches of the individual layers(Supporting Information). It is noted that unlike bulk materials,flexural modes are particularly important for surface systems asthey have the lowest frequency dispersion and they arenonlinear with respect to the wave vector. The role of suchvibrations in single graphene, silicene, and MoS2 has beenrecognized in many reports with theoretical and experimentalconsequences.38−40 Flexural modes have a large contribution tothe phonon DOS and they are responsible for the thermalconduction (even up to room temperature) for the individualgraphene, silicene, and MoS2. Such vibrations are dominatedmainly by boundary scattering as the phonon−phononscattering is relatively weak. The transport due to flexuralexcitations is almost ballistic with a characteristic frequencydispersion f = Dq2. Our simulations show that for graphene D =3.45 × 10−6 m2/s, for silicene D = 2.77 × 10−6 m2/s, and forMoS2 D = 4.68 × 10−6 m2/s along the Γ−M direction(Supporting Information).The transverse and longitudinal acoustic modes have linear

dispersion with characteristic group velocities displayed inTable 3. Comparing the phonon band structure for the

individual layers helps understand the thermal conductionproperties of the individual 2D systems. Phonon modes forgraphene are higher than those of MoS2 and silicene (by afactor of ∼3) indicating that the corresponding graphenevibrations carry more energy. This is an important factorcontributing to the graphene large thermal conductivity. On theother hand, the frequency gap between the acoustic and opticalregions in silicene and MoS2 forbids many phonon scatteringmechanisms indicating that the acoustic vibrations areprotected. Further examination of the dispersion shows thatthe GR/MoS2 flexural modes have departed from the quadraticwave vector dispersion and the frequency is f ∼ qx, where x =1.45. At the same time, this type of vibrations for the GR/SILsystem display a linear q-dependence along Γ−M (q − small).It is interesting to compare with other studied vdW structures.For example, for N ≤ 5 stacked graphenes the flexural modesare f ∼ qx where 1 ≤ x ≤ 2 (x = 1 for N = 5).35 While GR/MoS2 exhibits this intermediate flexural dispersion (x = 1.45),the flexural mode has acquired linear dispersion in GR/SIL.The departure from the f ∼ q2 behavior is associated withtransitioning of the system from an elastic 2D layer to lesselastic system which is not strictly two-dimensional.35

The results for the transverse and longitudinal acousticmodes in terms of their group velocities are also given in Table3. Comparing the obtained values, one finds that νTA,LA for theGR/SIL and GR/MoS2 HSs are significantly lower (by an orderof magnitude) than the corresponding values of the free

graphene. At the same time, while νTA for the considered HSs islarger than νTA for the free silicene and MoS2 components, theopposite trend is found for νLA for the HSs, which are slightlylarger than νLA for the individual silicene and MoS2.Nevertheless, there is a general phonon softening in the GR/SIL and GR/MoS2 systems which contributes to the decreaseof the thermal conductivity. In addition, the phonon modesdensity distribution for the HSs increases when compared tothe individual components, which means that the probabilitiesfor scattering processes is also increased. As a result, thescattering phonon time is going to be reduced resulting in adecreased thermal conductivity.Besides the acoustic vibrations, there are other low lying

frequency modes specific for stacking HSs. The two linear-likemodes starting at f = 0.085THz for GR/MoS2 are the shearmodes (Figure 4) with velocities shown in Table 3. Thecorresponding shear modes for GR/SIL start at two differentfrequencies, 0.117 THz and 0.135 THz, at Γ with linearvelocities in Table 3. In both cases, νS1,S2 have similar values toνTA,LA of single graphene. The next branch of the HSsconstitutes the breathing mode vibrations, characterized as anoptical mode, where the two layers move along a perpendicularto the layers direction. Figure 4 shows that the breathing startsat 2.11THz frequency for the GR/SIL systems, while the sametype of branch is found at 0.51 THz at the Γ-point for the GR/MoS2 system.The calculated phonon dispersion properties show that

graphene exhibits superior thermal transport because their lowenergy acoustic modes can carry much more energy ascompared to the ones for free silicene or MoS2. The thermalconduction capabilities, when compared with free graphene, arealso worsened when considering graphene vdW HSs, and theacoustic phonon softening is of importance here. Thetransformation of the flexural modes and the appearance ofshear and breathing modes, however, may be useful for probingother fundamental characteristics of the HSs.

■ CONCLUSIONS

Our investigation clearly demonstrates that the graphene andsilicene Dirac-like electronic properties of the vdW HSs aroundthe Fermi level are preserved, while MoS2 may exhibit direct toindirect semiconducting behavior. At the same time, theinterlayer hybridization results in the opening of several gaps inthe higher conduction and lower valence regions. Such gapsmay have a common behavior as they occur for all studiedsystems but for different energy ranges. This diversity suggestsan approach for tuning optical transitions in a particular layerby simply choosing a suitable component for the HS.Furthermore, the vdW interaction determines the vibrationalstability of the HSs. The flexural modes depart from thecharacteristic q2 dependence for the individual layers and theemergence of shear and breathing modes is demonstrated. Byshowing how the vibrational properties evolve, one canpotentially control the heat transfer in 2D systems,

■ COMPUTATIONAL METHODSThe first-principles simulations, reported in this work, are performedat the Density Functional Theory (DFT) level using the Vienna abinitio simulations package (VASP).41,42 The DFT Kohn−Shamequations are solved through the projector augmented wave (PAW)formalism43 with a plane wave basis set and periodic boundaryconditions. The exchange-correlation energy is described by thePerdew−Burke−Ernzerhof (PBE) functional.44 For all calculations, we

Table 3. Velocities of Transverse Acoustic (TA),Longitudinal Acoustic (LA), and Shear (S1, S2) Branches

structure νTA (m/s) νLA (m/s) νS1 (m/s) νS2(m/s)

GR/SIL 3706 7854 13 162 20 093GR/MoS2 4385 7053 11 075 16 189graphene 12 192 20 612silicene 4891 8561MoS2 3726 6150

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have used a plane wave cutoff of 600 eV and Brillouin zone samplingof 15 × 15 × 1 k-mesh for relaxation and density of states (DOS)calculations, and 25 × 25 × 25 k-mesh for obtaining the energy bandstructures. Atomic and cell variables are simultaneously relaxed with anenergy relaxation criteria of 10−5 eV until residual forces are found tobe less than −10−3 eV/Å.The long ranged vdW interaction is of key importance for holding

together the 2D HSs.45 Here, we use the vdW-DF2 functionalimplemented in VASP. This is a seamless way to take into accountlong-range electron correlation effects according to the Langreth−Lundqvist scheme.46 The vdW−DF2 nonlocal functional has beenextensively utilized for electronic structure calculations involving 2Dand 3D materials, in which vdW interactions may be present. Phononfrequency spectra of the examined structures are obtained using thePHONOPY package.47,48 With a sufficiently large relaxed supercell,finite atomic displacements with an amplitude of 0.01 Å areintroduced. The atomic forces within the supercell are calculatedusing VASP followed by phonon frequency calculations from thedynamical matrix represented in terms of the force constants.The unfolded band structures are obtained using BandUP,49 a state-

of-the-art code that enables obtaining a primitive cell representation ofa system simulated via the DFT supercell approach described above.Being able to generate an unfolded band structure projected on theparticular primitive cell for each layered component of the vdW HS isan important advantage. It provides common ground whencomparisons with experimental data obtained via angle-resolvedphotoemission spectroscopy (ARPES), for example.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acsami.6b00285.

Additional figures for the band structure and phononproperties (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: lmwoods@usf.edu.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSFinancial support from the Department of Energy under grantNo. DE-FG02-06ER46297 is acknowledged. We also acknowl-edge the use of the University of South Florida ResearchComputing facilities.

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