Superatomic Two-Dimensional SemiconductorXinjue Zhong,† Kihong Lee,† Bonnie Choi,† Daniele Meggiolaro,§,⊥ Fang Liu,† Colin Nuckolls,†

Abhay Pasupathy,‡ Filippo De Angelis,*,§,⊥ Patrick Batail,*,†,¶ Xavier Roy,*,† and Xiaoyang Zhu*,†

†Department of Chemistry and ‡Department of Physics, Columbia University, New York, New York 10027, United States§Computational Laboratory for Hybrid/Organic Photovoltaics (CLHYO), CNR-ISTM, Via Elce di Sotto 8, I-06123 Perugia, Italy⊥D3-CompuNet, Istituto Italiano di Tecnologia, Via Morego 30, 16163 Genova, Italy¶Laboratoire MOLTECH, CNRS UMR 6200, Universite d’Angers, 49045 Angers, France

*S Supporting Information

ABSTRACT: Structural complexity is of fundamental interest inmaterials science because it often results in unique physicalproperties and functions. Founded on this idea, the field of solidstate chemistry has a long history and continues to be highlyactive, with new compounds discovered daily. By contrast, the areaof two-dimensional (2D) materials is young, but its expansion,although rapid, is limited by a severe lack of structural diversity andcomplexity. Here, we report a novel 2D semiconductor with ahierarchical structure composed of covalently linked Re6Se8clusters. The material, a 2D structural analogue of the Chevrelphase, is prepared via mechanical exfoliation of the van der Waals solid Re6Se8Cl2. Using scanning tunneling spectroscopy,photoluminescence and ultraviolet photoelectron spectroscopy, and first-principles calculations, we determine the electronicbandgap (1.58 eV), optical bandgap (indirect, 1.48 eV), and exciton binding energy (100 meV) of the material. The latter isconsistent with the partially 2D nature of the exciton. Re6Se8Cl2 is the first member of a new family of 2D semiconductors whosestructure is built from superatomic building blocks instead of simply atoms; such structures will expand the conceptual designspace for 2D materials research.

KEYWORDS: Superatomic crystals, 2D semiconductor, exciton binding energy, van der Waals solid

The family of 2D materials1 includes the semimetalgraphene,2 semiconducting transition metal dichalcoge-

nides (TMDCs),3−5 and insulating hexagonal boron nitride (h-BN).6,7 Such materials have received widespread attention dueto their novel 2D properties that are distinct from their bulkcounterparts. Because of poor dielectric screening in the 2Dgeometry and quantum confinement, electronic excitations inthese materials are excitonic in nature.8−11 These uniqueproperties offer new possibilities for fundamental research andfor diverse applications in electronics, optoelectronics, andvalleytronics.12−15

Nearly all 2D materials to date are atomic solids withrelatively simple crystal structures. For example, graphene andh-BN consist of a single layer of atoms, and each TMDC iscomposed of a monolayer of transition metal atom sandwichedbetween two layers of chalcogen atoms. Beyond these simplelattices, there is a growing interest in designing 2D materialswith complex, hierarchical, or tunable structures.16−18 In thiscontext, cluster materials are attractive targets due to theirsynthetic flexibility and their exciting optical, electronic, andmagnetic properties that derive from the cluster units. Despitethe remarkable bulk properties of cluster materials,19−21 2Danalogues of such structure-type have not been prepared. Wehave recently reported a new family of “superatomic crystals”assembled from molecular clusters,22,23 some of which have

layered van der Waals structures.24 However, the lack ofcovalent bonding between the superatoms prevents theirexfoliation down to few layers.In this report, we investigate Re6Se8Cl2, a van der Waals

material derived from the Chevrel phase in which [Re6Se8]clusters are covalently linked into layers capped by terminal Clatoms.25 We show that the strong in-plane intercluster bondingand weak interlayer interactions allow mechanical exfoliation,and their stability under ambient conditions offers additionalbenefits. Re6Se8Cl2 was first reported in 1983 by Sergent andco-workers, but little is known about its electronic properties(e.g., the 2D nature of the band structure and associated strongexcitonic effect).26,27 To better understand these properties, wecarry out scanning tunneling microscopy/spectroscopy (STM/STS) measurement, combined with photoluminescence spec-troscopy (PL) and ultraviolet photoelectron spectroscopy(UPS), on freshly cleaved Re6Se8Cl2 crystals. The experimentalfindings are supported by density functional theory (DFT)calculations on both bulk and monolayer Re6Se8Cl2. We findthat bulk Re6Se8Cl2 is an indirect bandgap material with the

Received: December 15, 2017Revised: January 24, 2018Published: January 25, 2018

Letter

pubs.acs.org/NanoLettCite This: Nano Lett. 2018, 18, 1483−1488

© 2018 American Chemical Society 1483 DOI: 10.1021/acs.nanolett.7b05278Nano Lett. 2018, 18, 1483−1488

valence band maximum (VBM) located at the Γ point, and theconduction band minimum (CBM) at the T point inmomentum space. STS and PL spectroscopy reveal anelectronic bandgap of 1.58 ± 0.03 eV and an optical bandgapof 1.48 eV ± 0.01 eV, respectively. We thus deduce a largeexciton binding energy of ∼100 meV.28,29 On the basis of STScharacterization of atomic-scale defects and DFT calculations,we suggest that Cl vacancies are midgap states and areresponsible for n-type doping.All measurements are performed on single crystals of

Re6Se8Cl2 grown by chemical vapor transport. The material isfirst synthesized as microcrystalline powder by heating astoichiometric mixture of Re, Se, and ReCl5 to 1100 °C in afused silica tube sealed under vacuum. Millimeter-sized singlecrystals are then grown by chemical vapor transport in atemperature gradient of 970−920 °C in the presence of a smallexcess of ReCl5 as the transporting agent (see SyntheticDetails). The structure of isolated crystals is determined bysingle crystal X-ray diffraction (SCXRD), and the phase purityof each sample is confirmed by powder X-ray diffraction(PXRD) (Figure S1). The Re6Se8Cl2 lattice is built fromisolated Re6 octahedra enclosed in Se8 cubes. Each cluster unitis linked to four neighbors in the basal plane through strongRe2Se2 bonds and is capped by two terminal Cl atoms in theapical positions (Figure 1a). The layers are pseudosquarelattices of tilted clusters, with lattice parameters a = 6.60 Å, b =6.64 Å, and γ = 93.6°.26,30 The lattice parameter normal to thelayers is c = 9.07 Å.Our initial attempts at mechanical exfoliation using the

Scotch tape method produced rectangular flakes as thin as ∼15nm, as determined by atomic force microscopy (AFM) (Figure1b). Experiments to prepare Re6Se8Cl2 monolayers arechallenging and are presently underway. Here, we focus onthe 2D semiconducting properties of multilayer Re6Se8Cl2flakes and bulk samples by performing measurements onfreshly exfoliated surfaces.We determine the optical gap of Re6Se8Cl2 by optical

absorption and PL spectroscopies. By combining white lighttransmittance and reflectance measurements of thin flakes ontransparent substrates, we numerically solve for the refractiveindex and extinction coefficient. Figure 2a (red) presents theresulting absorption spectrum. The onset of absorption gives anoptical gap EOG = 1.49 ± 0.02 eV, in agreement with the PLspectrum peak at EOG = 1.48 ± 0.01 eV. The experimentallydetermined real and imaginary parts of the dielectric function

are in Figure S2. The valence band structure of the synthesizedRe6Se8Cl2 crystals are mapped out by UPS, Figure 2b, the onsetof which gives a valence band maximum (VBM) at EVBM = 1.45± 0.01 eV below the Fermi level (EF). This places EF close tothe conduction band minimum (CBM), implying thatRe6Se8Cl2 is an n-type semiconductor, in agreement with anearly report based on electrochemistry27 and our STSmeasurements discussed below.The temperature-dependent PL spectra in Figure 2c indicate

that the bandgap of Re6Se8Cl2 is indirect. The PL intensityincreases with increasing temperature over the broad temper-ature range of 80−300 K. The plot of PL intensity as a functionof temperature confirms that PL emission is thermally activatedwith an activation energy of 42.2 ± 1.4 meV (Figure S3). Thisis consistent with a radiative recombination mechanism in anindirect-bandgap semiconductor where phonons provide thenecessary momentum conservation.The indirect bandgap is confirmed by density functional

theory (DFT) calculations. We calculate the band structure of

Figure 1. Crystal structure and exfoliation of the 2D van de Waals solid Re6Se8Cl2. (a) Side view (top) of the ab plane and top view (bottom) of asingle layer. Color code: Re, blue; Se, red; Cl, green. (b) Exfoliated Re6Se8Cl2 flakes on SiO2/Si. The height profile in red (insert) shows thethickness of a ∼15 nm thin flake.

Figure 2. Electronic structure from spectroscopies and first-principlescalculations. (a) Optical absorption (red) and photoluminescence(black) spectra of Re6Se8Cl2. The onset of absorption spectrum at 1.49± 0.02 eV agrees with the PL peak position at 1.48 ± 0.01 eV. (b)Ultraviolet photoemission spectrum of Re6Se8Cl2 showing the VBM at1.45 eV below EF. (c) Temperature-dependent PL of Re6Se8Cl2showing an increase in PL intensity with increasing temperature,suggesting an indirect bandgap. (d) Calculated DFT band structurewith PBE-SOC (solid black line) and HSE06-SOC (blue dots).

Nano Letters Letter

DOI: 10.1021/acs.nanolett.7b05278Nano Lett. 2018, 18, 1483−1488

1484

Re6Se8Cl2 on the experimental geometry by using the Perdew−Burke−Ernzherof (PBE) functional31 and refine the calculationwith the Heyd−Scuseria−Ernzerhof (HSE06) functional,32

both including spin−orbit coupling (SOC). Figure 2d showsthe PBE-SOC band structure (black curves) and HSE06-SOCrefinements at selected high-symmetry k points (blue dots).The HSE06-SOC band structure gives an indirect bandgap ofEG = 1.49 eV between the VBM at Γ (0, 0, 0) and theconduction band minimum (CBM) at T (0, 0.5, 0.5).Compared to the results at the PBE-SOC level, HSE06-SOCmainly affects the valence band, down-shifting the VBM energyby ∼0.4 eV with respect to that calculated with PBE-SOC. Thecomputational results support the observed indirect bandgapand are in nearly quantitative agreement with the measuredbandgap from STS, as detailed below.We characterize the structure of the 2D plane of Re6Se8Cl2

using STM. Figure 3a shows an STM image at roomtemperature. The surface is ultraflat with average roughnessof only 0.4 Å; see also Figure S4 for large area AFM images.The inset in Figure 3a shows a step height of 8.9 Å along thered line, in agreement with the monolayer thickness determinedby SCXRD. A high-resolution STM image, Figure 3b, revealsthat the topmost Cl atoms arrange in a rhombic lattice structurewith lattice parameters of a = 6.5 ± 0.2 Å, b = 6.6 ± 0.3 Å, andα = 89°, respectively (Figure 3c), in good agreement withprevious reports.26,30 The tilt of the clusters is also noticeable inthe STM image, as suggested by the apparent off-centeredposition of the Cl atoms. A Fourier transform of the image(inset in Figure 3b) identifies the pseudo-4-fold symmetry ofthe 2D lattice plane.We determine the single-particle band structure by current−

voltage (I−V) measurement in STS. Figure 3d displays I−V(blue) and dI/dV−V (red) curves acquired on a cleavedRe6Se8Cl2 surface. Each I−V or dI/dV−V curve is an average

over 100 curves under the same tunneling conditions. Wedetermine the positions of the VBM and CBM by taking thelogarithm of dI/dV (see details in Figure S5). The VBM islocated at −1.50 V ± 0.03 V and the CBM at +0.08 ± 0.01 V.These give the electronic bandgap EG = ECBM − EVBM = 1.58 ±0.03 eV. The positions of the band edges relative to EF confirmn-doping.On the basis of the optical bandgap and the electronic

bandgap, we calculate an exciton binding energy of EB = EG −EOG = 100 ± 30 meV, which is one order of magnitude largerthan typical values in conventional 3D semiconductors (e.g., Si,Ge)33,34 but comparable to that in a typical 2D van der Waalslayered semiconductor such as MoS2.

28,29 To put the measuredEB = 100 ± 30 meV value in perspective, we calculate theexciton binding energies based on a 3D or a 2D Bohr model.35

We use the effective electron and hole masses (me* and mh*,respectively) from the PBE-SOC band structure in highsymmetry directions: mh* = 0.66me (in the Γ−V or Γ−Xdirection) and me* = 1.15me (in the T−V or T−X direction);me is the free electron mass. On the basis of the exciton reducedmass μ = 1/(mh*

−1 + me*−1) and the measured dielectric

constant εr* ≈ 10.5 at ∼1.5 eV (Figure S2), we calculate exciton

binding energies: = *μεℏ

E enB

3D2

4

2r

2 2 = 50 meV in 3D and

=*

μ

εℏ −( )E e

nB2D

2

4

2r

2 12

2 = 200 meV in 2D, where n = 1 for the

ground excitonic state. The experimental binding energy EB =100 ± 30 meV is between these two limiting values andsuggests a partial 2D nature of excitons in Re6Se8Cl2. This isexpected from a 2D layered van der Waals structure with weakinterlayer electronic coupling.Having established the band structure of Re6Se8Cl2, we now

turn to the electronic properties of defects and the origin of n-doping. We characterize defects on the surface of Re6Se8Cl2 by

Figure 3. In-plane structure and bandgap of Re6Se8Cl2 from STM/STS. (a) STM image at 292 K (80 × 80 nm2, U = 1.0 V, I = 50 pA). The lineprofile in the inset shows a step height of 8.9 Å, consistent with the thickness of a monolayer. (b) High-resolution STM image of Re6Se8Cl2 at 292 K(8 × 8 nm2, U = 0.6 V, I = 100 pA). The inset is the fast Fourier transform of the image. (c) Line profiles along the green and blue cuts in panel b.The average periodicity along the two directions is 6.5 ± 0.2 Å or 6.6 ± 0.3 Å, respectively. (d) STS spectrum with I−V curve in blue and the dI/dV−V curve in red. The VBM and CBM are designated by the black dashed lines, giving a bandgap of 1.58 eV.

Nano Letters Letter

DOI: 10.1021/acs.nanolett.7b05278Nano Lett. 2018, 18, 1483−1488

1485

STM/STS, in combination with DFT calculations. Figure 4ashows an atomic resolution image with defects appearing asdark spots at positive bias voltage (marked by blue arrows).The density of surface defects is ∼1.5%, as determined by STM.The inset shows an individual defect with apparent depth andwidth about 1.0 and 8 Å, respectively, consistent with Clvacancies (Figure S6). The loss of an electronegative atom froma polar semiconductor is expected to result in n-doping, as isalso known for S vacancies in MoS2.

36−38 STS spectra collectedon top of defects reveal a midgap peak at 0.67 eV below EF, asshown in Figure 4b.DFT calculations on a 2 × 2 × 2 supercell with one Cl

vacancy in the 2 × 2 supercell confirms the nature of thedefects. The projected density of states (PDOS) shows adistinct localized Kohn−Sham (KS) state in the middle of thebandgap (Figure 4d). This midgap defect state is associatedwith the unpaired electron on the Re atom, as illustrated in thereal space plot of the highest molecular orbital (HOMO) of theneutral Cl vacancy on the 2D sheet in Figure 4c.The results presented in this work establish Chevrel-type

Re6Se8Cl2 as the first member of the 2D hierarchicalsemiconductor family. An obvious research direction is tooptimize the exfoliation method to reach the monolayer limitand these efforts are underway in our laboratories. Ourcalculations at the HSE06-SOC level reveal that the bandgap ofRe6Se8Cl2 increases from 1.49 eV in the bulk to 1.72 eV at themonolayer limit and remains indirect (Figure S9). Compared toother 2D materials,1 the uniquely complex structure ofRe6Se8Cl2 offers stimulating prospects for designing multiplefunctions and studying novel properties. The presence ofsubstitutional labile Cl atoms on the surface of each Re6Se8Cl2layer opens the door to surface functionalization viasubstitution chemistry, which could allow tuning of theelectronic structure. Moreover, the limited interclusterelectronic coupling within each layer produces an electronic

structure with narrow bandwidth (≤0.5 eV in Figure 2d), whichis expected to be highly sensitive to phonon modes arising fromthe collective motions of the “superatomic” units. The 2Dhierarchical structure of Re6Se8Cl2 is thus an intriguing modelsystem for investigating strong electron−phonon coupling andrelated electronic phase transitions.

Synthetic Details. A mixture of Re (330 mg, 1.7 mmol), Se(190 mg, 2.4 mmol), and ReCl5 (200 g, 0.5 mmol) wasintimately ground in an inert atmosphere, pressed into a pellet,and sealed in a quartz tube under vacuum. The sample washeated to 1100 °C with a ramp of 1 °C/min and held at 1100°C for 3 days. The reaction took place in the presence of ReCl5vapor that was maintained by the addition of slight excess of Reand ReCl5. Large-single crystals of mm scale can be grown bysubsequent chemical transport using ReCl5 as the transportreagent with a temperature gradient of 970−920 °C. Largecrystals are deposited at the cooler end of the tube. Beforeopening the sealed tube, the excess ReCl5 that were depositedon the crystals was removed by condensing it to the cooler sideof the tube by maintaining the tube under a temperaturegradient of 300−25 °C for about 3 h.

Absorption/PL. Transmittance and reflectance spectra onthin films were collected and converted to absorption spectrum.Thin film samples were prepared by mechanically exfoliatingthe single crystals of Re6Se8Cl2 and then characterized withAFM. Two different white light sources were used to measure∼30 nm thin samples with 40× objectives. Transmitted andreflected lights were collected and spectrally resolved withPrinceton Instruments PhotonMAX EMCCD camera.Photoluminescence spectra were taken on bulk Re6Se8Cl2

crystal. Crystals were cleaved before mounting onto a cryostatto achieve clean surface. 100 W/cm2 532 nm CW laser wasilluminated on a crystal and the emission from sample wascollected with Princeton Instruments PyLoN-IR InGaAscamera. The sample was first cooled with liquid nitrogen, and

Figure 4. Defects on the Re6Se8Cl2 surface. (a) STM image of a Re6Se8Cl2 surface showing point defects marked by the blue arrows (32 × 32 nm, U= 0.6 V, I = 100 pA). The inset is a high-resolution image of a single defect. (b) dI/dV spectrum collected on top of the defect circled in panel a,showing a midgap state at −0.67 V. (c) Real space plot of the HOMO of a single neutral on the 2D sheet, indicating the localization of unpairedelectron on the Re site. (d) Log(PDOS) of the neutral Cl vacancy on the 2D sheet system, as calculated using HSE06-SOC.

Nano Letters Letter

DOI: 10.1021/acs.nanolett.7b05278Nano Lett. 2018, 18, 1483−1488

1486

spectra were acquired at temperature from 80 to 300 K (roomtemperature) in increments of 20 K.UPS. Measurements were carried out on cleaved Re6Se8Cl2

crystals with 39 eV extreme UV (XUV) radiation at roomtemperature. Freshly cleaved samples were transferred into anultrahigh vacuum chamber (∼10−10 Torr) where it was furtherannealed at 200 °C for 4 h. The XUV radiation forphotoemission was obtained from high harmonic generationin Ar, with a commercial ultrafast extreme UV source (KMLabs,XUUS) pumped by the fundamental laser output from aTi:sapphire amplifier (KMLabs, Wyvern, 5W, 40 fs, 10 kHz).The 25th harmonic output at 39 eV was selected with a gratingdownstream and applied for UPS measurements downstream.The XUV radiation was focused to a spot size of ∼150 μm witha spectral width of approximately 500 meV. The kinetic energyof the photoemitted electrons was measured using a hemi-spherical electron energy analyzer equipped with a 2D delayline detector (SPECS Phoibos-100).STM/STS. We carried out experiments on freshly cleaved

Re6Se8Cl2 crystals using the Omicron scanning tunnelingmicroscopy at room temperature (292 K) in an ultrahighvacuum (base pressure <4.0 × 10−10 mtorr). Although we didnot determine the exact thickness of the samples used in STM/STS, we estimated that they were thicker than those used inoptical absorption spectroscopy (∼30 nm), as judged fromoptical images. We obtained the STM images in the constant-current mode with an electrochemically etched tungsten tip. Toavoid tip artifacts, the STM tip was calibrated on a cleanAu(111) surface before all measurements. We obtaineddifferential conductance (dI/dV) spectra using a lock-inamplifier at an AC modulation of 10 mV and at a frequencyof 891.1 Hz. The corresponding current change was acquiredby keeping the tip fixed above the surface with the feedbackloop off. dI/dV spectra were consistent at various spots on thesurface with different tips at the same tunneling conditions andfrom different crystals.Computational Details. DFT calculations were performed

on the pristine 3D bulk (periodic boundary conditions) and 2Dsingle sheet of Re6Se8Cl2 by modeling both the pristine and Cldefective systems, that is, VCl in the supercell approach. Theequilibrium structures of the 3D bulk pristine and defectivesystems were found by relaxing ions positions while keeping thecell parameters fixed to the experimental values: a = 6.598 Å, b= 6.640 Å, c = 9.071 Å, α = 100.19°, β = 113.52°, and γ =93.64°.27 The 2D systems were modeled by fixing parameters aand b to the lattice constant and enlarging the cell along c witha vacuum layer of 12 Å. The VCl defective system wasinvestigated both in the bulk by modeling the vacancy in a 2 ×2 × 2 supercell and on the 2D sheet by creating the vacancy inthe 2 × 2 supercell.Geometry relaxations were performed by using the Perdew−

Burke−Ernzherof (PBE) exchange correlation functional,31

plane waves basis set, and ultrasoft pseudopotentials. A cutoffon the wave functions of 40 Ryd (320 Ryd on the chargedensity) and converged Monkhorst−Pack grids of k points inthe BZ were used. For all investigated systems, structures wererelaxed until forces acting on ions were less than 0.001 Ryd/Å.The electronic structures were then refined by using the hybridHSE06 exchange correlation functional32 including the spin−orbit interactions. Hybrid calculations were performed on theequilibrium structures optimized by PBE by using norm-conserving pseudopotentials with a cutoff on the wave

functions of 70 Ryd. All calculations were carried out byusing the Quantum Espresso software package.39

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.nano-lett.7b05278.

XRD characterizations of bulk Re6Se8Cl2; dielectricfunction and absorption coefficient; PL intensity versustemperature; AFM characterization on bulk Re6Se8Cl2;electronic band gap determination; line profiles ofdefects; statistics of VBM, CBM, and bandgap;evaluation of tip-induced band bending effects; DFTband structure calculations on monolayer Re6Se8Cl2(PDF)

■ AUTHOR INFORMATIONCorresponding Authors*E-mail: xyzhu@columbia.edu. Phone: 001-212-851-7768.*E-mail: xr2114@columbia.edu.*E-mail: patrick.batail@univ-angers.fr.*E-mail: filippo@thch.unipg.it.ORCIDColin Nuckolls: 0000-0002-0384-5493Abhay Pasupathy: 0000-0002-2744-0634Filippo De Angelis: 0000-0003-3833-1975Patrick Batail: 0000-0001-7125-5009Xavier Roy: 0000-0002-8850-0725Xiaoyang Zhu: 0000-0002-2090-8484Author ContributionsX.Zh. and K.L. contributed equally to this work.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSCrystal synthesis, sample preparation, STM/STS character-ization, and UPS experiments were supported by the NSFMRSEC program through the Center for Precision Assembly ofSuperstratic and Superatomic Solids (DMR-1420634). Theoptical spectroscopy experiments were supported by the US AirForce Office of Scientific Research (AFOSR) Grant No.FA9550-18-1-0020. We thank Enric Canadell and PereAlemany for initial DFT calculations. B.C. is supported bythe NSF Graduate Research Fellowship under Grant No. DGE11-44155.

■ REFERENCES(1) Novoselov, K. S.; Mishchenko, A.; Carvalho, A.; Castro Neto, A.H. Science 2016, 353, aac9439.(2) Novoselov, K. S.; Fal'ko, V. I.; Colombo, L.; Gellert, P. R.;Schwab, M. G.; Kim, K.; Ko, V. I. F.; Colombo, L.; Gellert, P. R.;Schwab, M. G.; Kim, K. Nature 2012, 490, 192−200.(3) Mak, K.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. Phys. Rev. Lett.2010, 105, 136805.(4) Splendiani, A.; Sun, L.; Zhang, Y.; Li, T.; Kim, J.; Chim, C. Y.;Galli, G.; Wang, F. Nano Lett. 2010, 10, 1271−1275.(5) Xu, X.; Yao, W.; Xiao, D.; Heinz, T. F. Nat. Phys. 2014, 10, 343−350.(6) Watanabe, K.; Taniguchi, T.; Kanda, H. Nat. Mater. 2004, 3,404−409.

Nano Letters Letter

DOI: 10.1021/acs.nanolett.7b05278Nano Lett. 2018, 18, 1483−1488

1487

(7) Song, L.; Ci, L.; Lu, H.; Sorokin, P.; Jin, C.; Ni, J.; et al. Nano Lett.2010, 10, 3209−3215.(8) Ramasubramaniam, A. Phys. Rev. B: Condens. Matter Mater. Phys.2012, 86, 115409.(9) Berkelbach, T. C.; Hybertsen, M. S.; Reichman, D. R. Phys. Rev.B: Condens. Matter Mater. Phys. 2013, 88, 45318.(10) Chernikov, A.; Berkelbach, T. C.; Hill, H. M.; Rigosi, A.; Li, Y.;Aslan, O. B.; Reichman, D. R.; Hybertsen, M. S.; Heinz, T. F. Phys.Rev. Lett. 2014, 113, 76802.(11) Ugeda, M. M.; Bradley, A. J.; Shi, S.-F.; da Jornada, F. H.;Zhang, Y.; Qiu, D. Y.; Mo, S.-K.; Hussain, Z.; Shen, Z.-X.; Wang, F.;Louie, S. G.; Crommie, M. F.; et al. Nat. Mater. 2014, 13, 1091−1095.(12) Koppens, F.; Mueller, T.; Avouris, P.; Ferrari, A.; et al. Nat.Nanotechnol. 2014, 9, 780−793.(13) Wang, Q. H.; Kalantar-Zadeh, K.; Kis, A.; Coleman, J. N.;Strano, M. S. Nat. Nanotechnol. 2012, 7, 699−712.(14) Xiao, D.; Liu, G. B.; Feng, W.; Xu, X.; Yao, W. Phys. Rev. Lett.2012, 108, 196802.(15) Mak, K. F.; Shan, J. Nat. Photonics 2016, 10, 216−226.(16) Jariwala, D.; Marks, T. J.; Hersam, M. C. Nat. Mater. 2017, 16,170−181.(17) Rahman, M.; Davey, K.; Qiao, S.-Z. Adv. Funct. Mater. 2017, 27,1606129.(18) Dou, L.; Wong, A. B.; Yu, Y.; Lai, M.; Kornienko, N.; Eaton, S.W.; Fu, A.; Bischak, C. G.; Ma, J.; Ding, T.; Ginsberg, N. S.; Wang, L.-W.; Alivisatos, A. P.; Yang, P. Science 2015, 349, 1518−1521.(19) Fischer, Ø. Appl. Phys. 1978, 16, 1−28.(20) Aurbach, D.; Lu, Z.; Schechter, A.; Gofer, Y.; Gizbar, H.;Turgeman, R.; Cohen, Y.; Moshkovich, M.; Levi, E. Nature 2000, 407,724−727.(21) Xie, W.; Luo, H.; Phelan, B. F.; Klimczuk, T.; Cevallos, F. A.;Cava, R. J. Proc. Natl. Acad. Sci. U. S. A. 2015, 112, E7048−54.(22) Roy, X.; Lee, C.-H.; Crowther, A. C.; Schenck, C. L.; Besara, T.;Lalancette, R. A.; Siegrist, T.; Stephens, P. W.; Brus, L. E.; Kim, P.;Steigerwald, M. L.; Nuckolls, C. Science 2013, 341, 157−160.(23) Turkiewicz, A.; Paley, D. W.; Besara, T.; Elbaz, G.; Pinkard, A.;Siegrist, T.; Roy, X. J. Am. Chem. Soc. 2014, 136, 15873−15876.(24) Choi, B.; Yu, J.; Paley, D. W.; Trinh, M. T.; Paley, M. V.; Karch,J. M.; Crowther, A. C.; Lee, C.-H.; Lalancette, R. A.; Zhu, X.-Y.; Kim,P.; Steigerwald, M. L.; Nuckolls, C.; Roy, X. Nano Lett. 2016, 16,1445−1449.(25) Gabriel, J.-C. P.; Boubekeur, K.; Uriel, S.; Batail, P. Chem. Rev.2001, 101, 2037−2066.(26) Le Nagard, N.; Perrin, A.; Sergent, M.; Levy-Clement, C. Mater.Res. Bull. 1985, 20, 835−843.(27) Leduc, L.; Perrin, A.; Sergent, M. Acta Crystallogr., Sect. C: Cryst.Struct. Commun. 1983, 39, 1503−1506.(28) Saigal, N.; Sugunakar, V.; Ghosh, S. Appl. Phys. Lett. 2016, 108,132105.(29) Komsa, H.-P.; Krasheninnikov, A. V. Phys. Rev. B: Condens.Matter Mater. Phys. 2012, 86, 241201.(30) Fischer, C.; Colell, H.; Tributsch, H. Surf. Sci. 1993, 280, 2−7.(31) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77,3865−3868.(32) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. J. Chem. Phys. 2003, 118,8207−8215.(33) Sturge, M. D. Phys. Rev. 1962, 127, 768−773.(34) McLean, T. P.; Loudon, R. J. Phys. Chem. Solids 1960, 13, 1−9.(35) Klingshirn, C. F. Semiconductor Optics; Springer: BerlinHeidelberg, 2012.(36) Santosh, K. C.; Longo, R. C.; Addou, R.; Wallace, R. M.; Cho, K.Nanotechnology 2014, 25, 375703.(37) Zhou, W.; Zou, X.; Najmaei, S.; Liu, Z.; Shi, Y.; Kong, J.; Lou, J.;Ajayan, P. M.; Yakobson, B. I.; Idrobo, J.-C. Nano Lett. 2013, 13,2615−2622.(38) Vancso, P.; Magda, G. Z.; Peto, J.; Noh, J.-Y.; Kim, Y.-S.;Hwang, C.; Biro, L. P.; Tapaszto, L. Sci. Rep. 2016, 6, 29726.(39) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.;Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I.;

Dal Corso, A.; de Gironcoli, S.; Fabris, S.; Fratesi, G.; Gebauer, R.;Gerstmann, U.; Gougoussis, C.; Kokalj, A.; Lazzeri, M.; Martin-Samos,L.; Marzari, N.; Mauri, F.; Mazzarello, R.; Paolini, S.; Pasquarello, A.;Paulatto, L.; Sbraccia, C.; Scandolo, S.; Sclauzero, G.; Seitsonen, A. P.;Smogunov, A.; Umari, P.; Wentzcovitch, R. M. J. Phys.: Condens.Matter 2009, 21, 395502.

Nano Letters Letter

DOI: 10.1021/acs.nanolett.7b05278Nano Lett. 2018, 18, 1483−1488

1488