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Yosuke Uchiyama, Alex Kutana, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Kana Kojima, Takahiko Endo, Yasumitsu Miyata, Hisanori Shinohara, [Ryo Kitaura](https://orcid.org/0000-0001-8108-109X)

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[Momentum-forbidden dark excitons in hBN-encapsulated monolayer MoS2](https://mdr.nims.go.jp/datasets/c0504290-ed28-4091-9f5b-3321d717c46d)

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Momentum-forbidden dark excitons in hBN-encapsulated monolayer MoS2ARTICLE OPENMomentum-forbidden dark excitons in hBN-encapsulatedmonolayer MoS2Yosuke Uchiyama1, Alex Kutana 2, Kenji Watanabe 3, Takashi Taniguchi3, Kana Kojima4, Takahiko Endo4, Yasumitsu Miyata4,Hisanori Shinohara1 and Ryo Kitaura1Encapsulation by hexagonal boron nitride (hBN) has been widely used to address intrinsic properties of two-dimensional (2D)materials. The hBN encapsulation, however, can alter properties of 2D materials through interlayer orbital hybridization. In thispaper, we present measurements of temperature dependence of photoluminescence intensity from monolayer MoS2 encapsulatedby hBN flakes. The obtained temperature dependence shows an opposite trend to that of previously observed in a monolayer MoS2on a SiO2 substrate. This is caused by the existence of stable momentum-forbidden dark excitons in the hBN-encapsulated MoS2.Ab-initio band-structure calculations have shown that orbital hybridization between MoS2 and hBN leads to upward shift of Γ-valleyof MoS2, which results in lowering of energy of the momentum-forbidden dark excitons. This work shows an important implicationthat the hBN-encapsulated structures used to address intrinsic properties of two-dimensional crystals can alter basic properties ofencapsulated materials.npj 2D Materials and Applications            (2019) 3:26 ; https://doi.org/10.1038/s41699-019-0108-4INTRODUCTIONRecently appearing two-dimensional (2D) materials, includinggraphene, phosphorene, transition metal dichalcogenides (TMDs),etc., have opened up a new field in the science of low-dimensionalmaterials.1–6 TMDs, in particular, provide a wide variety of 2Dlayered materials with various compositions and electronicstructures, giving us a widespread and excellent field forexploration of physics in the realm of the 2D world. In contrastto graphene, semiconducting 2D-TMDs can have a sizablebandgap up to ~2 eV, which offers an opportunity to exploreoptical responses at the 2D limit and develop TMD-basednanoelectronic devices.5,7,8 Furthermore, 2D-TMDs afford verticalor lateral heterostructures, whose electronic structure and physicalproperties can be tuned through selecting the combination andstacking angles of each layer. Coupled with the possibility arisingfrom the valley degree of freedom,9,10 TMDs have been yieldingnew perspectives and attracting a wide range of researchinterests.For exploration of the fascinating opportunities, one of theimportant things is to address intrinsic properties of TMDs. For thispurpose, TMDs encapsulated by hexagonal boron nitride (hBN),hBN/TMD/hBN, have been widely used.11–14 2D-TMDs are verysensitive to the external environment, such as substrates andadsorbents, because almost all atoms in a 2D-TMD locate at thesurface. SiO2/Si usually used as a substrate has a rough surfacewith dangling bonds, low-energy optical phonons, and chargedimpurities, which can significantly degrade the quality ofsamples.15 In contrast, hBN, a graphene analog insulator (bandgap~6 eV), is free from these degradation factors, providing an idealenvironment to address intrinsic properties of 2D-TMDs.Up to now, quite a few studies have been done with hBN/TMD/hBN to investigate intrinsic properties of 2D-TMDs. For example,high-mobility devices with hBN-encapsulated structures havebeen reported, showing carrier mobility of 19–94 cm2/V s at roomtemperature in a monolayer MoS2 (ML-MoS2) encapsulated byhBN flakes; typical mobilities of ML-MoS2 on silicon substratesrange from 1 to 10 cm2/V s.16,17 The enhancement in carriermobility arises from suppression of the extrinsic carrier scatteringsin hBN-encapsulated samples. The high quality of hBN-encapsulated samples has also been observed in opticalmeasurements. Photoluminescence (PL) spectra of an ML-TMDon a silicon substrate show a relatively broad peak arising fromradiative recombination of excitons; for example, monolayer WS2on a silicon substrate shows a PL peak whose full-width at half-maximum (FWHM) is typically 50–55 or 75meV. In contrast, the PLspectrum of a hBN/WS2/hBN shows a corresponding PL peak witha much smaller FWHM of ~26meV, and this small FWHM mainlyresults from suppression of inhomogeneous broadening arisingfrom substrates.18–20 These results strongly indicate that hBN-encapsulated samples are essential to address intrinsic propertiesof 2D-TMDs.In this work, we have focused on the electronic structure of oneof the most popular TMDs, ML-MoS2, encapsulated by hBN, hBN/MoS2/hBN. As discussed above, hBN-encapsulated structures areprobably the best structure for investigations of intrinsic proper-ties of TMDs, but a question here is “does the hBN encapsulationreally preserve the original electronic structure of a 2D-TMD ornot?” In multi-layer systems assembled through van der Waals(vdW) interaction, it has been reported that the band structure ofvdW stacks can be modulated by interlayer interaction. Bilayergraphenes are one of the most significant examples. A recentwork has revealed that interlayer interaction causes a flat band ina bilayer graphene, which leads to the Mott insulating state andeven superconductivity at low temperature.21,22 InterlayerReceived: 18 March 2019 Accepted: 27 June 20191Department of Chemistry, Nagoya University, Nagoya 464-8602, Japan; 2Department of Materials Science and Nanoengineering, Rice University, Houston, TX 77005, USA;3National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan and 4Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, JapanCorrespondence: Ryo Kitaura (r.kitaura@nagoya-u.jp)www.nature.com/npj2dmaterialsPublished in partnership with FCT NOVA with the support of E-MRShttp://orcid.org/0000-0001-6405-6466http://orcid.org/0000-0001-6405-6466http://orcid.org/0000-0001-6405-6466http://orcid.org/0000-0001-6405-6466http://orcid.org/0000-0001-6405-6466http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119https://doi.org/10.1038/s41699-019-0108-4mailto:r.kitaura@nagoya-u.jpwww.nature.com/npj2dmaterialsinteraction in hBN/TMD/hBN, at first sight, is not the case, becausehBN have a large bandgap of ~6 eV and the valence bandmaximum (VBM) and conduction band minimum (CBM) of TMDlocate away from those of hBN, but is this really the case?In this paper, we show that modification of the band structureof ML-MoS2 occurs through interlayer interaction between ML-MoS2 and hBN flakes. Through detailed PL measurements andfirst-principles band-structure calculations, we have found that thevalence band (VB) at the Γ-point of ML-MoS2 shows upshift due toorbital hybridization, which leads to the existence of stablemomentum-forbidden dark excitons. The stable K–K direct excitonis one of the most significant features of ML-MoS2; however, in thecase of hBN/MoS2/hBN, the K–K direct excitons are not the moststable exciton anymore. This band-structure alternation is notsensitive to the relative angle between MoS2 and hBN, alteringsignificantly optical responses of MoS2. This has importantimplications for investigation of valley-related optical responsesat low temperature.RESULTSML-MoS2 flakes were grown on exfoliated hBN flakes on a quartzsubstrate with the chemical vapor deposition (CVD) method usingMoO3 and elemental sulfur as precursors; a high growthtemperature of 1100 °C was applied to improve the crystallinityof grown ML-MoS2. A flake of hBN with a thickness of ~15 nm wasthen transferred onto a ML-MoS2 crystal grown on an hBN flake.After the transfer, the nano-“squeegee” technique23 was used toremove contaminations encapsulated between the ML-MoS2 andthe hBN flakes. Figure 1 shows an optical microscope image of theML-MoS2 encapsulated by hBN flakes. No bubble is visible in theoptical image, indicating that the ML-MoS2 contacts hBN flakeswell to form a high-quality hBN-encapsulated structure. An AFMheight image of the hBN/MoS2/hBN (Fig. 1b) shows an atomicallyflat surface, giving a height of MoS2 as ~0.8 nm that is consistentwith a monolayer structure. The RMS roughness evaluated at theML-MoS2 region is ~0.1 nm, which clearly demonstrates theatomically flat surface of the prepared sample. This atomicallyflat structure is essential to suppress inhomogeneous broadeningin observations of optical responses.Figure 2a shows a PL spectrum of the prepared hBN/MoS2/hBNmeasured at 300 K. A single peak arising from radiativerecombination of excitons is seen in the PL spectrum, where thecontribution from trions is not dominant (a detailed spectraldecomposition is shown in Supplementary Fig. 1). The FWHM ofthe exciton PL peak is 39 meV, which is much smaller than thoseof samples on silicon substrates (typically ~70 or 56 meV).24,25Figure 2b shows a PL image of the sample, where the red-dashedFig. 1 Microscopy images of hBN/MoS2/hBN. a An optical image of the hBN/MoS2/hBN prepared. The scale bar corresponds to 10 μm. b AnAFM image of an MoS2 part in the hBN/MoS2/hBN. The scale bar corresponds to 1.5 μmFig. 2 A photoluminescence spectrum and image of hBN/MoS2/hBN. a A photoluminescence spectrum of hBN/MoS2/hBN measured at roomtemperature. Excitation wavelength of 488 nm was used. b A photoluminescence image of hBN/MoS2/hBN. Bright part corresponds toencapsulated monolayer MoS2. The red dotted square shows the place where cleaning with contact-mode AFM was performed. The redsquare drawn by the solid red line corresponds to the place where integration of PL intensity was performed for evaluation of thetemperature dependence of PL intensity. The scale bar corresponds to 5 μmY. Uchiyama et al.2npj 2D Materials and Applications (2019)    26 Published in partnership with FCT NOVA with the support of E-MRS1234567890():,;rectangle corresponds to the place cleaned by the nano-“squeegee” technique. The PL image, in particular at the redrectangle, clearly shows uniform PL, which represents a high-quality clean interface between ML-MoS2 and hBN. The brighterPL at the cleaned place indicates that non-radiative decay, whichis caused by contaminants, is suppressed.19,26,27Figure 3a shows PL spectra measured at temperatures rangingfrom 220 to 320 K. PL peaks arising from radiative recombinationof excitons show blueshift as temperature decreases, whichoriginates from bandgap widening caused by theelectron–phonon interaction. The temperature dependence iswell described by Varshni’s equation, which is shown inSupplementary Fig. 2; the obtained parameters are consistentwith previously reported values. As you can clearly see, intensitiesof the PL peaks become weak as temperature decreases. Toevaluate the intensity decrease precisely, we measured PLintensity from the red rectangular regions in PL images; PLintensities are averaged over the area to minimize the position-dependent fluctuation. As clearly seen in Fig. 3b, PL intensitymonotonically decreases as temperature decreases, and PLintensity at 260 K is two-thirds of that at 320 K.In a previous report, PL intensity of ML-MoS2 on a siliconsubstrate increased as temperature decreased.28 Ab-initio band-structure calculation tells us that ML-MoS2 is a direct-gapsemiconductor, and bright excitons might be the lowest-energyexcited state. This is consistent with the previously reportedtemperature dependence of PL intensity because the populationof bright excitons is expected to increase as temperaturedecreases if the bright state is the lowest-energy state. A recenttheoretical investigation, however, has suggested that lower-energy dark excitons can exist in an ML-MoS2, where dark excitonscorrespond to holes located at the Γ-valley29; excitons with Γ-valley holes are dark state because direct recombination isforbidden due to the momentum conservation. The momentum-forbidden dark excitons can have lower energy than K–K directexcitons because of a difference in exciton binding energy. Whenenergy difference between the momentum-forbidden darkexcitons and direct excitons is very small, PL intensity in MoS2/SiO2 can still increase as temperature decreases because popula-tion of another type of dark excitons, K–K direct excitons with acenter-of-mass momentum exceeding the light cone, decreases astemperature decreases.Figure 4 shows the temperature dependence of time-dependent PL intensity measured with the time-correlatedsingle-photon counting technique. As clearly seen, PL decaybecomes faster as temperature becomes lower. Coupled with theobserved decrease in PL at low temperature, it is stronglysuggested that there is a dark state, whose energy is lower thanthe bright state, in hBN/MoS2/hBN. This dark state should havelower energy than the momentum-forbidden dark states observedin MoS2/SiO2 because temperature dependence in PL intensity ofhBN/MoS2/hBN is opposite to that of MoS2/SiO2. To extract theenergy difference between bright and dark excitons in the hBN/MoS2/hBN, we have fitted the temperature dependence in Fig. 3bwith the following equation.I Tð Þ / αmKKmKK þmKK0 þmKΓeβΔEKΓ: (1)Assuming that PL intensity is proportional to quantum yield, thisequation for temperature dependence of PL intensity, I(T), can bederived (for details, please see Supplementary Note 1). In thisequation, temperature-dependent change in the population ofspin-forbidden excitons (K–K′ excitons) and momentum-forbiddendark excitons is considered; there are two kinds of momentum-forbidden dark excitons, inter-valley indirect excitons (K–Γexcitons) and direct excitons with momentum exceeding thelight cone. mKK, mKK′, and mKΓ in this equation represent excitonFig. 3 Temperature dependence of PL spectra and intensity. a Temperature dependence of PL spectra of hBN/MoS2/hBN. All measurementswere performed with excitation wavelength of 532 nm. All PL spectra are normalized to their maximum PL intensity. b Temperaturedependence of PL intensity obtained from PL images. The dotted line corresponds to a fitted line with Eq. (1)Fig. 4 Temperature dependence of a time-resolved PL intensity. Atime-resolved PL intensity of hBN/MoS2/hBN measured with a time-correlated single-photon counting (TCSPC) technique at varioustemperatures of 100, 250, 270, and 300 K. Dots and solid linescorrespond to measured points and fitted curves assuming singleexponential decayY. Uchiyama et al.3Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2019)    26 effective masses of K–K bright excitons, K–K′ and K–Γ darkexcitons; effective masses of excitons can be defined by the sumof effective mass of electrons and holes at each valley. In thisanalysis, we use 0.835me for mKK, mKK′, and 3.175me for mKΓ basedon a previous work.30 β and ΔEKΓ in the equation are 1/kBT (kB andT correspond to the Boltzmann constant and temperature) andthe energy difference between K–Γ and K–K excitons. As shown bythe dashed line in Fig. 3b, the equation reproduces the observedtemperature dependence well, giving ΔEKΓ of 83 meV. This ismuch larger than the previously reported value for ML-MoS2 on asilicon substrate, which strongly indicates that the electronicstructure is modified in hBN/MoS2/hBN.To address the origin of the dark state in hBN/MoS2/hBN, wehave performed ab-initio density functional band structurecalculations. Figure 5a shows the band structure of isolated ML-MoS2 and ML-MoS2 sandwiched by monolayer hBN. Prior tocalculation of hBN/MoS2/hBN, we performed full structuraloptimization of isolated ML-MoS2, and the optimized structure(optimized primitive vectors and geometry) was used in thecalculation of hBN/MoS2/hBN; we used a 4 × 4 and 5 × 5 supercellsfor MoS2 and hBN to minimize the difference in unit cells.Interlayer distance between MoS2 and hBN in hBN/MoS2/hBN wasevaluated with the vdW-DF method (Supplementary Fig. 3). Asyou can see, CBM and VBM locate at the K valley in ML-MoS2,which is consistent with the band structure previously reported.On the other hand, the VB at the Γ-valley shows upward shift andthe VBM locates at the Γ-valley in the hBN/MoS2/hBN; i.e. hBN/MoS2/hBN is an indirect semiconductor. Because we used theoptimized primitive vectors of MoS2 for the calculation of hBN/MoS2/hBN, the observed change in band structure should becaused not by unrealistic strain arising from difference in unit cellsbut by interlayer interaction between hBN and MoS2. The direct-to-indirect change in band structure is consistent with a previousDFT calculation.This upward shift is very sensitive to interlayer distancebetween MoS2 and hBN, showing exponential decay against theinterlayer distance (Supplementary Fig. 4). This strong interlayerdependence indicates that the upward shift in the VBM at the Γ-valley originates not from long-range interaction, such aselectrostatic interaction, but from orbital hybridization arisingfrom overlap in wave functions between MoS2 and hBN. It shouldbe noted that accurate estimation of interlayer distance based onDFT is not straight forward and the degree of the upward shiftshould be influenced by the accuracy. Because the upward shift iscaused by orbital hybridization between hBN and MoS2, theupward shift should also be sensitive to stacking structure, MoS2/Fig. 5 Band structures of MoS2 and hBN/MoS2/hBN. a Band structures around valence bands of monolayer MoS2 (left) and hBN/MoS2/hBN(right). Insets show structure models used in these calculations, where 4 × 4 and 5 × 5 supercells were used for MoS2 and hBN, respectively, tominimize the lattice mismatch between MoS2 and hBN. b Cross-section of charge density (Ψ2) of hBN/MoS2/hBN at the Γ-valley projectedalong the a-axis. The contour lines are drawn in such a way that the differences of charge density at adjacent lines are double. All calculationswere performed with Quantum Espresso with energy cut-off of 45 Ry and Monkhorst-Pack k-point mesh of 7 × 7 × 1 were usedY. Uchiyama et al.4npj 2D Materials and Applications (2019)    26 Published in partnership with FCT NOVA with the support of E-MRShBN and hBN/MoS2/hBN. Supplementary Figure 5 shows the PLspectra of MoS2/hBN and hBN/MoS2/hBN measured at roomtemperature. As seen in the PL spectra, PL intensity of hBN/MoS2/hBN is only half of that of MoS2/hBN; we used the same monolayerMoS2 for both measurements. In the case of MoS2/hBN, upwardshift of VBM is expected to be smaller than that in hBN/MoS2/hBNbecause the interlayer orbital hybridization, which causes theupward shift of VBM, is less significant in MoS2/hBN. The weakerPL intensity observed is consistent with the expected difference inthe band structure.Figure 5b shows a 2D contour plot of the squared wavefunction of the VBM of hBN/MoS2/hBN at the Γ-point; the squaredwave function was summed over the a-axis. As shown in thefigure, there is contribution from the π-band of hBN in the wavefunction of hBN/MoS2/hBN. A close inspection has revealed thatthere is a node between MoS2 and hBN, and this means that anti-bonding coupling between wavefunctions of MoS2 and hBN existsin hBN/MoS2/hBN. This anti-bonding coupling leads to the upwardshift in VBM at the Γ-valley, resulting in the transformation from adirect gap to an indirect gap. The difference in VB energy of hBNand MoS2 at the Γ-point is ~400meV, which is much smaller thanthat in CB, and this relatively small energy difference allows theorbital hybridization between hBN and MoS2. In addition, there isonly a vdW gap between the hBN and MoS2 layers, and the wavefunction of MoS2 at the Γ-point has a significant contribution fromsulfur atoms. Both of them contribute to significant spatial overlapbetween the wave functions of hBN and MoS2 at the Γ-point,leading to the direct-to-indirect transition.DISCUSSIONIn contrast to the wavefunction of the VBM at the Γ-point, thewavefunction at the K valley of MoS2 localizes around molybde-num atoms. This localized nature of the wavefunction plays amajor role in small coupling at the K-point; the spatial overlappingbetween wavefunctions at K-points should be much smaller thanthat at the Γ-point. In addition, the difference in VB energybetween hBN and MoS2 at the K-point strongly depends onrelative angle. The smallest energy difference appears when therelative angle is zero, which is not the case in real samples.Consequently, in real samples, the upward shift of VB energy ofMoS2 at the K-point should be small, which probably contributesto the observed large ΔEKG of 83meV.Another scenario that can contribute to the band-structurechange is structural distortion. Due to the vdW force actingbetween the layers, there is a possibility that encapsulated MoS2can slightly distort along the direction perpendicular to the 2Dplane. The vertical distortion leads to biaxial tensile strain alongthe direction parallel to the 2D plane, resulting in modification ofthe band structure (Supplementary Fig. 6). Calculated verticaldistortion dependence on the total energy of MoS2 gives Young’smodulus of 225 GPa, which means that 225 MPa is needed toinduce 0.1% vertical distortion. Therefore the contribution fromdistortion cannot be a dominant factor.In conclusion, we have revealed that the band structure of MoS2in hBN/MoS2/hBN is significantly altered by interlayer interactionbetween hBN and MoS2. Through detailed PL measurements,including the temperature dependence of PL intensity and time-resolved PL intensity, we have shown the existence of darkexcitons, whose energy is 83 meV lower than that of the brightexcitons. DFT band structure calculation has revealed that the darkexcitons should be momentum-forbidden dark excitons, whereelectrons and holes locate at the K-point and Γ-point, respectively.The existence of the lower-energy momentum-forbidden excitonsin pristine monolayer MoS2, originating from the large excitonbinding energy, was already pointed out in a previous report. Wefound, however, that monolayer MoS2 in hBN/MoS2/hBN showsdrastically different optical responses due to the orbitalhybridization between MoS2 and hBN. This should have an impacton valley-related properties of MoS2, in particular, propertiesarising from valley-polarized holes.METHODSCVD growth of MoS2 on exfoliated hBNWe have grown monolayer MoS2 crystals onto hBN flakes by CVD method.We used elemental sulfur (Sigma-Aldrich, 99.98%) and molybdenum oxide(MoO3; Sigma-Aldrich, 99.5%) as precursors for the CVD growth. MoO3/sulfur was placed in/on a quartz tube with an 8.5 mm inner diameter, andthe 8.5 mm inner diameter quartz tube was placed in a 26mm innerdiameter quartz tube to avoid unwanted reaction before reaching the hBNflakes. The hBN flakes were prepared on a quartz substrate by themechanical exfoliation method, and the quartz substrate with hBN flakeswas placed in the downstream of the 8.5 mm diameter quartz tube. Thequartz tubes were heated with three-zone furnace at 200°, 750°, and 1100°for 20min under Ar flow of 200 sccm; sulfur, MoO3, and a quartz substratewere placed at the coolest medium and hottest zone, respectively.Fabrication of hBN-encapsulated heterostructureshBN flakes were prepared on an SiO2/Si substrate by the mechanicalexfoliation method. One of the hBN flakes on an SiO2/Si was picked up by aPMMA (Microchem A11)/PDMS (Shin-Etsu Silicone KE-106) film on a glassslide, and the picked-up hBN flake was transferred onto a monolayer MoS2grown on an hBN flake to form an hBN/MoS2/hBN. To achieve sufficientinterlayer contact, we have used the nano-“squeegee” technique, whereAFT tip squeezes out contamination and bubbles from interface betweenhBN and MoS2.Optical measurementsRoom temperature PL spectra were measured by using a confocal Ramanmicroscope (Renishaw InVia Raman and Horiba Jobin Yvon LabRAM HR-800) with 488 nm CW laser excitation (COHERENT Sapphire 488 LP). Inmeasurements of temperature dependence of PL spectra and time-resolved PL measurements, we used a home-build microspectroscopysystem equipped with a spectrometer (Princeton Instruments IsoPlaneSCT320) and a supercontinuum laser system (NKT Photonics SuperKEXTREME); laser beam from the supercontinuum laser was monochro-mated by a spectrometer (Princeton Instruments SP2150i). In low-temperature measurements, we placed a sample in a cryostat (CryoVacKONTI-Cryostat-Micro) with continuous flowing of liquid N2 under vacuumof ~10−4 Pa; CryoVac TIC 304-MA was used to control temperature.Objective lenses (×50–100 and 0.7–0.85 NA) were used for allmeasurements.First-principles calculationsFirst-principles density functional theory (DFT) calculations were per-formed using the Quantum Espresso.31 Ion–electron interactions wererepresented by all-electron projector augmented wave potentials,32 andthe generalized gradient approximation (GGA) parameterized byPerdew–Burke–Ernzerhof (PBE)33 were used to account for the electronicexchange and correlation. The wave functions were expanded in a planewave basis with energy cut-off of 45 Ry. Prior to band-structure calculationof MoS2 and hBN/MoS2/hBN, the structure of MoS2 was fully relaxed untilthe components of Hellmann–Feynman forces on the atoms were less than10–5 Ry/Å. For band-structure calculation, the optimized structure of MoS2was expanded to a 4 × 4 supercell to minimize the lattice mismatchbetween hBN and MoS2.DATA AVAILABILITYThe authors have confirmed that the data supporting the findings of this study areavailable within the article and the Supplementary Information. Raw data areavailable on reasonable requests from the authors.ACKNOWLEDGEMENTSThis work was supported by JSPS KAKENHI Grant numbers JP16H06331, JP16H03825,JP16H00963, JP15K13283, JP25107002, and JST CREST Grant Number JPMJCR16F3.Y. Uchiyama et al.5Published in partnership with FCT NOVA with the support of E-MRS npj 2D Materials and Applications (2019)    26 We thank K. Itami and Y. Miyauchi for sharing the Raman and AFM apparatus. We aregrateful to S. Okada for fruitful discussion on ab-initio calculation.AUTHOR CONTRIBUTIONSY.U. prepared hBN/MoS2/hBN samples and performed all optical measurementsreported in this paper. K.W. and T.T. provided the high-quality single crystalline hBN.K.K., T.E., and Y.M. have contributed to the sample preparation. R.K. performed ab-initio band-structure calculations. Y.U. and A.K. analyzed temperature dependence ofPL intensity. R.K. designed the experiments and wrote the manuscript. All authorsdiscussed the results and commented on the manuscript at all stages.ADDITIONAL INFORMATIONSupplementary information accompanies the paper on the npj 2D Materials andApplications website (https://doi.org/10.1038/s41699-019-0108-4).Competing interests: The authors declare no competing interests.Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claimsin published maps and institutional affiliations.REFERENCES1. Kitaura, R. et al. Chemical vapor deposition growth of graphene and relatedmaterials. J. Phys. Soc. Jpn 84, 121013-1-13 (2015).2. Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically thin MoS2: a newdirect-gap semiconductor. Phys. 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The images or other third partymaterial in this article are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is not included in thearticle’s Creative Commons license and your intended use is not permitted by statutoryregulation or exceeds the permitted use, you will need to obtain permission directlyfrom the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2019Y. Uchiyama et al.6npj 2D Materials and Applications (2019)    26 Published in partnership with FCT NOVA with the support of E-MRShttps://doi.org/10.1038/s41699-019-0108-4http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Momentum-forbidden dark excitons in hBN-encapsulated monolayer MoS2 Introduction Results Discussion Methods CVD growth of MoS2 on exfoliated hBN Fabrication of hBN-encapsulated heterostructures Optical measurements First-principles calculations Supplementary information Acknowledgements ACKNOWLEDGMENTS Author contributions Competing interests ACKNOWLEDGMENTS