Evolution of the Valley Position in Bulk Transition-Metal Chalcogenides

Letter

pubs.acs.org/NanoLett

Evolution of the Valley Position in Bulk Transition-Metal Chalcogenides and Their Monolayer Limit † ‡ † ‡ § ∥ † ⊥ # ∇ ○ ◆ Hongtao Yuan, , Zhongkai Liu, , , , Gang Xu, Bo Zhou, , Sanfeng Wu, Dumitru Dumcenco, , † ‡ # # ¶ □ □ Kai Yan, , Yi Zhang, Sung-Kwan Mo, Pavel Dudin, Victor Kandyba, Mikhail Yablonskikh, □ † ‡ † ‡ ○ ∇ Alexei Barinov, Zhixun Shen, , Shoucheng Zhang, , Yingsheng Huang, Xiaodong Xu, # † ‡ † ‡ ▲ § ∥ ⊥ ¶ Zahid Hussain, Harold Y. Hwang,*, , Yi Cui,*, , , and Yulin Chen*, , , , † Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, United States ‡ Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States § School of Physical Science and Technology, ShanghaiTech University, Shanghai 200031, China ∥ CAS-Shanghai Science Research Center, 239 Zhang Heng Road, Shanghai 201203, China ⊥ Physics Department, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom # Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States ∇ Department of Physics, Department of Materials Science and Engineering, University of Washington, Seattle, Washington 98195, United States ○ Department of Electronic and Computer Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan (ROC) ◆ Electrical Engineering Institute, Ecole Polytechnique Federale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland ¶ Diamond Light Source, Didcot, Oxfordshire OX11 0BW, United Kingdom □ Elettra-Sincrotrone Trieste ScPA, Trieste, Basovizza 34149, Italy ▲ Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, United States

*S Supporting Information

ABSTRACT: Layered transition metal chalcogenides with large spin orbit coupling have recently sparked much interest due to their potential applications for electronic, optoelec- tronic, spintronics, and valleytronics. However, most current understanding of the electronic structure near band valleys in momentum space is based on either theoretical investigations or optical measurements, leaving the detailed band structure Downloaded via STANFORD UNIV on January 14, 2019 at 01:08:05 (UTC). elusive. For example, the exact position of the conduction band valley of bulk MoS2 remains controversial. Here, using angle- resolved photoemission spectroscopy with submicron spatial

See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. resolution (micro-ARPES), we systematically imaged the conduction/valence band structure evolution across representative chalcogenides MoS2,WS2, and WSe2, as well as the thickness dependent electronic structure from bulk to the monolayer limit. These results establish a solid basis to understand the underlying valley physics of these materials, and also provide a link between chalcogenide electronic band structure and their physical properties for potential valleytronics applications. KEYWORDS: angle-resolved photoemission spectroscopy, band structure, transition metal dichalcogenides, valleytronics

ecent eﬀorts on graphene-like layered materials with novel valleys in k-space and the resulting suppression of intervalley R properties have attracted much attention for not only scattering, the valley index can be used in analogy to the spin in − potential electronic and spintronic devices1 8 but also more spintronics, opening a new research direction called “valley- 9 10,11 generally for energy storage and catalytic applications. tronics”.12,14,15 Moreover, having heavy 4d/5d elements with With a layered honeycomb lattice, transition metal dichalcogenides MX2 (M = Mo, W; X = S, Se, Te) have two inequivalent Received: December 14, 2015 valleys in the k-space electronic structure in the hexagonal Revised: June 21, 2016 − Brillouin zone (BZ).12 14 Because of the large separation of Published: June 30, 2016

− − Figure 1. Crystal and electronic structure of layered 2H MoS2. (a) Layered crystal structure of 2H MX2, where red balls represent M (Mo or W) atoms and blue balls represent X (S, Se, or Te) atoms. The in-plane lattice parameter (a) and the distance between the M and X layers (d) are fl indicated, which have a direct in uence on the band structure. (b) Schematic of the 3D Brillouin zone (BZ) of MX2 and its projection onto the surface Brillouin zone, where high symmetry points are labeled. (c) 3D illustration of the band structure of bulk MoS2 obtained by ARPES measurements. A clear band splitting at K is observed. (d) Constant energy plot shows the splitting at K point. (e) 3D constant energy plots at ff Γ fi di erent energy levels (the energy level of the VBM at is de ned as 0) show the evolution of band dispersion. (f) Band structure of bulk MoS2 measured after K-dosage. Evidently, the CBM sits at the K point, whereas the VBM is at Γ, showing an indirect band gap (1.4 eV as indicated) for the bulk MoS2. We note that the band dispersion is slightly broadened due to the additional scattering of photoelectrons by the K atoms doped on to the sample surface (this broadening also causes the splitting at K point slightly smeared). (g) Constant energy contours at the CBM and VBM (appearing at the corners and the center of the BZ), respectively. strong spin−orbital interaction (SOI),12,16,17 the monolayer by van der Waals force (Figure 1a; we use “mono-layer” to refer MX2 compounds show polarized spin texture in the electronic to one such triple-layer unit), with the adjacent monolayers 8,18,19 ° structure, as demonstrated theoretically and supported by rotated by 180 with respect to each other. The 3D BZ of MX2 optical investigations5,7,20 and thus are promising candidates for is illustrated in Figure 1b with high symmetry points indicated. − a new type of valley-coupled spintronics applications.4,5,20 22 Because of the lack of inversion symmetry in each monolayer, a However, despite these exciting developments, the detailed net in-plane electric dipole moment is present at the M atoms, electronic structure of MX2 compounds, especially the valley which induces out-of-plane spin polarization near the valleys at loci and their evolution, remain elusive. For example, different K points via spin−orbit interaction (SOI).8,21 Remarkably, as theories propose the location of the conduction band valley in two adjacent monolayers restore inversion symmetry by A−B bulk MoS2 to be either at high-symmetry K points, the corner stacking order (Figure 1a), the band structure of such bilayer Γ− fl of the BZ, or at nonsymmetric points along K MX2 akes remains spin-degenerate. As a result, the band 23−25 direction. structure of MX2 chalcogenides can change dramatically from In this work, we directly studied the electronic structure of bi- to monolayer and leads to valley locus evolution due to the − representative transition metal chalcogenides MoS2,WS2, and change of interlayer coupling, for example the indirect direct 23,24,27 WSe2 by high resolution ARPES and observed the valley band gap transition. evolution in the band structure between different compounds. Figure 1c−g show the overall electronic structure of bulk 2 We found that although the valence band maximum (VBM, MoS2, the most broadly studied MX2 compound. Evidently, Γ Γ hole valley) of bulk MX2 compounds always resides at , the the VBM valley of MoS2 clearly resides at the point (Figure conduction band minimum (CBM, electron valley) loci shift 1c,e,f) and is ∼0.5 eV above the top of the valence band at the Γ Γ from K (MoS2) toward (WS2 and WSe2). Moreover, by K point. From to K, the valence band evolves into two utilizing the novel spatially resolved ARPES technique (with subbands with ∼180 meV splitting (at K points, see Figure 1c) 800 nm spatial resolution) recently developed,26 we studied caused by the strong SOI, in good agreement with previous fl ff 23,24,27 28,29 MoS2 and WSe2 micro akes with di erent thickness and theoretical calculations, ARPES measurements, and observed the evolution of the electronic band structure and the our ab initio calculations (see Figure S1 and Part I in the band gap geometry from the bulk to the monolayer limit. Our Supporting Information, SI). This splitting in the band observations provide a solid understanding on the underlying structure at the K points also results in two triangular pockets − valley physics of MX2 materials and guidance for the design and in the constant energy contours (e.g., at 0.8 eV, see Figure the development of novel electronic/spintronics/valleytronics 1d,e). The difference between the valence band-top at K and Γ devices. points is as large as 0.5 eV. In addition to the kx-ky dispersions, Typical Valence and Conduction Band Structures in we also investigate the kz-dispersion of the band structure of − Bulk MoS2. The crystal structure of 2H MX2 chalcogenides MoS2 with the photon energy dependent ARPES study (the 4 (Figure 1a, with D6h symmetry and the P63/mmc space group) details can be found in Part II of SI and Figure S2), which comprised of stacked ···X−M−X··· triple-layer groups bonded indicates that the bands around Γ disperse dramatically along

4739 DOI: 10.1021/acs.nanolett.5b05107 Nano Lett. 2016, 16, 4738−4745 Nano Letters Letter

Γ− Figure 2. Band structure of as-cleaved and K-dosed bulk MX2 crystals. (a) Band dispersion along the K direction of as-cleaved bulk MoS2,WS2, ff Γ and WSe2 in panels (i), (ii), and (iii), respectively. The band splitting and the energy di erence between the apexes of the valence band at and K are indicated. (b) Band dispersions measured after K-dosing (as in Figure 1f, the dispersions are slightly broadened). (c) Zoomed-in view of the band dispersion expanded from the regions marked in (b); the intensity in panels (ii) and (iii) were enhanced by a factor of 10 to allow better visibility of Λ the conduction band. One can clearly see that the CBM of MoS2 (i) is located at the K point, whereas the CBM of WSe2 (iii) is located at . For Λ WS2 (ii), the bottoms of the conduction band at K and are nearly degenerate. (d) Fermi-surface map of K-doped MoS2 (i), WS2 (ii), and WSe2 Λ (iii), also showing the CBM evolution from K in MoS2 (i) to in WSe2 (iii). kz, whereas those around K do not. This two-dimensional Determination of CBM/VBM Valley Positions in Bulk behavior of the bands around K supports the band calculations MX2. In contrast to the small SOI in the MoS2, W-based MX2 2 2 indicating their origin as the localized in-plane Mo dx −y and compounds such as WS2 and WSe2 have a larger SOI strength, Mo dxy orbitals, whereas the three-dimensional behavior of the which will potentially result in large spin splitting with the bands around Γ originate from the delocalized out-of-plane Mo broken inversion symmetry. Therefore, we performed further 2 2 28 d3z −r and S pz orbitals. This observation clearly suggests that ARPES measurements on WS2 and WSe2. As illustrated in both decreasing sample thickness and changing elements in the Figure 2a(i−iii), with the increase of atomic mass from Mo to compounds would tune the out-of-plane orbitals, change the W and from S to Se, the splitting of the VBM valleys at the K Γ ∼ ∼ bands around and play a critical role in changing the valley points increases (MoS2, 180 meV; WS2, 470 meV; and ∼ positions in the band structure. WSe2, 500 meV) due to the increased atomic SOI. An Because the Fermi energy (EF) of as-grown MoS2 samples is interesting observation is that although the VBM valley still pinned inside the band gap close to the CBM by impurity resides at Γ for all three materials, the difference between peaks states, we cannot directly observe the conduction band (Figure of the valence band at Γ and K dramatically decreases from 0.5 − 1c e). In order to investigate the conduction band, we eV [MoS2, Figure 1f and Figure 2a(i)] to 0.05 eV [WSe2, performed in situ electron doping by introducing a small Figure 2a(iii)]. The fact that the valence band maxima of WSe2 amount of potassium onto the sample surface29 (with K at Γ and K are very close to each other may have important coverage as low as 0.0003 layer; details can be found in SI Part implications for hole-type spin based device applications,19,30 II) and shift EF. Note that the band structure of MoS2 should such as recent demonstration of electrical control of spin fi not have any modi cation with such a small amount of dopant polarization and spin transport by tuning EF to the vicinity of 8 coverage. Using this method, we successfully lifted EF into the the apexes at the K points. conduction band [Figure 1f,g and Figure 2a−d(i)] and clearly To compare the CBM positions of the three compounds, we observed that the CBM valleys of bulk MoS2 are located at the again performed in situ K-doping on the sample surface (Figure K point, which differs from most current band calcula- 2b−d). As expected, all three compounds show an indirect − tions16,23 25 that suggest the CBM is located at some band gap (Figure 2b,c). Remarkably, although the bulk band nonsymmetric point (here denoted as Λ) along the Γ− K gap remains indirect for all three compounds, the CBM Λ direction. From Figure 1f, the indirect band gap of MoS2 is location evolves from the K point (MoS2) to the point ∼ Γ found to be 1.4 eV and the VBM valley of MoS2 resides at (WSe2), as is evident in both the band dispersions (Figure 2c) (Figure 1d,f) and is ∼0.5 eV above the apex of the valence band and the Fermi surface (FS) maps (Figure 2d), a direct at the K point. From our measurement, the effective mass of experimental observation that pins down the exact CBM ∼ Γ ∼ ff the hole pockets is 0.8 m0 for the VBM at and 0.5 m0 for position and the size of the direct/indirect band gap in di erent the VBM at K, which is also consistent with our ab initio MX compounds. This finding not only clarifies the controversy 2 − calculations (more details of the effective mass can be found in on the CBM loci16,23 25 but also provides critical information 27−29 Part I of SI) and other recent ARPES reports. for designing function devices with MX2 materials (e.g., in

4740 DOI: 10.1021/acs.nanolett.5b05107 Nano Lett. 2016, 16, 4738−4745 Nano Letters Letter

fl Figure 3. In uence of lattice parameters on band valley loci in electronic structure of bulk MoS2. (a) Evolution of the calculated MoS2 band structure as a function of the in-plane lattice constant a. (with all other parameters fixed to the fully relaxed value) From left to right, a values are 3.11 Å, 3.15 Å, 3.19 Å (relaxed value), 3.23 Å, and 3.27 Å, respectively. The red line is the lowermost conduction band, and the blue line is the uppermost valence band. (b) Similar to a but as a function of the out-of-plane lattice constant d. From left to right, d values are 1.524 Å, 1,544 Å, 1,564 Å (relaxed ff Λ Δ CB value), 1.584 Å, 1.604 Å, respectively. (c) Variation of the energy di erence between the two conduction subband valleys at K and points ( EΛK = CB − CB ff Γ Δ VB VB − VB EΛ EK , red line and dots)), and the energy di erence between the two valence subband maxima at K and points ( EΓK = EΓ EK , blue line Δ CB Δ CB and dots), as a function of a and d, respectively. (d) Phase diagram of EΛK as a function of a and d, in which EΛK < 0 indicates that the conduction Λ Δ CB Δ CB “ ” band at K is higher than , whereas EΛK > 0 indicates the opposite. Thicker black line indicates the boundary where EΛK = 0; and the red + sign Δ CB indicating the position of the calculated EΛK of MoS2 with relaxed parameters.

“valleytronics”, the operation depends on the band minima/ To understand why the conduction band valley loci change maxima positions). with lattice parameters, we need to know the orbital Ab Initio Calculations for CBM/VBM Valley Positions. components for the energy bands at K and Λ points. Note To understand the discrepancy between previous theoretical that the band valleys at K and Λ points originate from two − reports,16,23 25 we performed systematic ab initio studies on different subbands with different orbital components: the 2 2 the band structure of these materials, which demonstrated that subband near K points mainly consists of Mo d3z −r along the the crystal structural parameters (e.g., in-plane lattice parameter out of plane direction, whereas the subband near the Λ point 2 2 a and out-of-plane parameter d of MX , see Figure 1a and mainly comes from Mo dx −y and Mo dxy orbitals, which are 2 fi − discussed below) can have a strong influence on the band con ned in the 2D (x y) plane, far away from the ligand S/Se Λ structure. These results are summarized in Figure 3 with more atoms. Therefore, we can see that the valley position at point discussion in the SI, Part I. For example, as can be seen in has almost no change in the energy scale with the lattice 2 2 − Λ constant. However, for the d3z −r orbital, because its lobes point Figure 3a c, the local valley locus of MoS2 at point moves up (with respect to that at K) with either increasing a or to the ligand S/Se atoms, the minimum at K point becomes very sensitive to the distance to the ligand atoms. The overlap decreasing d; and one can see that changing the a (or d) value of the d 2− 2 orbital decreases with increasing a, lowering the by only ±2.5% will dramatically change the band structure and 3z r energy level of the valleys at the K points (Figure 3a). On the the relative position of the valley loci at Γ and K. This effect can other hand, when d increases, the overlap of the d 2 orbital also be summarized in Figure 3d, where the 2D phase diagram z ff increases, lifting up the energy level of the valleys at the K shows the energy di erence between the conduction band points. Therefore, the increase of a and d have opposite effects Λ Δ CB CB − CB minima at and K ( EΛK = EΛ EK ) as a function of fl Δ CB on the valley loci evolution (directly re ected by EΛK and parameters a and d. Importantly, our calculation results using Δ VB VB − VB EΓK = EΓ EK ). relaxed lattice parameter (red dot in Figure 3d) indeed shows a Interestingly, these two opposite effects from a and d have CB positive ΔEΛ (i.e., the CBM located at K rather than Λ), in fl Δ CB K nearly the same in uence (in both cases, EΛK linearly shifts agreement with the ARPES observation (Figure 1f). Such around 0.9 eV when the parameter changes ∼5% in total, see strong dependence of the band structure on lattice parameters Figure 3c). This helps to explain the valley loci evolution from ff indicates that strain engineering could be an e ective method MoS2,WS2 to WSe2: Compared to MoS2, the parameter a for ∼ to modulate the electronic structure of MX2 materials in WSe2 increases 4.2%, whereas the distance d of WSe2 is practical applications (e.g., induced indirect−direct band gap enlarged more than 7%. Because the changing of d is greater − transition by external strain).31 34 than a, it dominates the evolution of the valley locus. As we

4741 DOI: 10.1021/acs.nanolett.5b05107 Nano Lett. 2016, 16, 4738−4745 Nano Letters Letter

fl fi Figure 4. Fabrication of ultrathin MoS2 akes via mechanical exfoliation and precise layer number identi cation. (a) Schematic diagram of the − fl ff fi fl spatially resolved ARPES setup. (b) (d) Optical (b,c) and AFM (d) images of exfoliated MoS2 akes with di erent magni cation. A monolayer ake fi fl is shown in (d) with an AFM depth pro le scan showing the 0.7 nm thickness. (e) Typical room temperature Raman spectra on MoS2 akes from bulk (black) to monolayer (red), which clearly exhibit sensitive thickness dependence. For a monolayer, these Raman modes occur at 384 and 403 −1 ff −1 fi fl cm , with the energy di erence of 19 cm con rming the single layer form of MoS2. Inset: the optical image of the akes used, and the A, B, and C indication of the mono-, bi-, and multilayer regions measured. (f) Comparison of room temperature photoluminescence (PL) on bulk and fl fl monolayer MoS2 and WSe2 akes. Green and purple are from monolayer akes, and black is from bulk WSe2. Clearly, the strong PL is only observed in monolayer flakes (with direct band gap).

fl fl Figure 5. Band valley evolution from multi-, bi- to monolayer MoS2 nano akes. (a) 2D photoemission spectra intensity contrast map of MoS2 akes (measured at the Fermi level), with different magnifications from large area (i) to small area (iii), demonstrating the processes to locate the target fl fl fl monolayer ake. Panel (iv) gives the optical image of the same ake, where the mono-, bi- and multilayer MoS2 akes can be clearly seen. Points − fl P1 P3 indicate the three measurement positions for mono-, bi-, and multilayer MoS2 akes. (b) Constant energy plots measured at monolayer − − − (point P1), bilayer (point P2), and multilayer (point P3) spots, with the energy positions at E EVBM = 0 eV and E EVBM = 0.5 eV, respectively. (c) Band dispersions along the high symmetry K−Γ−K and M−Γ−M directions from points P1−P3, showing the band valley evolution with different flake thicknesses.

Δ CB have observed in Figure 2, the EΛK becomes negative, and the Evolution of Valley Positions from Bulk, Bilayer to Λ point becomes the CBM valley in WSe2, which is quite Monolayer MX2. Many of the potential applications of these ff di erent from the case of MoS2. In addition, we calculated a materials are based on few-layers devices. Therefore, it is of hypothetical system with a and d both enlarged by 4.2%. Very great importance to investigate the valley evolution in the similar to MoS2 itself, the CBM valley of the hypothetical electronic structure of MX2 materials with thickness down, system still sits at the K point, which further confirms the ideally, to the monolayer limit. For the layer-dependent band picture that the band valleys at K and Λ points originate from structure study, we mechanically exfoliated bulk samples (the subbands with different orbital components. same samples used for the ARPES study in Figures 1 and 2)

4742 DOI: 10.1021/acs.nanolett.5b05107 Nano Lett. 2016, 16, 4738−4745 Nano Letters Letter fl fl and acquired bi- and monolayer akes. As the lateral size of of WSe2 akes was investigated and we observed the same these flakes is typically only several micrometers (as shown in evolution of the VBM valley position from K to Γ when the Figure 4b−d), which is much smaller than the photon beam flake thickness increases from one to two layers (see Figure S6 used in typical ARPES, we adopted the recently developed in the SI); the band structures of bilayer and multilayer flakes ∼ spatially resolved (spatial resolution 800 nm) ARPES also show general similarity. Interestingly, in WSe2, the energy technique for our study, which allowed the measurement of difference of the valence band between K and Γ is ∼100 meV the band structure of submicron samples27,28 (the schematic of [see Figure S6c(iii) in the SI], which is 5 times smaller than fi ff the instrument we used and the measurement geometry is that of MoS2 [Figure 5c(iii)]. Such signi cant di erence implies depicted in Figure 4a; more details can be found in SI Part III). that the hole spin may be more robust in bilayer WSe2 than fl Interestingly, the same akes used in the spatially resolved MoS2, making it a promising system for bilayer based spin and ARPES measurements can also be directly used for other valley device applications.21 measurements (e.g., optics and transport) and device With the systematic study of the electronic structure of three fabrication - thus establishing a direct link between the band representative MX2 compounds and their valley locus evolution structure and their important physical properties. Compared with thickness down to the monolayer limit, we establish a solid with the molecular beam epitaxy and chemical vapor deposition basis to understand the underlying physics of these materials. fi methods that have been used to obtain single layer MX2 lms, This work further provides important guidance for new the exfoliation method not only is much simpler but also materials design and novel valleytronics device development provides the opportunity to study the band structure of layered and also demonstrates the power of the in situ study of the materials with different thicknesses in the same flake. band structure of submicron size semiconductors used in Figures 4b−d show the optical micrograph and atomic force functional devices. microscopy (AFM) images of a typical exfoliated MoS2 Method Section. All PES experiments were performed in ultrathin flake used in our spatially resolved ARPES study. ultrahigh vacuum chambers under a base pressure better than 5 − Similar to graphene,35 39 one can determine the thickness of × 10−10 Torr. High-resolution ARPES experiments for bulk the flakes by their reflective colors, which is further confirmed samples were performed at beamline 10.0.1 at the Advanced by AFM (Figure 4d) and spatially resolved Raman spectros- Light Source, using incident photon energies from 35 to 75 eV fl 40 copy (Figure 4e) on a MoS2 ake. As illustrated in Figure 4d, with energy resolution of 15 meV and angular resolution of the atomically flat surfaces of different thicknesses can typically 0.2°. The samples were cleaved in situ and kept at 20 K during span a few microns laterally, which is sufficiently large given our the ARPES measurements. Spatially resolved ARPES data were submicrometer spatial resolution. To illustrate the unique obtained at the Spectromicroscopy beamline at the Elettra properties of monolayer MX2, photoluminescence spectroscopy Synchrotron Light Laboratory, using photon energies 74 eV, (Figure 4f) was also performed at room temperature with with energy and angle resolutions of 50 meV and 0.2°, excitation energy of 2.33 eV, yielding pronounced exciton respectively. The spatial resolution was 800 nm, and the sample emission from MoS2 and WSe2 monolayer but is largely was maintained at 100 K during the measurements. After suppressed in bulk.7,20,21 loading the sample into the ultrahigh vacuum chamber for In Figure 5, we summarize the spatially resolved ARPES ARPES measurement, an annealing process at 400 °C for 20 results on the same flake used for the study in Figure 4e. We min was performed to clean the sample surface. fi fl were able to scan across the substrate and nd the same ake by To experimentally access a full map of the MX2 band acquiring a photoemission intensity map [Figure 5a(i)−(iii), structure in the monolayer limit, in addition to the technical with different magnification levels]. Comparing these maps to difficulty of the large beam size in normal ARPES (typically the optical image [Figure 5a(iv)], we could easily identify the hundreds of micrometers) for measuring small samples, the fl ff − ake areas with di erent thicknesses, and three points (P1 P3) very low conductivity of monolayer MX2 and the resulting with mono-, bi-, and multilayers were chosen in our charging effects impose serious technical difficulties. In this − − fl investigation. The band structures measured at points P1 P3 study, after a 2H MoS2 single crystal was exfoliated into akes are illustrated in Figure 5b,c, where Figure 5b shows the maps with varying thicknesses, we transferred them onto a CVD- of the constant energy contours at 0 and 0.5 eV binding energy graphene covered SiO2/Si wafer. The graphene layer not only away from the top of VBM and Figure 5c gives the band mechanically supports but also electrically grounds the MoS2 dispersion along Γ−K and Γ−M high-symmetry directions. flakes, and thus greatly suppresses the charging effect in the Γ fl Indeed, a sudden switch of the VBM valley from K to occurs MoS2 ultrathin akes. The combination of the application of a when the thickness of the flake increases from monolayer (spot conducting graphene-covered wafer and the implementation of P1) to bilayer (spot P2), which can be seen both in Figure 5b spatially resolved ARPES, as schematically shown in Figure [where the constant energy surface spots (valley loci) in panels 4a,b, enables us to measure ultrathin MoS2 samples with high (i) and (iii) are located at the K and Γ points, respectively] and spatial resolution. Micro-Raman spectroscopy was performed Figure 5c [where the VBM valleys of panels (i) and (iii) are under ambient conditions with pump radiation operating at a located at the K and Γ points, respectively]. In contrast to this wavelength of 532 nm and with the Si Raman band at 520 cm−1 valley shift between mono- and bilayer flakes, the band as the reference. The Raman emission was collected by a 100× structure of bilayer (spot P2) and multilayers (spot P3) are objective in a backscattering geometry and with instrumental quite similar, and both have the valley sitting at the center of spectral resolution of 1.0 cm−1. To perform microphotolumi- the BZ. This observation unambiguously demonstrates that the nescence, the excitation laser was at normal incidence on the interlayer interaction plays a critical role in the band structure sample at room temperature, with a spot size of 2 μm. The laser evolution and also the position of the VBM valleys changes intensity was 100 W/cm2 at a wavelength of 532 nm. from the Γ to K point with decreasing thickness (the direct to Electronic structure calculations were performed within the indirect band gap transition from mono- to bilayer context of density functional theory using the Projector flakes25,27,28). Similarly, the thickness dependent band structure augmented wave pseudopotentials method with plane wave

4743 DOI: 10.1021/acs.nanolett.5b05107 Nano Lett. 2016, 16, 4738−4745 Nano Letters Letter basis as implemented in the VASP code. The exchange- (4) Zeng, H. L.; Dai, J. F.; Yao, W.; Xiao, D.; Cui, X. D. Valley correlation functional was treated using the Perdew−Burke− polarization in MoS2 monolayers by optical pumping. Nat. Nano- Ernzerhof generalized-gradient approximation.41 The kinetic technol. 2012, 7, 490−493. energy cutoff was fixed to 400 eV. A 24 × 24 × 6 k-mesh was (5) Mak, K. F.; He, K. L.; Shan, J.; Heinz, T. F. Control of valley used for the self-consistent calculation, and spin−orbit coupling polarization in monolayer MoS2 by optical helicity. Nat. Nanotechnol. 2012, 7, 494−498. was taken into account. The lattice constant and internal ff (6) Cao, T.; Wang, G.; Han, W. P.; Ye, H. Q.; Zhu, C. R.; Shi, J. R.; atomic positions were fully relaxed with the force cuto energy et al. Valley-selective circular dichroism of monolayer molybdenum of 0.01 eV/Å. disulphide. Nat. 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F. photon energy dependence of MX band structures Engineering the surface structure of MoS2 to preferentially expose 2 active edge sites for electrocatalysis. Nat. Mater. 2012, 11, 963−969. showing 2D/3D signatures, (III) spatially resolved (11) Voiry, D.; Yamaguchi, H.; Li, J. W.; Silva, R.; Alves, D. C. B.; ARPES measurements. (PDF) Fujita, T.; et al. Enhanced catalytic activity in strained chemically exfoliated WS2 nanosheets for hydrogen evolution. Nat. Mater. 2013, ■ AUTHOR INFORMATION 12, 850−855. (12) Xiao, D.; Liu, G. B.; Feng, W. X.; Xu, X. D.; Yao, W. Coupled Corresponding Authors spin and valley physics in monolayers of MoS2 and other group-VI *E-mail: [email protected]. Fax: +44 (0)1865 dichalcogenides. Phys. Rev. Lett. 2012, 108, 196802. 272400. (13) Shan, W. Y.; Lu, H. Z.; Xiao, D. Spin Hall effect in spin-valley *E-mail: [email protected]. coupled monolayers of transition metal dichalcogenides. Phys. Rev. B: *E-mail: [email protected]. Condens. Matter Mater. Phys. 2013, 88, 125301. Author Contributions (14) Yao, W.; Xiao, D.; Niu, Q. Valley-dependent optoelectronics from inversion symmetry breaking. Phys. Rev. B: Condens. Matter H.T.Y., Z.K.L., and G.X. equally contributed. H.T.Y. and Y.L.C. Mater. Phys. 2008, 77, 235406. conceived and designed experiments. Y.L.C., H.T.Y., B.Z., Y.Z., (15) Rycerz, A.; Tworzydlo, J.; Beenakker, C. W. J. Valley filter and V.K., M.Y., and A.B. performed ARPES measurements. G.X. valley valve in graphene. Nat. Phys. 2007, 3, 172−175. and S.C.Z. performed all DFT calculations. H.T.Y., S.W., and (16) Zhu, Z. Y.; Cheng, Y. C.; Schwingenschlogl, U. Giant spin-orbit- K.Y. fabricated devices. S.W. and X.X. operated optical induced spin splitting in two-dimensional transition-metal dichalcoge- measurements. D.D. and Y.S.H. grew MX2 crystals. Z.X.S., nide semiconductors. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, S.C.Z., Y.C., H.Y.H., and X.D.X. led experiments and 84, 153402. discussions. H.T.Y. and Y.L.C. wrote the manuscript, with (17) Li, X.; Zhang, F.; Niu, Q. Unconventional Quantum Hall effect input from all authors. and tunable spin Hall effect in Dirac materials: application to an isolated MoS2 trilayer. Phys. Rev. Lett. 2013, 110, 066803. Notes (18) Cheng, Y. C.; Zhu, Z. Y.; Tahir, M.; Schwingenschlogl, U. Spin- The authors declare no competing financial interest. orbit-induced spin splittings in polar transition metal dichalcogenide monolayers. E.P.L. 2013, 102, 57001. ■ ACKNOWLEDGMENTS (19) Lu, H. Z.; Yao, W.; Xiao, D.; Shen, S. Q. Intervalley scattering and localization behaviors of spin-valley coupled dirac Fermions. Phys. Y.L.C. acknowledges the support of the EPSRC Platform Grant Rev. Lett. 2013, 110, 016806. (Grant No.EP/M020517/1) and Hefei Science Center CAS (20) Ross, J. S.; Wu, S. F.; Yu, H. Y.; Ghimire, N. J.; Jones, A. M.; (2015HSC-UE013). H.T.Y., Z.K.L., G.X., Z.H., S.C.Z., Z.X.S., Aivazian, G.; et al. Electrical control of neutral and charged excitons in H.Y.H., and Y.C. acknowledge support from the Department of a monolayer semiconductor. Nat. Commun. 2013, 4, 1474. Energy, Office of Basic Energy Sciences, Division of Materials (21) Wu, S. F.; Ross, J. S.; Liu, G. B.; Aivazian, G.; Jones, A.; Fei, Z. Sciences and Engineering, under contract DE-AC02- Y.; et al. Electrical tuning of valley magnetic moment through − 76SF00515. S.W. and X.X. are supported by DoE, BES, symmetry control in bilayer MoS2. Nat. Phys. 2013, 9, 149 153. Division of Materials Sciences and Engineering (DE- (22) Yeh, P.-C.; Jin, W.; Zaki, N.; Zhang, D.; Liou, J. T.; Sadowski, J. SC0008145). We are also grateful to the beamtime at the T.; Al-Mahboob, A.; Dadap, J. I.; Herman, I. P.; Sutter, P.; Osgood, R. spectramicroscopy beamline granted by the Elettra synchro- M. Layer-dependent electronic structure of an atomically heavy two- tron. dimensional dichalcogenide. Phys. Rev. B: Condens. Matter Mater. 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4745 DOI: 10.1021/acs.nanolett.5b05107 Nano Lett. 2016, 16, 4738−4745