Supplementary information for. Evolution of the Valley Position in Bulk Transition-Metal Chalcogenides and. their Mono-Layer Limit

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1 Supplementary information for Evolution of the Valley Position in Bulk Transition-Metal Chalcogenides and their Mono-Layer Limit Hongtao Yuan 1,2, Zhongkai Liu 1,2,3,4, Gang Xu 1, Bo Zhou 5,6, Sanfeng Wu 7, Dumitru Dumcenco 8,9, Kai Yan 1,2, Yi Zhang 6, Sung-Kwan Mo 6, Pavel Dudin 10, Victor Kandyba 11, Mikhail Yablonskikh 11, Alexei Barinov 11, Zhixun Shen 1,2, Shoucheng Zhang 1,2, Yingsheng Huang 8, Xiaodong Xu 7, Zahid Hussain 6, Harold Y. Hwang 1,2*, Yi Cui 1,2,12*, and Yulin Chen 3,4,5,10* 1 Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA 2 Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA 3 School of Physical Science and Technology, ShanghaiTech University, Shanghai , China 4 CAS-Shanghai Science Research Center, 239 Zhang Heng Road, Shanghai , China 5 Physics Department, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK 6 Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 7 Department of Physics, Department of Materials Science and Engineering, University of Washington, Seattle, Washington 98195, USA 8 Department of Electronic and Computer Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan (ROC) 9 Electrical Engineering Institute, Ecole Polytechnique Federale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland 10 Diamond Light Source, Didcot, Oxfordshire, UK 11 Elettra-Sincrotrone Trieste ScPA, Trieste, Basovizza 34149, Italy 12 Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA * Correspondence should be addressed to: hyhwang@stanford.edu, yicui@stanford.edu, Yulin.Chen@physics.ox.ac.uk (Fax: +44 (0) ) S1

2 Part I: Typical ARPES band structure of bulk MoS 2 compared with ab initio calculation Ab initio calculation of the electronic structure was performed by density functional theory (see the methods part for details). We note that the band structure calculated based on the published experimental bulk lattice parameters showed very different features from our ARPES observations, while those based on the fully relaxed lattice parameters agrees closely with the measurements (Fig. S1 and Table S1) - indicating that the lattice parameters of the surface layers and cleaved thin flakes needed to be carefully chosen for the band structure calculation to reflect the real electronic structure. Figure S1: The comparison of our ARPES band structure (bulk MoS 2 ) and ab initio calculation with relaxed lattice parameters (white lines). As discussed in the main text, the valence band maximum (VBM) of MoS 2 resides at Γ (Fig. 1d and f) and is ~0.5 ev above the apex of the valance band at K. From Γ to K, the valence bands evolve into two sub-bands with ~180 mev splitting (at K points) caused by the strong spin-orbit interaction (SOI), in good agreement with our calculations (Fig. S1). From our measurement, the effective mass of the hole pockets is ~0.8 m 0 for VBM at Γ and ~0.5 m 0 for VBM at K, also consistent with ab initio calculations. In general, our ab inito calculation and ARPES measurements on all three MX 2 materials we studied are summarized in Table S1 and S2 below, where they show excellent agreement: S2

3 Table S1: Comparison of the key parameters of electronic band structures in relaxed bulk MX 2 a (Å) c (Å) d (Å) gap (ev) E Γ (ev) CB E ΛK K VB E ΓK (ev) VB E KK (ev) Cal. Exp. Cal. Exp. Cal. Exp. Cal. Exp. MoS > WS WSe < Table S2: Comparison of the effective masses in relaxed bulk MX 2 a (Å) c (Å) d (Å) * * mcb Λ ( m0 ) * * mcb K m0 mvb Γ ( m0 ) mvb K ( m0 ) Cal. Exp. Cal. Exp. Cal. Exp. Cal. Exp. MoS N/A ± ± ±0.1 WS ± ± ± ±0.07 WSe ± N/A ± ±0.05 Part II: Surface alkaline-metal doping and photon energy dependence of MX 2 band structures showing 2D/3D signatures The valence band information obtained from ARPES can be well captured by our ab initio calculations, as indicated in Fig. S1 above. However, the exact location of the conduction band minimum (CBM) in MX 2 has been quite controversial in prior theoretical band calculations. Taking MoS 2 as an example, most of the band calculations to date (Ref 16, 20, 23, 24, 25 in main text) suggest that the CBM sits somewhere along Γ-K (Λ point). Nevertheless, a conclusive understanding of where the exact CBM position is in momentum space remains elusive, particularly due to the fact that the as-grown and even n-doped MoS 2 (also other MX 2 ) samples typically form some impurity bands inside the band gap and the Fermi energy (E F ) is always pinned inside the band gap, making direct probe of the conduction bands difficult in ARPES measurements. S3

4 Figure S2: MoS 2 electronic band structure measured with various photon energies from 35 ev to 75 ev a) Band dispersions along the Γ-K high symmetry direction; b) and c) Energy Distribution Curves (EDCs) at K and Γ, respectively. To observe the conduction bands, we introduced potassium atoms (by in situ evaporation) onto the MX 2 sample surface, which allowed us to raise E F to reach the CBM. Potassium atoms were evaporated from an alkali metal dispenser (getter source from SAES Inc.). The evaporating current and duration was set at 5.7 A and 10 minutes, respectively. We can roughly estimate the K coverage by calculating the sheet carrier density from the size of the Fermi surface ( electrons per MoS 2 unit cell, or electrons/cm 2 ). With the assumption that each K atom donates one electron only to the first monolayer of MoS 2, the coverage is as low as layer. Such a low K coverage suggests that the K dosage in our measurement should not have observable effect in modifying the band structure in MX 2 crystals. As can be seen in Fig. 1 e (before K-dosage) and f (after K-dosage), although the band structure became slightly blurred due to the additional scattering by the random potassium atoms on the surface, the CBM was clearly identified at the K points after the potassium dosing, showing a 1.4 ev indirect band gap with respect to the VBM at the Γ point (Fig. 1e). Our S4

5 result provides the most direct measure of the CBM loci in momentum-space and shows a significant difference from most calculations. To investigate the origin and the dimensionality of the bands at high symmetry points, photon energy dependent ARPES study was performed and the k z -dispersion of the band structure of MoS 2 is illustrated in Fig. S2, from which one can clearly see that the band around Γ point moves down dramatically with increasing photon energies from 35 ev (corresponding to k z = 0) to 50 ev (corresponding to k z = π), while the band around the K points remains unchanged. Such clear difference indicates the bands around Γ disperse dramatically, while those around K show almost no dispersion along the k z momentum. Figure S3. The band valleys at K and Λ points originate from two different sub-bands with different orbital components. Valence band near the Γ point and conduction band near the K point originate from out-of-plane Mo- d orbital ( 2 2 d in figure) while conduction band near Λ point and valence 2 3z r z band near K point originate from in-plane Mo- 2 2 dx y and Mo- d xy orbitals. S5

6 The different photon energy dependence of the bands around Γ and Κ is consistent with our band calculation (Fig. S3) which shows that the 2D signature of the bands around K originates from the localized in-plane Mo- 2 2 dx y and Mo- d orbitals, while the 3D signature of the bands around Γ xy comes from the delocalized out-of-plane Mo- d and S-p 2 2 z orbitals. Indeed, the strong k z dispersion in the center of the BZ and its dramatic change with dimension plays a critical role in the indirect-direct band gap transition with decreasing thickness. 3z r Part III: Spatially resolved ARPES measurements The MoS 2 and WSe 2 flakes used for the spatially-resolved ARPES study were exfoliated from bulk single crystals. MX 2 flakes with varied thickness were transferred onto a CVD-graphene covered SiO 2 /Si wafer. The SiO 2 /Si wafer was used to enhance the optical contrast of flakes with different thicknesses (so they can be visually identified). The intermediate graphene layer is used to provide electrical conduction for ARPES measurements. The flake transferring process is as following: 1. Spin coat Polyvinyl alcohol (PVA) on a bared SiO 2 /Si substrate with a speed of 3000 rpm for 60 seconds and baking at 80 ºC for 5 minutes; 2. Spin coat PMMA (950 A5) on top of PVA with 3000 rpm for 60 seconds and baking at 80 ºC for 10 minutes; 3. Cleave MX 2 flakes on top of PMMA with tape mechanical exfoliation method; 4. Peel off the PMMA (with supported MX 2 flakes) with wet method and pick up the PMMA film with a washer; 5. Using the downward face of the PMMA, place it onto the surface of the target Graphene/SiO 2 /Si wafer, and heat the wafer to 120 ºC and press the PMMA onto the wafer surface for 5 minutes; 6. Remove the washer and dissolve the PMMA with acetone and further clean the wafer surface with IPA before loading into ultra high vacuum (UHV) for annealing. Fig. S4 shows optical images of typical samples (exfoliated MoS 2 and WSe 2 flakes on the substrate). The sample was annealed at 400 ºC for 20 minutes after loading into the ARPES UHV chamber. S6

7 Figure S4. a) Schematic of the samples measured in spatially resolved ARPES experiments (MX 2 flakes on graphene covered SiO 2 /Si wafer). b) and c) Optical images of the MoS 2 and WSe 2 flakes used in the main text with regions of different thicknesses labeled. A schematic of the spatially resolved ARPES spectrometer is illustrated in Fig. S5. The beam spot size is ~800 nm, and the stability of the beam position during measurements is ~100 nm. The photon energy used for the experiments is 74 ev. The hemispherical dispersive analyzer mounted on a goniometer located inside the main UHV chamber has an energy resolution of ~50 mev with the photon energy used. More details please refer to SI Ref [1]. Figure S5: Schematic of the spatially resolved ARPES spectrometer. The main components are Schwarzschild objectives (SO1 and SO2), electron analyzer (EA), goniometer (G), sample holder (SH), scanning stage (SS) and cryostat (C). S7

8 To perform spatially resolved ARPES measurements, we first scanned the samples to obtain their contrast map of the (angle integrated) photoemission signal. Judging from these contrast maps (and comparing to the optical image if necessary, see Fig. 5 in the main text and Fig. S6 below), we could accurately identify the MX 2 flakes with different thicknesses. We then positioned the photon beam (~800 nm in size) to different flakes and performed the ARPES study to obtain the band structure of flakes with different thicknesses. We observed the same evolution of the VBM valley position from K to Γ when the flake thickness increases from one to two layers (Fig. S6); the band structure of bi-layer and multi-layer flakes also show general similarity. In WSe 2, the energy difference of the valence band between K and Γ is ~100 mev [Fig. S6c(iii)], which is 5 times smaller than that of MoS 2 [Fig. 5c(iii)]. Figure S6: Band valley evolutions from multi-, bi- to mono-layer WSe 2 nano-flakes. a) 2D photoemission spectra intensity contrast map of WSe 2 flakes (measured at the Fermi level), with different magnifications from large area (i) to small area (iii), demonstrating the processes to locate the target mono-layer flake. Panel (iv) gives the optical image of the same flake, where the mono-, bi- and multi-layer WSe 2 flakes can be clearly seen. Points P1-P3 indicate the three measurement S8

9 positions for mono-, bi- and multi-layer WSe 2 flakes. b) Constant energy plots measured at monolayer (point P1), bilayer (point P2) and multilayer (point P3) spots, with the energy positions at E- E VBM = 0 ev and E-E VBM = ev, respectively. c) Band dispersions along the high symmetry K-Γ- K and M-Γ-M directions from point P1-P3, showing the band valley evolution with different flake thicknesses. Reference: (1) Dudin, P., Lacovig, P., Fava, C., Nicolini, E., Bianco, A., Cautero, G., Barinov, A. J. Synchrotron Rad , S9