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1 Direct observation of the transition from indirect to direct bandgap in atomically thin epitaxial MoSe 2 Yi Zhang, Tay-Rong Chang, Bo Zhou, Yong-Tao Cui, Hao Yan, Zhongkai Liu, Felix Schmitt, James Lee, Rob Moore, Yulin Chen, Hsin Lin, Horng-Tay Jeng, Sung-Kwan Mo *, Zahid Hussain, Arun Bansil and Zhi-Xun Shen * * SKMo@lbl.gov; zxshen@stanford.edu A: Surface lattice mismatch and orientation between bilayer graphene (BLG) substrate and MoSe 2 Our substrate is BLG terminated SiC(0001). The lattice constant of graphene is 2.46 Å [S1], which is obviously smaller than that of MoSe 2 (3.29 Å) [S2] (Fig. S1b). However, the ratio of their lattice constants is opportunely very close to 3:4. Furthermore, the low-energy electron diffraction (LEED) pattern of 0.6 monolayer (ML) MoSe 2 film (Fig. S1d) shows that they are always in the same lattice orientation when in the layer-by-layer growth mode. For these reasons, we expect that the superlattice MoSe 2 (3 3)/graphene(4 4) interface will produce a periodic ~0.99 nm Moiré pattern, which can be verified by scanning tunneling microscopy in future research. Since the lattice constant of graphene is smaller than that of MoSe 2, the Brillouin zone (BZ) of graphene (red line in Fig. S1e) is larger than that of MoSe 2 (green line in Fig.S1e). Therefore, the K point of graphene s BZ (K G ) is outside of the BZ of MoSe 2, and the LEED pattern of graphene is also outside of the pattern of MoSe 2 (Fig. S1d). B: Co-existing BLG and MoSe 2 band in <2 ML MoSe 2 films NATURE NANOTECHNOLOGY 1

2 Fig. S1 Lattice mismatch and orientation. Top view of a 3 3 MoSe 2 superlattice with superlattice constant 9.87Å and b 4 4 graphene superlattice with superlattice constant 9.84Å. The superlattice constant mismatch between 3 3 MoSe 2 and 4 4 graphene is only ~0.3%. c. Side view of MoSe 2 (3 3)/graphene(4 4) interface. The Se-C bond-length is about 4.2Å. d. LEED pattern of 0.6 ML MoSe 2 film. Green and red dotted circles indicate the co-existing LEED patterns of both substrate BLG and epitaxial MoSe 2 film, respectively. e. Surface Brillouin zone (BZ) of graphene (red line) and MoSe 2 (green line). The K point of graphene BZ (K G ) is outside of the BZ of MoSe 2. k x and k y refer to the momentum along the Γ-Κ and Γ-M direction, corresponding with the x-axis and y-axis shown in a-c, respectively. Figures S2a S2d are the reflection high-energy electron diffraction (RHEED) patterns of MoSe 2 films, with increasing coverage from 0.6 ML to 1.2 ML. When the MoSe 2 coverage is <1 ML, we can observe the co-existing RHEED patterns of both substrate BLG and epitaxial MoSe 2 (Figs S2a and S2b), implying that there exists some exposed area of substrate BLG. When the MoSe 2 coverage is >1 ML, the RHEED pattern of BLG is completely absent (Figs S2c and S2d), 2 NATURE NANOTECHNOLOGY

3 SUPPLEMENTARY INFORMATION Fig. S2 Co-existing BLG and MoSe 2 band. a-d RHEED patterns of MoSe 2 films with increasing coverage from 0.6 ML to 1.2 ML. Green and red dotted circles in a indicate the co-existing diffraction spots of both graphene and MoSe2, respectively. In c and d, the pattern of graphene is completed disappeared. e-l ARPES spectra with increasing coverage from 0.6 ML to 2.0 ML. The yellow dashed line indicates the Fermi level. The green dotted lines indicate the Γ point and K point of MoSe 2 surface BZ, and the red dotted line indicates the K point of graphene s BZ (K G ) outsides the BZ of MoSe 2. m MDCs along the white dashed line shown in e with difference coverage. The green and red line indicates the position of MoSe 2 and BLG peaks, respectively. The BLG peaks are completely disappeared in 2.0 ML MDC line. implying that the substrate BLG is fully covered with MoSe 2 films. However, despite the fully covered MoSe 2 film in >1 ML samples, we can still observe the angle-resolved photoemission spectroscopy (ARPES) signal from substrate BLG in <2 ML MoSe 2 films, indicating the electron escape length is longer than 1 ML but shorter than 2 ML MoSe 2. Figures S2e S2l shows the ARPES spectra of MoSe 2 films with different coverage from 0.6ML to 2.0ML by increasing only 0.2 ML per figure. Fig S2m is the momentum dispersion curves (MDCs) at the energy position along the white dashed line shown in Fig S2e with different coverage. It is clear that the BLG peaks become gradually weaker with increasing coverage, and then completely absent in the spectra of 2.0 ML MoSe 2 film. This disappearance of BLG peaks means that the very short escape length of the photoelectrons minimizes the ARPES signal from BLG substrate for the samples thicker than 2.0 ML. NATURE NANOTECHNOLOGY 3

4 C: The influence of substrate BLG to MoSe 2 band structure in ARPES In order to study possible influence of substrate BLG to MoSe 2 band structure, we carefully analyzed the band structure of substrate BLG in 0.6 ML, 1.0 ML and 1.4 ML MoSe 2 films, and compared its dispersion with previous literatures [S3, S4]. Figures S3a S3c are the zoom-in ARPES spectra of 0.6 ML, 1.0 ML and 1.4 ML MoSe 2 films. We can clearly observe the linear-dispersion bands of the two Dirac cones in BLG [S3]. This band structure is the same to the previous ARPES report (Fig. S3i) [S4]. In Figs S3d and S3h, we cannot observe any signal of BLG band, because the ARPES signal is nearly completely buried by 2.0 ML MoSe 2 film as shown in the previous section (Fig. S2m). To get the band dispersion of our BLG, we use double Lorentz peaks to fit the MDC lines in Figs S3e S3g. The red lines are the fitting curves, and the fitting peaks are indicated in the Figs S3a S3c with green circles. We found these peaks in the 0.6 ML and 1.0 ML spectra keep good linear dispersion. In the 1.4 ML spectra, since the BLG signal is severely suppressed by the stronger signal from Fig. S3 Substrate BLG band dispersion. a-d zoom-in ARPES spectra of 0.6ML, 1.0Ml, 1.4ML and 2.0 ML MoSe 2 films. e-h MDCs of ARPES spectra a-d. The red lines in e-g are the double Lorentz peaks fitting results of MDCs near BLG bands. These peaks positions are indicated in a-c with green circles. The green lines in a-c are the linearly fitting results of those peaks. i Previous report of APRES spectra of BLG [S4]. 4 NATURE NANOTECHNOLOGY

5 SUPPLEMENTARY INFORMATION MoSe 2 around the band-crossing point, we cannot get good fitting peaks for the left branch of the two BLG bands. But the one on the right still keeps good linear dispersion. By simply using equation E = h v k to linearly fit those peaks, we can get the Fermi k F velocity v of our substrate BLG is ~ m/s. This value is also the same as in the previous F reports [S4, S5]. Since the band structure of substrate BLG is keeping exactly the same linear dispersion in different coverage MoSe 2 films, without any deviation from previously reported ARPES data, and the Fermi velocity is the same as in the previous reports [S4, S5], we can conclude that our expitaxial MoSe 2 film does not affect the band structure of substrate BLG. In other words, the interaction between BLG and MoSe 2 film is minimal, if any. This also implicates that the mutual influence on the respective band structure is minimal, thus is consistent with the substrate not affecting the band structure of MoSe 2, nor the indirect to direct band gap transition in monolayer MoSe 2. Fig. S4 (left) Top view and side view of MoSe 2 (3 3)/BLG(4 4) supercell. (Right) Computed band structure of freestanding MoSe 2 (3 3) (blue lines) and MoSe 2 (3 3)/BLG(4 4) supercell (red dots). NATURE NANOTECHNOLOGY 5

6 D: Computation including the influence of BLG substrate In order to assess effects of the substrate on the electronic structure, we consider a MoSe 2 (3 3)/BLG(4 4) supercell (Fig. S4, left panel). After structural relaxation, we found that the atomic positions of MoSe 2 do not change significantly, and the Se-C bond-length is about 4.2 Å, implying weak interaction between MoSe 2 with BLG substrate. The band structure of freestanding MoSe 2 (blue solid lines in Fig. S4) is shown superposed on that of MoSe 2 (3 3)/BLG(4 4) supercell (red dots in Fig. S4). The BZ here is for MoSe 2 (3 3), so that the K-point of the freestanding MoSe 2 folds to the Γ-point of the supercell. A comparison between the band structure of the freestanding MoSe 2 with that of the supported film shows that the band structure of MoSe 2 remains essentially intact in the presence of the substrate, despite the appearance of a substrate induced band. Notably, although the coupling between MoSe 2 and graphene is weak, the hexagonal symmetry is retained since MoSe 2 film and graphene have the same orientation. References S1. Chung, D.D.L., Journal of Materials Science, 37, 1475 (2002) S2. Kumar, A. and P.K. Ahluwalia, The European Physical Journal B, 85, 186 (2012) S3. Ho, Y.H., et al., Philosophical Transactions of the Royal Society A, 368, 5445 (2010) S4. Ohta, T., Science, 313, 951 (2006) S5. Avila, J., et al., Scientific Reports, 3, 2439 (2013) 6 NATURE NANOTECHNOLOGY