Supplementary Information. Interfacial Properties of Bilayer and Trilayer Graphene on Metal. Substrates

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1 Supplementary Information Interfacial Properties of Bilayer and Trilayer Graphene on Metal Substrates Jiaxin Zheng, 1,2, Yangyang Wang, 1, Lu Wang, 3 Ruge Quhe, 1,2 Zeyuan Ni, 1 Wai-Ning Mei, 3 Zhengxiang Gao, 1 Dapeng Yu, 1 Junjie Shi, 1 and Jing Lu 1,* 1 State Key Laboratory for Mesoscopic Physics and Department of Physics, Peking University, Beijing , P. R. China 2 Academy for Advanced Interdisciplinary Studies, Peking University, Beijing , P. R. China 3 Department of Physics, University of Nebraska at Omaha, Omaha, Nebraska These authors contributed equally to this work. *Corresponding author: jinglu@pku.edu.cn Figure S1. Band structure of bilayer graphene (BLG) on Al (111) substrate. The Fermi level is set at zero. Blue and red lines depict the bands with weight projected on the contacted and uncontacted graphene layer, respectively, with the radius of spots representing the weight. S1

2 Figure S2. Schematic representation of the relation between the Fermi level shift and work function of (a) SLG on metal and BLG (b) physisorbed and (c) strongly chemisorbed on metal. We ignore the band distortion. S2

3 metal Figure S3. Band gap E g as a function of ΔE f in ABA-stacked TLG physisorbed on the metal surfaces. The black dash-dot line is the boundary of the n- and p-type doping region. The blue squares and red circles are for the data obtained from the CASTEP and VASP codes, respectively. (a) (b) n d C-M d 0 z 0 z 1 z 2 z 3 (c) E E 1 E 2 (d) Figure S4. (a) Schematic of the TLG/metal contacts. Average value of difference electron density Δn(z) in planes parallel to the interface of (b) ABA-stacked TLG/Al and (c) ABA-stacked TLG/Pt, and (d) ABC-stacked TLG/Pt, reflecting the charge displacement upon formation of the TLG/metal contacts. To explore the mechanisms to open band gaps in ABA- and ABC-stacked TLG, we consider a TLG/metal contact model 1,2. We utilize the plane-averaged excess electron density Δn(z) = n TLG/M n TLG n M to visualize the electron redistribution. As shown in Figure S2b, S2c and S2d, the sign and size of the interface dipole are consistent with the system s band structures. Besides, ABA- and ABC-stacked TLG show little difference in the charge redistribution. The transferred electron density on the metal surface is Δn = (Δn 1 + Δn 2 + Δn 3 ), where Δn i is the electron density change of the i layer. The excess electrons on metal and TLG assumedly induce a uniform electric field E between metal and TLG and E i, i = 1 and 2, S3

4 between the graphene layers as illustrated in Figure 4a. The changes in potential energy of adjacent layers are given by 1,2 ΔU 21 =U 2 U 1 = α(δn 2 + Δn 3 ) Δ c (1) ΔU 32 = U 3 U 2 = αδn 3 (2) Where U i (i = 1, 2, and 3) is the potential of each graphene sheet, α = ed 0 /ε 0, ε 0 is the vaccum permittivity and d 0 is the interlayer distance of TLG, and Δ c is the potential step resulting from the overlap of the metal and graphene wave functions, with a value of around 0.55 ev as noted previously. In addition, we neglect the interaction between graphene layers, since the van der Waals interaction between graphene layers is much weaker than Δ c. Obviously, there are ΔU 21 ΔU 32 = αδn 2 Δ c 0, and ΔU 31 = U 3 U 1 = α(δn 2 + 2Δn 3 ) Δ c 0. The mirror symmetry of the potential difference between adjacent layers of ABA-stacked TLG is broken by ΔU 21 ΔU 32 0, while the inversion symmetry of ABC-stacked TLG is broken by ΔU As a result, a band gap is induced for both ABA and ABC-stacked TLG, which has been predicted by the tight-binding calculations 1,2. We can estimate the electron density Δn 2 and Δn 3 by integrating Δn(z) between the nodes z 1 and z 2, z 2 and z 3, respectively, as show in the Figure S2b, Δ n i z i z i 1 Δ n ( z ) dz / S cell where S cell is the area of the interface supercell. For ABA-stacked TLG on Al substrate we derive ΔU 21 ΔU 32 = 0.86 ev from Δn 2 = e/ǻ 2 and Δn 3 = e/ǻ 2, while for ABC-stacked TLG on Al substrate ΔU 31 = 1.12 ev, from Δn 2 = e/ǻ 2 and Δn 3 = e/ǻ 2, which results in a band gap of ev in ABA-stacked TLG and ev in ABC-stacked TLG. The latter value is in reasonably agreement with the DFT calculation result 0.14 ev in Zhang et al. s work 3. Besides, at ΔE f = 0, there is ΔU 31 = Δ c = 0.55 ev shown in Figure 6, resulting in a band gap of ev, which is also consistent with the DFT calculation result 0.08 ev of Zhang et al. 3. According to the work by Zhang et al. 3, the band gap of ABC-stacked TLG is approximately proportional to the ΔU 31 when ΔU 31 < 2 ev (when ΔU 31 > 2 ev, the gap approaches its maximum value). In the n-type doping region (Δn i > 0, ΔE f < 0), with the increasing ΔE f, the more charge is transferred, and Δn 2 + 2Δn 3 gets larger, leading to a larger ΔU 31 and thus a larger E g. In the p-type doping region (Δn i < 0), as αδn 2 > 0 and αδn 3 > 0, they conteract Δ c ( Δ c < 0), and ΔU 31 are smaller than those in the n-type doping S4

5 PDOS (ev -1 ) cases at the same doping level Δn (or ΔE f ). Therefore, the band gap of ABC-stacked TLG at the same ΔE f in the p-type doping region is smaller than that in the n-type doping region, and the observed asymmetry of electron and hole doping in the band gap opening of ABC-stacked TLG is explained. The electron-hole asymmetry of the band gaps of ABA-stacked TLG can also be attributed to the nonvanishing Δ c term. Notably, it is shown both theoretically 3-6 and experimentally 4,7 that the conduction and valence bands are overlapped in ABA-stacked TLG under a uniform external electric field. The cause lies in that the on-site energy differences between the adjacent graphene layers are the same, i.e. ΔU 21 = ΔU 32, therein. 4 BLG in the lead with Ti contact E-E f (ev) Figure S5. Projected density of states (PDOS) of BLG in the lead with Ti electrodes. S5

6 (a) (b) Figure S6. Band structures of ABA-stacked trilayer graphene (TLG) on Ru (0001) substrate calculated by using the (a) CASTEP and (b) VASP codes, respectively. The Fermi level is set at zero. In the right panel, TLG-dominated bands are plotted against the metal projected bands (green). Blue and red lines depict the bands with weight projected on the innermost graphene layer and the outer graphene bilayer, respectively, with the blueness and redness representing the weight. The inset shows the relaxed structure of ABA-stacked TLG/Ru contact, which is consistent with that in Ref. 8. The first and second layers of graphene are denoted by black and gray balls, respectively. S6

7 References 1 Avetisyan, A. A., Partoens, B., & Peeters, F. M., Electric field tuning of the band gap in graphene multilayers. Phys. Rev. B 79 (3), (2009). 2 Avetisyan, A. A., Partoens, B., & Peeters, F. M., Electric-field control of the band gap and Fermi energy in graphene multilayers by top and back gates. Phys. Rev. B 80 (19), (2009). 3 Zhang, F., Sahu, B., Min, H., & MacDonald, A. H., Band structure of ABC-stacked graphene trilayers. Phys. Rev. B 82 (3), (2010). 4 Lui, C. H., Li, Z., Mak, K. F., Cappelluti, E., & Heinz, T. F., Observation of an electrically tunable band gap in trilayer graphene. Nat. Phys. 7 (12), (2011). 5 Tang, K. C. et al., Electric-field-induced energy gap in few-layer graphene. J. Phys. Chem. C 115 (19), 9458 (2011). 6 Bao, W. et al., Stacking-dependent band gap and quantum transport in trilayer graphene. Nat. Phys. 7 (12), (2011). 7 Craciun, M. F. et al., Trilayer graphene is a semimetal with a gate-tunable band overlap. Nat. Nanotech. 4 (6), (2009). 8 Sutter, P., Hybertsen, M. S., Sadowski, J. T., & Sutter, E., Electronic structure of few-layer epitaxial graphene on Ru(0001). Nano Lett. 9 (7), (2009). S7