Indirect Interlayer Bonding in Graphene–Topological Insulator van der

Indirect Interlayer Bonding in Graphene− Topological Insulator van der Waals Heterostructure: Giant Spin−Orbit Splitting of the Graphene Dirac States Shivani Rajput,*,† Yao-Yi Li,† Michael Weinert,† and Lian Li†,‡ †

Department of Physics, University of Wisconsin, Milwaukee, Wisconsin 53211, United States Department of Physics and Astronomy, West Virginia University, Morgantown, West Virginia 26506, United States

‡

S Supporting Information *

ABSTRACT: van der Waals (vdW) heterostructures of twodimensional materials exhibit properties and functionalities that can be tuned by stacking order and interlayer coupling. Although direct covalent bonding is not expected at the heterojunction, the formation of an interface nevertheless breaks the symmetries of the layers, and the orthogonal requirement of the wave functions can lead to indirect interfacial coupling, creating new properties and functionalities beyond their constituent layers. Here, we fabricate graphene/topological insulator vdW heterostructure by transferring chemical vapor deposited graphene onto Bi2Se3 grown by molecular beam epitaxy. Using scanning tunneling microscopy/spectroscopy, we observe a giant spin−orbit splitting of the graphene Dirac states up to 80 meV. Density functional theory calculations further reveal that this splitting of the graphene bands is a consequence of the breaking of inversion symmetry and the orthogonalization requirement on the overlapping wave functions at the interface, rather than simple direct bonding. Our findings reveal two intrinsic characteristicsthe symmetry breaking and orthogonalization of the wave functions at the interfacethat underlines the properties of vdW heterostructures. KEYWORDS: graphene, topological insulator, van der Waals heterostructures, spin−orbit splitting, STM, DFT

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graphene/hexagonal boron nitride heterostructures, the inplane rotational freedom leads to the formation of Moiré patterns that strongly modify the Dirac spectrum with new Dirac cones appearing in both valence and conduction bands.7 In heterostructures of monolayer TMDs, strong interlayer electronic coupling in WSe2/MoS28 and interlayer excitons in MoSe2/WSe29 have also been observed. Here, we carry out an integrated theoretical and experimental investigation to determine how properties of vdW heterostructures emerge in the absence of direct bonding at the interface. We synthesize a prototypical vdW heterojunction by transferring chemical vapor deposited (CVD) graphene onto the topological insulator Bi2Se3 grown by molecular beam epitaxy (MBE). Using scanning tunneling microscopy/spectroscopy (STM/S), we observe a giant spin−orbit splitting of

he successful experimental isolation of graphene in 2004 has propelled great interests in layered materials that are essentially stacks of two-dimensional (2D) building blocks, with each unit consisting of one to a few atomic planes that are covalently bonded in-plane, and weakly bonded by van der Waals (vdW) forces across the planes.1 This anisotropic bonding facilitates the exfoliation or epitaxial growth of atomically thin 2D materials, which host fascinating physical phenomena ranging from ballistic carrier transport in graphene,2 remarkable optical properties of transition metal dichacolgenides (TMDs) such as MoSe2 monolayers,3 and symmetry-protected helical edge states in topological insulators such as Bi bilayers.4 Furthermore, the weak vdW interlayer bonding also facilitates new avenues for “materials by design” through the mechanical assembly or vdW epitaxy of heterostructures of highly mismatched 2D layers.1 Albeit weakly bonded, new properties and functionalities not present for the constituent 2D layers nevertheless emerge in these heterostructures.1,5,6 Most notably, in exfoliated vdW © 2016 American Chemical Society

Received: May 22, 2016 Accepted: September 12, 2016 Published: September 12, 2016 8450

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to extract the dispersion of the graphene bands (Supporting Figure 1).

the graphene Dirac states of up to 80 meV, several orders of magnitude larger compared to its intrinsic value,10 with a spatial variation of ±20 meV. Our density functional theory (DFT) calculations show that this is a result of the proximity to Bi2Se3, which breaks the inversion and horizontal mirror symmetries of the graphene, thus lifting the 4-fold degeneracy of its bands at the Dirac point (ED).11 The calculations further reveal that the transfer of the spin−orbit coupling (SOC) is through Bi character introduced into the graphene Dirac states due to orthogonalization to the Bi2Se3 states, rather than the direct coupling between the Dirac states of the two systems as suggested in previous calculations.12,13 The direct mechanism, which is expected to be strongest when original states have nearly the same energies, is also invoked in ref 14. where a spin−orbit gap of 20 meV of Cs-doped graphene/Bi2Te2Se was inferred by comparing angle resolved photoemission spectra (ARPES) to DFT calculations. Moreover, we find that the strong spatial fluctuations of the transferred SOC in graphene both in energy and crystal momentum is due to the inherent nonepitaxial relation at the graphene/Bi2Se3 vdW heterojunction. These findings reveal two intrinsic characteristics, that is, the symmetry breaking and orthogonalization of the wave functions at the interface that are key to determining the properties of vdW heterostructures. Calculations were carried out using the Full-potential Linearized Augmented Plane Wave (FLAPW) method as implemented in f lair.15 A (√3 × √3) graphene overlayer on (1 × 1) Bi2Se3(0001) results in a compressed C−C bond length (1.38 Å vs the nominal 1.42 Å) (Figure 1a), suggesting that a simple epitaxial relationship with the Bi2Se3 substrate is unlikely. Because of their different lattices, the K (K′) points of the graphene Brillouin zone (BZ) fold back to around Γ of the Bi2Se3 BZ (Figure 1b); thus a k-projection technique was used

RESULTS AND DISCUSSION Calculations were initially done for graphene on one side of a 7 quintuple-layer (QL) Bi2Se3(0001) film (Figure 1c), where Dirac states are found on the free surface.16,17 When interfaced with graphene, the Bi2Se3 Dirac states are modified and shifted to the interface spatially, as well as energetically toward EF. The TI interface Dirac point depends sensitively on the separation between graphene and Bi2Se3; for a separation of 3.85 Å, a shift of 0.13 eV is found (Supporting Figure 2). To address whether the induced spin−orbit splitting requires the existence of Bi2Se3 Dirac states, similar calculations were performed for graphene on a single QL Bi2Se3 (Figure 1c), at which point there is not enough bulk for the TI Dirac states to fully develop.16 In both cases, the bands resemble spinless bilayer graphene with two degenerate bands at ED, and another set of upward and downward dispersing bands split away from it.11 This indicates that the transferred SOC is not the hybridization of the graphene and Bi2Se3 Dirac states. Moreover, when the SOC is set to zero (Figure 1c), the graphene bands exhibit the spindegenerate linear dispersion, confirming that transferred SOC is responsible for the splitting. [Note that the graphene Dirac point is shown above EF, a result of the difference in calculated work functions for Bi2Se3 (5.51 eV) and the compressed graphene (3.97 eV). This is consistent with the recent ARPES study, where p-type doping of graphene is found in graphene/ Bi2Te2Se heterostructures.14] The physics behind the calculated bands can be understood by noting that the formation of the vdW junction lowers the graphene symmetry, even though significant direct bonding between the layers is not expected due to the inherent vdW interlayer bonding. For free-standing graphene, which has D6h symmetry, the small group of the K (K′) points is D3h and the Dirac states belong to a doubly degenerate single group irreducible representation (irrep). With SOC, these four states (with spin) break into two 2-fold degenerate irreps of the double group, and thus, a gap opens at K. When graphene is in proximity to a substrate, however, both its inversion and horizontal mirror (σh) symmetries are broken. The loss of inversion symmetry implies that the SOC bands need not be 2-fold spin degenerate, whereas the loss of σh symmetry reduces the small group of K to C3v. Though nonrelativistically, the four states at ED still transform as the doubly degenerate Γ3 irrep of the single group (c.f., Figure 1c), with SOC, Γ3 →Γ4 (2-fold) + Γ5 (1-fold) + Γ6 (1-fold). Thus, the SOC bands of graphene/Bi2Se3 around ED consist of two linearly dispersing states (Γ4, gapless) and two spin−orbit split states (Γ5, Γ6), as shown in Figure 1c. Taking into account the difference in translational symmetry of the graphene and Bi2Se3(0001), the remaining Γ4 degeneracy is broken, resulting in a small gap (∼15 meV in Figure 1c), that varies from 1.3 to 18 meV depending on the separation and registry between graphene and the substrate (c.f., Figure 2). Because the intrinsic SOC of carbon is small, the large spin− orbit splitting of the graphene bands must arise from Bi2Se3 character−particularly the Bi states due to their large relativistic effects−hybridized into graphene wave functions. Figure 1d shows the density (scalar relativistic) of graphene states at Dirac point for the heterojunction. In addition to the expected π state density of graphene, significant weight is clearly seen on the Bi atoms, but essentially none on the uppermost Se atoms.

Figure 1. (a) Model of graphene/Bi2Se3(0001) exhibiting a √3 × √3 epitaxial relationship. Yellow: carbon; blue: Bi; red: Se. (b) Bi2Se3 and graphene BZ with high symmetry points marked. The colored lines show different cuts along high symmetry directions around Γ and K, K′. (c) The k-projected bands for graphene on 7 and 1 quintuple-layer (QL) Bi2Se3, and on the 7 QL without SOC, respectively, for a separation of 3.75 Å. (d) Density corresponding to the graphene Dirac states at the graphene/Bi2Se3 junction; the wave function weight on the Bi atoms accounts for the transferred SOC. (Isosurface = 10−4 e−/a3B; maximum of the R−G−B color is 0.125 e−/a3B.). 8451

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Figure 2. (a) Structural models of three different registries between graphene and Bi2Se3 (yellow, carbon; blue, Bi; red, Se). (b) Corresponding bands (K + K′) along the Γ−K′ line of Figure 1b for each registry and three separations.

Figure 3. (a) STM image of an as-grown 30 nm Bi2Se3 film. (It = 0.1 nA, Vs = −0.81 V). (b) dI/dV spectrum of as-grown Bi2Se3 with ED marked. Inset: Atomic resolution image of Bi2Se3 (It = 0.15 nA, Vs = −0.6 V). (c) Raman spectrum of graphene/Bi2Se3. Inset: close-up view of the characteristic graphene bands. (d) STM image of graphene/Bi2Se3 (It = 0.1 nA, Vs = −1.89 V). (e) Atomic resolution image of graphene continuously covering a Bi2Se3 step edge (It = 0.5 nA, Vs = −0.1 V).

bonding between the Bi2Se3 Dirac states and the graphene π states is not responsible for the calculated spin−orbit splitting. Instead, for vdW heterojunctions where direct hopping/ bonding is expected to be weak, orthogonalization requirements on the overlapping wave functions alone18 can lead to gaps at band crossings and mix in substrate wave function character into the graphene states throughout the bands, and not just when the states coincide in energy. This orthogonaliza-

Because the surface state of the 1 QL Bi2Se3 (and the Dirac states for Bi2Se3 > 5 QL) have significant Se character and spatially overlap with the graphene π orbitals (Supporting Figure 3a), if direct bonding were dominant, then the graphene Dirac states should have significant weight on the Se atoms also. Thus, this lack of surface Se character in the hybridized graphene bands indicates that the simple picture of direct 8452

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Figure 4. (a) Representative dI/dV spectra taken on graphene/Bi2Se3. Inset: atomic resolution image of the graphene honeycomb structure (2 × 2 nm2, Vs = −0.1 V, It = 0.5 nA). (b) Close-up view of boxed region in (a), red and green dashed lines are the 1/ E1 − E and 1/ E − E2 fits to the two spin−orbit peaks with Gaussian broadening. Inset: Calculated spin−orbit split bands of graphene/Bi2Se3 at 3.875 Å separation and offset registry (c.f., Figure 2), which provides the best fit. (c) dI/dV spectra taken on a flat terrace at positions 1−10 marked in the STM image in inset (It = 0.1 nA, Vs = −0.4 V). Line c marks the Bi2Se3 bulk conduction band edge. (d,e) Histograms of the graphene Dirac point position and spin−orbit splitting.

∼250 meV below EF, attributed to the ED (Figure 3b). Consistent with earlier studies, the n-type doping is due to Se vacancies often present in MBE grown films.22,23 The transfer of graphene was done immediately after the Bi2Se3 was removed from ultrahigh vacuum (UHV), and confirmed by Raman spectroscopy (Figure 3c). The strong peaks at 128 and 171 cm−1 correspond to in-plane E2g and outof-plane A21g vibrational modes of Bi2Se3, respectively.23 Three characteristic graphene peaks: the defect-induced D band, the in-plane vibrational G band, and the two phonon (2D) band, appear at 1333, 1582, and 2656 cm−1, respectively.24 The fullwidth-at-half-maximum of the graphene 2D band (∼38 cm−1) and the intensity ratio of the 2D to G peaks (I2D/IG = 2.02) are both consistent with single layer graphene (Figure 3c inset). The low intensity of the D peak, IG/ID = 2.26, further indicates high quality graphene with minimal defect density. Upon reintroduction back into UHV, STM imaging reveals a network of graphene ridges a few nanometers in height (Figure 3d).25 Underneath the graphene, Bi2Se3 growth spirals are still clearly visible. Although some of the graphene ridges are formed during CVD growth, new ones can also develop, preferentially along Bi2Se3 step edges (one is indicated by the arrow in Figure 3d). Between ridges, graphene is atomically flat without nanoscale ripples, in contrast to graphene transferred onto SiO2/Si substrates26,27 and hydrogen-terminated SiC.28 Moreover, Moiré patterns are also not observed, unlike graphene/BN vdW junctions7 and epitaxial graphene/ Ru(0001).29 This may be due to the introduction of adsorbates on the Bi2Se3 surface during graphene transfer, which typically n-dopes the surface30,31 and shifts ED from ∼ −0.25 eV for asgrown films to ∼ −0.4 eV (Supporting Figure 4). However, the graphene honeycomb lattice is clearly resolved on the flat terraces and is also continuous across the step edges of the Bi2Se3 (Figures 3e and 4a inset). A representative dI/dV spectrum of graphene/Bi2Se3 taken on a flat terrace is shown in Figure 4a, where two high

tion of the graphene π states to the Bi2Se3 states is achieved by forming an approximate nodal plane near the Se layer with decaying weight on the Bi and deeper substrate planes (Supporting Figure 3b). Next, to reflect the inherent lack of an epitaxial relationship in the graphene/Bi2Se3 vdW heterostructures, different registries and separations are also considered with the uppermost Se atoms in the hollow or top sites of graphene, or slightly shifted (Figure 2). Clearly, the magnitude of the splittings and the prominence of the Rashba-type features19 exhibits a strong dependence on the separation and registry. Note that this Rashba-type splitting is not the commonly referred to Rashba SOC term.19 As shown in Figure 1b, the graphene K and K′ points correspond to Γ of different zones and also different directions in the Bi2Se3 BZ. Without an epitaxial relation (middle and bottom panels, Figure 2), the intensity around K and K′ and along the different directions vary with momentum (Supporting Figure 1c), leading to a Rashba-type splitting that is absent in the variant with epitaxial relationship (top panel, Figure 2). In addition, different registries show different splittings even for the same separations, indicating that spatial fluctuations in splittings and intensities are to be expected. These noticeable differences in the dispersion are in principle observable in angle-resolved photoemission. For probes that integrate over kspace, the Rashba-type splitting can lead to van Hove singularity in the density of states,20,21 which can be directly measured by dI/dV tunneling spectroscopy as shown below. Graphene/Bi2Se3 vdW junctions were fabricated by transferring CVD graphene onto MBE grown Bi2Se3(0001) films, which exhibit growth spirals characterized by atomically flat terraces separated by steps of 0.95 nm, consistent with one Bi2Se3 QL (Figure 3a).17 Though the terrace shows a closedpack structure with a periodicity of ∼4.1 Å (inset, Figure 3b), characteristic of (1 × 1) Bi2Se3(0001), dI/dV tunneling spectrum typically exhibits a V-shape with a minimum at 8453

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ACS Nano tunneling conductance regions are seen below EF and above 0.33 eV, likely due to the conductance of the Bi2Se3 bulk valence and conduction bands, respectively. Within the gap the conductance does not reach zero, but exhibits variations that can be better seen in the close-up view in Figure 4b. Additional local maxima at 60 and 160 meV are evident, separated by a minimum at 110 meV. Comparison with the calculated band structure for a separation of 3.875 Å (inset) shows that this minimum can be assigned to the graphene Dirac point (c.f., Figure 2). (The calculated density of states also shows two small peaks separated by the proximity induced gap discussed earlier, but are not resolved here at LN2 temperature likely due to thermal broadening (Supporting Figure 5).) The two peaks at 60 and 160 meV can be attributed to the spin−orbit splitting of the degenerate graphene bands. As shown in Figure 2, spin−orbit and broken inversion symmetry split the graphene Dirac state into a cone at ED plus two spin− orbit split states that have quadratic dispersion near the band edges and then (approximately) linear dispersion slightly away. The density of states should thus be V-shaped around ED, show jumps at the energies corresponding to the spin−orbit split states (due to the quadratic 2-D dispersion), and then again be V-shaped, but with approximately twice the slope compared to that around ED (c.f., Supporting Figure 5). Broken translational symmetry due to the interaction with the substrate will induce a gap at ED, and Rashba-like shifts that will cause square-root singularities at the band edges. The asymmetrical dI/dV line shape due to the Rashba-type splitting (c.f., Figure 2) is confirmed by fitting with 1/ E1 − E (red dashed line) and 1/ E − E2 (green dashed line), a defining characteristic of the van Hove singularity in the 1D density of states (Supporting Figure 6), similar to those seen in the surface bands of Pb and Bi/Ag(111).20 This indicates that proximity to Bi2Se3 results in a spin−orbit splitting of the graphene bands by ∼50 meV (half of the peak separation), an enhancement of several orders of magnitude compared to the intrinsic values of 24−50 μeV.10 As discussed above, due to the lack of epitaxial relationship between graphene and Bi2Se3, a spatial fluctuation of the spin− orbit splitting is expected (c.f., Figure 2), which is confirmed here by spatially resolved dI/dV spectroscopy. As shown in Figure 4c, all spectra exhibit the two local maxima due to the SOC split bands, however with fluctuations of up to ∼50 meV in position (c.f., spectra 1 and 10). While there is no significant change in the positions of peak “b”, peak “a” shows significant spatial variations, leading to fluctuations in the magnitude of the spin−orbit splitting. Analysis of more than 100 such spectra shows a distribution of 142 ± 23 and 60 ± 19 meV in the graphene Dirac point and spin−orbit splitting, respectively (Figure 4d,e). Graphene ridges also provide opportunities to investigate the effect of separation between the graphene and Bi2Se3 on the spin−orbit splitting. Figure 5a shows an STM image of a tall ridge where graphene is likely decoupled from the substrate (height ranges from 5 to 50 Å). dI/dV spectra taken along the ridge exhibit a general V-shape (Figure 5b), characteristic of freestanding graphene, consistent with the calculated bands when the separation between the graphene and Bi2Se3 is greater than 4 Å.

Figure 5. (a) STM image of a graphene ridge with variable height, ranging from 5 to 50 Å (It = 0.1 nA, Vs = −0.4 V), where graphene is completely decoupled from the Bi2Se3. (b) dI/dV spectra taken at positions marked in (a), showing the characteristic V-shape expected for freestanding graphene. Inset is the expanded region of the dI/dV spectra for the same energy range as that of Figure 4b for direct comparison between decoupled graphene and graphene on Bi2Se3.

symmetry of the graphene, thus lifting the 4-fold degeneracy of its bands at the Dirac point, resulting in giant spin−orbit splittings of up to 80 meV in its Dirac states. A spatial fluctuation of ±20 meV is also observed, as a result of the inherent nonepitaxial relation at the graphene/Bi2Se3 interface. Our DFT calculations further show that the transfer of the SOC to graphene is through the hybridization of Bi2Se3 character into the graphene wave functions and not through intrinsic spin−orbit effects in graphene itself due to, for example, the substrate electric field (i.e., the traditional Rashba interaction). The lack of surface Se character in the hybridized graphene Dirac states further indicates that the simple picture of direct bonding between the Bi2Se3 and the graphene Dirac states is not responsible for the observed spin−orbit splitting. Instead, orthogonalization requirements on the overlapping wave functions alone can mix in Bi2Se3 wave function character into the graphene states, opening gaps at band crossings. These findings reveal two intrinsic characteristicsthe symmetry breaking and orthogonalization of the wave functions at the interfacethat determine the properties of vdW heterostructures, an enabling step toward the effective engineering of their desired properties.

MATERIALS AND METHODS Sample Preparation. Nitrogen-doped 6H-SiC(0001) substrates (Cree Inc.) were prepared by hydrogen etching at 1600 °C in H2/Ar atmosphere to remove mechanical polishing damages.17,23 The as-etched SiC(0001) substrates were annealed at 1300 °C in ultrahigh vacuum (UHV) to grow epitaxial graphene.17,23 Bi2Se3 films were grown on the epitaxial graphene/SiC(0001) at 275−325 °C using MBE.23 Bi and Se were supplied via separate Knudsen cells at 460 and 250 °C, respectively, with a Se/Bi ratio of ∼10:1. Immediately after the samples were removed from UHV, CVD graphene (Graphene Supermarket Inc.) was transferred on top of the Bi2Se3 film using standard polymer (PMMA) based techniques.32 The transfer of graphene was then confirmed and characterized by Raman spectroscopy (with a 633 nm HeNe laser), and the samples were reintroduced back into UHV for STM/STS analysis.

CONCLUSION In summary, we synthesize graphene/Bi2Se3 vdW heterostructure and show that the formation of interface lowers the 8454

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(3) Zhang, Y.; Chang, T.-R.; Zhou, B.; Cui, Y.-T.; Yan, H.; Liu, Z.; Schmitt, F.; Lee, J.; Moore, R.; Chen, Y.; Lin, H.; Jeng, H.-T.; Mo, S.K.; Hussain, Z.; Bansil, A.; Shen, Z.-X. Direct Observation of the Transition from Indirect to Direct Bandgap in Atomically Thin Epitaxial MoSe2. Nat. Nanotechnol. 2013, 9, 111−115. (4) Drozdov, I. K.; Alexandradinata, A.; Jeon, S.; Nadj-Perge, S.; Ji, H.; Cava, R. J.; Andrei Bernevig, B.; Yazdani, A. One-dimensional Topological Edge States of Bismuth Bilayers. Nat. Phys. 2014, 10, 664−669. (5) Ponomarenko, L. A.; Geim, A. K.; Zhukov, A. A.; Jalil, R.; Morozov, S. V.; Novoselov, K. S.; Grigorieva, I. V.; Hill, E. H.; Cheianov, V. V.; Fal’ko, V. I.; Watanabe, K.; Taniguchi, T.; Gorbachev, R. V. Tunable Metal-Insulator Transition in Double-Layer Graphene Heterostructures. Nat. Phys. 2011, 7, 958−961. (6) Terrones, H.; López-Urías, F.; Terrones, M. Novel HeteroLayered Materials with Tunable Direct Band Gaps by Sandwiching Different Metal Disulfides and Diselenides. Sci. Rep. 2013, 3, 1549. (7) Yankowitz, M.; Xue, J.; Cormode, D.; Sanchez-Yamagishi, J. D.; Watanabe, K.; Taniguchi, T.; Jarillo-Herrero, P.; Jacquod, P.; LeRoy, B. J. Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride. Nat. Phys. 2012, 8, 382−386. (8) Fang, H.; Battaglia, C.; Carraro, C.; Nemsak, S.; Ozdol, B.; Kang, J. S.; Bechtel, H. A.; Desai, S. B.; Kronast, F.; Unal, A. A.; Conti, G.; Conlon, C.; Palsson, G. K.; Martin, M. C.; Minor, A. M.; Fadley, C. S.; Yablonovitch, E.; Maboudian, R.; Javey, A. Strong Interlayer Coupling in van der Waals Heterostructures Built from Single-Layer Chalcogenides. Proc. Natl. Acad. Sci. U. S. A. 2014, 111, 6198−6202. (9) Rivera, P.; Schaibley, J. R.; Jones, A. M.; Ross, J. S.; Wu, S.; Aivazian, G.; Klement, P.; Seyler, K.; Clark, G.; Ghimire, N. J.; Yan, J.; Mandrus, D. G.; Yao, W.; Xu, X. Observation of Long-Lived Interlayer Excitons in Monolayer MoSe2−WSe2 Heterostructures. Nat. Commun. 2015, 6, 6242. (10) Han, W.; Kawakami, R. K.; Gmitra, M.; Fabian, J. Graphene Spintronics. Nat. Nanotechnol. 2014, 9, 794−807. (11) Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K. The Electronic Properties of Graphene. Rev. Mod. Phys. 2009, 81, 109−162. (12) Jin, K.-H.; Jhi, S.-H. Proximity-Induced Giant Spin-Orbit Interaction in Epitaxial Graphene on a Topological Insulator. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 075442. (13) Zhang, J.; Triola, C.; Rossi, E. Proximity Effect in GrapheneTopological-Insulator Heterostructures. Phys. Rev. Lett. 2014, 112, 096802. (14) Lee, P.; Jin, K.-H.; Sung, S. J.; Kim, J. G.; Ryu, M.-T.; Park, H.M.; Jhi, S.-H.; Kim, N.; Kim, Y.; Yu, S. U.; Kim, K. S.; Noh, D. Y.; Chung, J. Proximity Effect Induced Electronic Properties of Graphene on Bi2Te2Se. ACS Nano 2015, 9, 10861−10866. (15) Weinert, M.; Schneider, G.; Podloucky, R.; Redinger, J. FLAPW: Applications and Implementations. J. Phys.: Condens. Matter 2009, 21, 084201. (16) Zhang, Y.; He, K.; Chang, C.-Z.; Song, C.-L.; Wang, L.-L.; Chen, X.; Jia, J.-F.; Fang, Z.; Dai, X.; Shan, W.-Y.; Shen, S.-Q.; Niu, Q.; Qi, X.-L.; Zhang, S.-C.; Ma, X.-C.; Xue, Q.-K. Crossover of the ThreeDimensional Topological Insulator Bi2Se3 to the Two-Dimensional Limit. Nat. Phys. 2010, 6, 584−588. (17) Liu, Y.; Li, Y. Y.; Rajput, S.; Gilks, D.; Lari, L.; Galindo, P. L.; Weinert, M.; Lazarov, V. K.; Li, L. Tuning Dirac States by Strain in the Topological Insulator Bi2Se3. Nat. Phys. 2014, 10, 294−299. (18) Harrison, W. Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond; Dover Books on Physics; Dover Publications: Mineola, NY, 2012; p 536. (19) Rashba, E. I. Graphene with Structure-Induced Spin-Orbit Coupling: Spin-Polarized States, Spin Zero Modes, and Quantum Hall Effect. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79, 161409. (20) Ast, C. R.; Wittich, G.; Wahl, P.; Vogelgesang, R.; Pacilé, D.; Falub, M. C.; Moreschini, L.; Papagno, M.; Grioni, M.; Kern, K. Local Detection of Spin-Orbit Splitting by Scanning Tunneling Spectroscopy. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 75, 201401.

Scanning Tunneling Microscopy and Spectroscopy. Scanning tunneling microscopy and spectroscopy experiments were performed in an UHV system with a base pressure below 1 × 10−10 Torr. STM images were taken at room temperature and 77 K with electrochemically etched polycrystalline W tips or mechanically sharpened Pt tips. The dI/dV tunneling spectra were acquired at 77 K by turning off the feedback loop, applying a small ac modulation of 9 mV (r.m.s.) at 860 Hz to the bias voltage, and measuring the corresponding changes in tunneling current by lock-in detection. The tip is calibrated by carrying out dI/dV measurements on Ag(111) films grown on a 6H-SiC(0001) surface.33 Density Functional Theory Calculations. DFT calculations were carried out using the Full-potential Linearized Augmented Plane Wave (FLAPW) method as implemented in f lair. The in-plane lattice constant was fixed to that of Bi2Se3, 4.138 Å, with the graphene in a √3 × √3 epitaxial relationship. The positions of the Bi and Se atoms in the 1and 7-QL slabs were held fixed at their relaxed positions obtained previously.17,23 The planar graphene was placed on one surface at different separations and registries as shown in Figure 2. The wave functions and density/potential cutoffs were 200 and 2000 eV, respectively. The SOC was included via a second variation approach using scalar-relativistic wave functions as a basis. The Perdew, Burke, and Ernzerhof form of the generalized gradient approximation34 was used for exchange correlation. The Brillouin zone was sampled with a 18 × 18 k-point mesh in the 2-D Brillouin zone of Bi2Se3. The kprojected bands were calculated using the self-consistent densities and potential and weighted by their spatial localization on the graphene.

ASSOCIATED CONTENT S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.6b03387. Additional information about k-projected graphene− Bi2Se3 bands, calculated bands at the interface of the graphene/Bi2Se3, spatial distribution of graphene and Bi2Se3 Dirac states, impact of water exposure on Bi2Se3 Dirac states, calculated graphene density of states, Van Hove singularity in graphene−Bi2Se3 bands, and additional references. (PDF)

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS Supported by U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-FG02-05ER46228. REFERENCES (1) Geim, A. K.; Grigorieva, I. V. Van der Waals Heterostructures. Nature 2013, 499, 419−425. (2) Baringhaus, J.; Ruan, M.; Edler, F.; Tejeda, A.; Sicot, M.; TalebIbrahimi, A.; Li, A.-P.; Jiang, Z.; Conrad, E. H.; Berger, C.; Tegenkamp, C.; de Heer, W. A. Exceptional Ballistic Transport in Epitaxial Graphene Nanoribbons. Nature 2014, 506, 349−354. 8455

DOI: 10.1021/acsnano.6b03387 ACS Nano 2016, 10, 8450−8456

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DOI: 10.1021/acsnano.6b03387 ACS Nano 2016, 10, 8450−8456