Letter pubs.acs.org/NanoLett
Electronic States at the Graphene−Hexagonal Boron Nitride Zigzag Interface Robert Drost,† Andreas Uppstu,‡ Fabian Schulz,† Sampsa K. Ham ̈ al̈ aï nen,† Mikko Ervasti,‡ Ari Harju,‡ ,† and Peter Liljeroth* †
Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, 00076 Aalto, Finland COMP Centre of Excellence and Helsinki Institute of Physics, Department of Applied Physics, Aalto University School of Science, P.O. Box 11100, 00076 Aalto, Finland
‡
S Supporting Information *
ABSTRACT: The electronic properties of graphene edges have been predicted to depend on their crystallographic orientation. The so-called zigzag (ZZ) edges haven been extensively explored theoretically and proposed for various electronic applications. However, their experimental study remains challenging due to the difficulty in realizing clean ZZ edges without disorder, reconstructions, or the presence of chemical functional groups. Here, we propose the ZZterminated, atomically sharp interfaces between graphene and hexagonal boron nitride (BN) as experimentally realizable, chemically stable model systems for graphene ZZ edges. Combining scanning tunneling microscopy and numerical methods, we explore the structure of graphene−BN interfaces and show them to host localized electronic states similar to those on the pristine graphene ZZ edge. KEYWORDS: Graphene, hexagonal boron nitride, interface, zigzag, scanning tunneling microscopy (STM)
T
The problematic edge chemistry can be circumvented by passivating the graphene edge with a 2D insulator, thus preserving any edge states lying within the band gap of the insulating material. Hexagonal boron nitride (BN), a wide band gap insulator isostructural to graphene, is well-suited to stabilize graphene edges.15−20 Here, we have used graphene islands with ZZ edges as templates for BN growth19 to obtain atomically sharp and chemically stable ZZ oriented graphene−hexagonal boron nitride (G−BN) interfaces. We study their electronic structure using low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS) and demonstrate the presence of interface states. These experimental results, together with density functional theory (DFT) and tight binding (TB) calculations, show that the interface state has very similar electronic properties to pristine graphene ZZ edge states.6 We grew ZZ-oriented G−BN interfaces in ultrahigh vacuum (UHV) using a combination of temperature-programmed growth (TPG) of epitaxial graphene on a (111)-terminated iridium single crystal,21−23 followed by deposition of BN.24,25 In order to decouple the heterolayer from the substrate and to reduce the interface reconstruction, we intercalated the G−BN layer with 5−10 monolayers of gold. Details of the sample
he electronic properties of graphene edges depend on their crystallographic orientation and the so-called zigzag (ZZ) edges are expected to host one-dimensional states with a flat dispersion.1−5 These edge states have been extensively explored theoretically and proposed for various electronic applications including devices based on spintronics and valleytronics: using the spin degree of freedom of the electron or the valley degree of freedom inherent to the band structure of honeycomb crystals to transmit and process information.2,6−8 The half-metallic ZZ edge state resides on a single sublattice of the crystal1−3,5 and should be susceptible to spinpolarization at suitable doping levels. Furthermore, in contrast to armchair-edged ribbons, the band structure of ZZ-edged ribbons contains two independent momentum valleys close to the charge neutrality point, a prerequisite for valleytronics.6 Despite strong theoretical attention, experimental realization of clean ZZ edges without disorder, reconstructions, or chemical functional groups that could cause scattering between the different spin and valley channels remains challenging.2,4,6,9−14 Pioneering studies on unzipped carbon nanotubes have shown that the chemical edge termination can be controlled, but the crystallographic direction of the edge cannot be a priori selected.10,12,14 In addition, the transfer techniques involved in producing graphene-based devices rely on solution-based chemistry that may in general cause unknown and uncontrollable changes to the chemistry of the graphene edges. © 2014 American Chemical Society
Received: May 21, 2014 Revised: July 16, 2014 Published: July 31, 2014 5128
dx.doi.org/10.1021/nl501895h | Nano Lett. 2014, 14, 5128−5132
Nano Letters
Letter
Figure 1. Overview of the epitaxial G−BN sample. (a) Large scale topography of the intercalated G−BN sample with an overlaid color scale indicating the clean gold surface (yellow), graphene (red), and BN (blue) islands (feedback parameters 0.5 V, 0.1 nA). (b) Low-bias spectroscopy showing the Au(111) surface state on bare gold (black line) and graphene (red) and BN (blue) covered surfaces. (c) Field-emission resonance spectroscopy allowing us to identify the different surface regions based on their work functions.
reconstruction of the gold surface. BN on the other hand retains a corrugated moiré-like structure even on top of the gold thin film. While some interface reconstruction prevails on the intercalated sample, the overall length and quality of the interfaces is significantly improved compared to the nonintercalated G−BN directly on the Ir(111) surface (see Figure S1 in the Supporting Information). Finally, the surface state of Au(111) only shifts slightly under graphene and BN (Figure 1b) again indicating weak interaction between the G−BN layer and the substrate. In the following, we will focus our investigation on highquality ZZ-terminated interfaces between graphene and BN. We observe a distinct lobe structure in the STM images at low bias on the ZZ oriented parts of the interfaces, which is not visible on interfaces with other terminations. An example of the lobe structure is shown in Figure 2a. The slight variation of the lobe intensity along the interface is due to the herringbone reconstruction of the underlying gold substrate. STS performed on the lobes of the G−BN interfaces shows a clear peak in the local density of states (LDOS, see black lines in Figure 2b,c). The sets of spectra shown in Figures 2b and 22c were acquired with different microtips causing slight variations in the background signal. The peak, close to zero bias, is completely absent in the spectra taken next to the interface on either graphene or BN (red and blue lines in Figure 2b,c). The energetic position of the peak is similar to the earlier experiments on free graphene edges resulting from unzipped carbon nanotubes or chemically synthesized graphene nanoribbons.12,26 G−BN interfaces can be formed with either nitrogen- or boron-terminated BN and it is not directly possible to discern the different elements from the STM images. Yet, the atomic structure of the interface is important in terms of, for example, charge transfer to or from the graphene edge state. We have studied the effect of B and N termination on the interface by DFT using the FHI-aims package31 (details given in the Supporting Information). Simulated tunneling current maps, evaluated for periodic graphene ZZ ribbons embedded in BN,
preparation can be found in the Supporting Information. Graphene and passivated graphene edges have been demonstrated to be only weakly coupled to gold surfaces.26−28 The resulting G−BN layer was characterized by low-temperature STM at T = 4.2 K. STM experiments on the sample reveal that graphene and BN connect along the ZZ high symmetry direction (see Figures S1 and S2 in the Supporting Information). Graphene grown on Ir(111) by the TPG method exposes only ZZ terminated edges. As a result of the graphene moiré pattern on Ir(111), small kinks appear in the edges of graphene islands.29 This limits the length of atomically perfect G−BN interfaces to that of the moiré period, ca. 2.4 nm, even in the absence of any additional strain or reconstruction. Because of the strong modulation of the BN to Ir(111) interaction,25 the G−BN interface exhibits strong reconstruction on this surface, which further limits the length of high quality interfaces. We reduce the G−BN to surface interaction by intercalating gold underneath the samples. The reduced interaction upon intercalation results in higher quality interfaces, some of which exceed the length of the graphene moiré on Ir(111). Figure 1a shows an overview of the gold-intercalated G−BN layer. After intercalation, most of the graphene and BN domains are embedded within the first Au layer. The Au adlayer exhibits the well-known Au(111) herringbone reconstruction and shows a surface state at ca. −500 mV bias (Figure 1b), demonstrating the bulklike quality of the gold thin film. Tunneling spectroscopy in the field emission regime,30 shown in Figure 1c, reveals resonances related to the local work function of the surface. Graphene (first resonance at 4.7 V) and BN (4.7 and 5.0 V) show a lower work function than clean gold (5.2 V) and can be distinguished from each other by the characteristic split peak resonance of BN.25 The position and shape of the first field emission resonance are spectroscopic fingerprints that allow for the clear identification of gold, graphene, and BN regions on the sample. Graphene forms a smooth adlayer without any discernible superstructure on the Au thin film, its corrugation following the herringbone 5129
dx.doi.org/10.1021/nl501895h | Nano Lett. 2014, 14, 5128−5132
Nano Letters
Letter
Figure 3. Scattering at graphene zigzag edges and comparison between theory and experiment. (a) High-resolution STM image of the G−BN interface along the ZZ high symmetry direction. Scale bar 2 nm, feedback parameters 0.1 V, 1 nA. (b) Calculated band structure for a BN-terminated graphene nanoribbon. The interface bands are indicated by the red and blue lines. The bending of the interface state is indicated by ΔE and the bulk bandgap by ΔEc. (c) STM image showing the G−BN interface state with an overlaid model of the atomic structure (0.1 V, 1 nA). (d) Local density of states (LDOS) map calculated by TB on the G−BN interface with the same atomic structure as in the experimental image shown in panel (c).
Figure 2. Geometric and electronic structure of the interface between graphene and BN. (a) STM image of the G−BN interface showing the interface state local density of states. Scale bar 1 nm, feedback parameters −1 V, 3 nA. (b,c) Wide energy range (b) and highresolution (c) tunneling spectra measured on graphene (red), BN (blue), and at the interface (black). (d) Simulated tunneling current maps of G−BN interfaces based on DFT calculations with either nitrogen- (left) or boron (right) terminated BN edge. The maps have been calculated at the bias corresponding to the maximum LDOS of the interface state (0.1 V for nitrogen and −0.2 V for boronterminated BN edges, respectively).
that the localized states observed at the interface are a property of the interface itself and do not arise from, for example, interaction of the G−BN layer with the gold surface state. We have developed a TB model that allows us to treat large G−BN structures numerically (see Supporting Information for details).34−37 Results are in good agreement with DFT based on LDOS maps and band structures for smaller systems (Figure S4 in the Supporting Information). Figure 3b shows the calculated band structure for a narrow graphene ribbon forming a C−B interface with BN with the TB model. Quantum confinement opens a gap in the graphene band structure at the K and K′ points (bulk bands indicated by gray lines). The red and blue lines in Figure 3b show the dispersion of the interface state. The downward bending between the K and K′ points (energy shift of ΔE w.r.t to the Dirac point) is caused by the edge potential resulting from bonding with the boron atoms.5,35 For a nitrogen-terminated G−BN interface, our model predicts a corresponding bending to higher energies, which is in agreement with earlier DFT calculations.35 The interface state is only fully localized at the edge of the first Brillouin zone (BZ) and propagates throughout the graphene bulk for states between k = 2π/(3a) and k = 0. Theoretically, a dispersive interface state will lead to the formation of localized standing waves along finite interface segments. Here, the standing waves have an additional modulation of π, because the edge band is centered at k = π/ a. The standing waves occur at different energies depending also on the length of the segment, akin to states found in a onedimensional quantum well. For short segments, there are only a few possible modes between the allowed interval of edge states with k values between 2π/(3a) and 4π/(3a). Therefore, this model predicts standing wave states for which in the STM spectra the number of peaks and their energies depend on the length of the segment and ΔE. Our STS measurements, however, show only a single peak that is always located close to the Fermi level. This statement holds for both the different lobes on a single interface as well as
are shown in Figure 2d. The results indicate that a C−B termination is not only energetically favorable (on the order of an electronvolt per edge carbon atom)32 but also reproduces the experimental lobe structure far better than a C−N connection. The lobes at the C−B interface are elongated, which is consistent with the experimental image shown in Figure 2a. In addition, the energetic position of the main interface state peak in simulated tunneling spectra (Figure S3 in the Supporting Information) agrees well with the experimental results considering the known doping of graphene by the gold substrate. Our results suggest that the G−BN interfaces are formed between graphene- and boron-terminated BN with the interface state arising from C−B bonding states. An atomically resolved STM image of a G−BN interface is shown in Figure 3a. The ZZ high symmetry direction of the graphene sheet is extracted from the atomic positions far from the interface region and highlighted in the figure, demonstrating that the G−BN interface is aligned along the ZZ direction. The ZZ interface state appears as a series of bright lobes in lowbias STM scans that are entirely confined to within one atomic row of the interface. The fact that the state is attenuated on the short armchair sections of the interface is further evidence that it is derived from the ZZ symmetry at the graphene edge. The ZZ interface results in a characteristic scattering pattern close to the interface, where one of the graphene sublattices is imaged with significantly higher intensity than the other (indicated by a black arrow in Figure 3a). This type of scattering pattern results from broken sublattice symmetry in the absence of intervalley scattering in graphene, suggesting that the interface state could carry valley-polarized currents.11,12,14 On the other hand, defects in the graphene lattice (lower right-hand corner of Figure 3a) are surrounded by the well-known (√3 × √3)R30° pattern (indicated with a white arrow), which results from intervalley scattering.33 Finally, no scattering pattern is found on the BN side of the interface as the ZZ interface state lies within the BN bandgap. This shows 5130
dx.doi.org/10.1021/nl501895h | Nano Lett. 2014, 14, 5128−5132
Nano Letters
■
for separate interfaces of different lengths. Thus, based on our experiments, ΔE is small, i.e. the dispersion of the interface state is low. This may be partly due to screening caused by the substrate, which may result in an increase of the effective edge potential on the graphene flake and subsequently a reduced dispersion of the interface state.5 We validate the TB model by comparing the G−BN interface state structure measured experimentally (Figure 3c with an overlaid atomic model of the interface) with the result of the TB calculation (Figure 3d) on the same atomic structure. The excellent correspondence between theory and experiment further evidences the C−B bonding and absence of intervalley scattering at the G−BN interfaces. Furthermore, the short armchair segments do not significantly affect the interface state properties, which is important for potential applications. Theory predicts the pure graphene ZZ edge state to be spinpolarized with opposite spin ground states on opposite sublattices. The spin polarization is a result of the nearly flat dispersion of the ZZ edge state that occurs exactly at the charge neutrality point. While it is not clear if the G−BN interface states are spin-polarized, the sharpness of the peak observed in our experiments indicates a highly degenerate electronic state that should be susceptible to spin polarization with appropriate gating or doping. In conclusion, we prepared atomically sharp and well-defined ZZ G−BN interfaces and showed the existence of an interfacelocalized state near zero bias using STS. The G−BN ZZ interface is an experimentally realizable, chemically stable model system to study the fundamental properties of the graphene ZZ edge state. Our results show that the electronic structure of the ZZ G−BN interface is similar to that of the free graphene ZZ edge state and many important properties of the graphene edge state are preserved. Most notably, the distinct valley channels persist at the G−BN interface and our results suggest the possibility of graphene valleytronics in experimentally realizable structures.
■
REFERENCES
(1) Nakada, K.; Fujita, M.; Dresselhaus, G.; Dresselhaus, M. S. Edge State in Graphene Ribbons: Nanometer Size Effect and Edge Shape Dependence. Phys. Rev. B 1996, 54, 17954−17961. (2) Son, Y.-W.; Cohen, M. L.; Louie, S. G. Half-Metallic Graphene Nanoribbons. Nature 2006, 444, 347−349. (3) Akhmerov, A. R.; Beenakker, C. W. J. Boundary Conditions for Dirac Fermions on a Terminated Honeycomb Lattice. Phys. Rev. B 2008, 77, 10. (4) 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. (5) Yazyev, O. V. A Guide to the Design of Electronic Properties of Graphene Nanoribbons. Acc. Chem. Res. 2013, 46, 2319−2328. (6) Rycerz, A.; Tworzydlo, J.; Beenakker, C. W. J. Valley Filter and Valley Valve in Graphene. Nat. Phys. 2007, 3, 172−175. (7) Yazyev, O. V.; Katsnelson, M. I. Magnetic Correlations at Graphene Edges: Basis for Novel Spintronics Devices. Phys. Rev. Lett. 2008, 100, 047209. (8) Gunlycke, D.; White, C. Graphene Valley Filter Using a Line Defect. Phys. Rev. Lett. 2011, 106, 136806. (9) Wassmann, T.; Seitsonen, A. P.; Saitta, A. M.; Lazzeri, M.; Mauri, F. Structure, Stability, Edge States, and Aromaticity of Graphene Ribbons. Phys. Rev. Lett. 2008, 101, 096402. (10) Li, X. L.; Wang, X. R.; Zhang, L.; Lee, S. W.; Dai, H. J. Chemically Derived, Ultrasmooth Graphene Nanoribbon Semiconductors. Science 2008, 319, 1229−1232. (11) Koskinen, P.; Malola, S.; Häkkinen, H. Self-Passivating Edge Reconstructions of Graphene. Phys. Rev. Lett. 2008, 101, 115502. (12) Tao, C.; Jiao, L.; Yazyev, O. V.; Chen, Y.-C.; Feng, J.; Zhang, X.; Capaz, R. B.; Tour, J. M.; Zettl, A.; Louie, S. G.; et al. Spatially Resolving Edge States of Chiral Graphene nanoribbons. Nat. Phys. 2011, 7, 616−620. (13) Kim, K.; Coh, S.; Kisielowski, C.; Crommie, M. F.; Louie, S. G.; Cohen, M. L.; Zettl, A. Atomically Perfect Torn Graphene Edges and Their Reversible Reconstruction. Nat. Commun. 2013, 4, 6. (14) Zhang, X.; Yazyev, O. V.; Feng, J.; Xie, L.; Tao, C.; Chen, Y.-C.; Jiao, L.; Pedramrazi, Z.; Zettl, A.; Louie, S. G.; et al. Experimentally Engineering the Edge Termination of Graphene Nanoribbons. ACS Nano 2012, 7, 198−202. (15) Sutter, P.; Cortes, R.; Lahiri, J.; Sutter, E. Interface Formation in Monolayer Graphene-Boron Nitride Heterostructures. Nano Lett. 2012, 12, 4869−4874. (16) Levendorf, M. P.; Kim, C.-J.; Brown, L.; Huang, P. Y.; Havener, R. W.; Muller, D. A.; Park, J. Graphene and Boron Nitride Lateral Heterostructures for Atomically Thin Circuitry. Nature 2012, 488, 627−632. (17) Liu, Z.; Ma, L.; Shi, G.; Zhou, W.; Gong, Y.; Lei, S.; Yang, X.; Zhang, J.; Yu, J.; Hackenberg, K. P.; et al. In-Plane Heterostructures of Graphene and Hexagonal Boron Nitride with Controlled Domain Sizes. Nat. Nanotechnol. 2013, 8, 119−124. (18) Gao, Y.; Zhang, Y.; Chen, P.; Li, Y.; Liu, M.; Gao, T.; Ma, D.; Chen, Y.; Cheng, Z.; Qiu, X.; et al. Toward Single-Layer Uniform Hexagonal Boron Nitride−Graphene Patchworks with Zigzag Linking Edges. Nano Lett. 2013, 13, 3439−3443. (19) Liu, L.; Park, J.; Siegel, D. A.; McCarty, K. F.; Clark, K. W.; Deng, W.; Basile, L.; Idrobo, J. C.; Li, A.-P.; Gu, G. Heteroepitaxial Growth of Two-Dimensional Hexagonal Boron Nitride Templated by Graphene Edges. Science 2014, 343, 163−167. (20) Kim, S. M.; Hsu, A.; Araujo, P. T.; Lee, Y.-H.; Palacios, T.; Dresselhaus, M.; Idrobo, J.-C.; Kim, K. K.; Kong, J. Synthesis of Patched or Stacked Graphene and hBN Flakes: A Route to Hybrid Structure Discovery. Nano Lett. 2013, 13, 933−941. (21) Coraux, J.; N’Diaye, A. T.; Engler, M.; Busse, C.; Wall, D.; Buckanie, N.; Meyer zu Heringdorf, F.-J.; van Gastel, R.; Poelsema, B.; Michely, T. Growth of Graphene on Ir(111). New J. Phys. 2009, 11, 023006. (22) Hämäläinen, S. K.; Sun, Z.; Boneschanscher, M. P.; Uppstu, A.; Ijäs, M.; Harju, A.; Vanmaekelbergh, D.; Liljeroth, P. Quantum-
ASSOCIATED CONTENT
S Supporting Information *
Details on the experimental and computational methods and additional results. This material is available free of charge via the Internet at http://pubs.acs.org.
■
Letter
AUTHOR INFORMATION
Corresponding Author
*E-mail: peter.liljeroth@aalto.fi. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This research made use of the Aalto Nanomicroscopy Center (Aalto NMC) facilities and was supported by the European Research Council (ERC-2011-StG No. 278698 “PRECISENANO”), the Finnish Academy of Science and Letters and the Academy of Finland (Centres of Excellence in Low Temperature Quantum Phenomena and Devices No. 250280 and in Computational Nanoscience No. 251748). We acknowledge the computational resources provided by Aalto Science-IT project and Finland’s IT Center for Science (CSC). 5131
dx.doi.org/10.1021/nl501895h | Nano Lett. 2014, 14, 5128−5132
Nano Letters
Letter
Confined Electronic States in Atomically Well-Defined Graphene Nanostructures. Phys. Rev. Lett. 2011, 107, 236803. (23) Subramaniam, D.; Libisch, F.; Li, Y.; Pauly, C.; Geringer, V.; Reiter, R.; Mashoff, T.; Liebmann, M.; Burgdörfer, J.; Busse, C.; et al. Wave-Function Mapping of Graphene Quantum Dots with Soft Confinement. Phys. Rev. Lett. 2012, 108, 046801. (24) Corso, M.; Auwärter, W.; Muntwiler, M.; Tamai, A.; Greber, T.; Osterwalder, J. Boron Nitride Nanomesh. Science 2004, 303, 217−220. (25) Schulz, F.; Drost, R.; Hämäläinen, S. K.; Demonchaux, T.; Seitsonen, A. P.; Liljeroth, P. Epitaxial Hexagonal Boron Nitride on Ir(111): A Work Function Template. Phys. Rev. B 2014, 89, 235429. (26) van der Lit, J.; Boneschanscher, M. P.; Vanmaekelbergh, D.; Ijäs, M.; Uppstu, A.; Ervasti, M.; Harju, A.; Liljeroth, P.; Swart, I. Suppression of Electron−Vibron Coupling in Graphene Nanoribbons Contacted Via a Single Atom. Nat. Commun. 2013, 4, 2023. (27) Leicht, P.; Zielke, L.; Bouvron, S.; Moroni, R.; Voloshina, E.; Hammerschmidt, L.; Dedkov, Y. S.; Fonin, M. In Situ Fabrication of Quasi-Free-Standing Epitaxial Graphene Nanoflakes on Gold. ACS Nano 2014, 8, 3735−3742. (28) Li, Y.; Zhang, W.; Morgenstern, M.; Mazzarello, R. Electronic and Magnetic Properties of Zigzag Graphene Nanoribbons on the (111) Surface of Cu, Ag, and Au. Phys. Rev. Lett. 2013, 110, 216804. (29) Li, Y.; Subramaniam, D.; Atodiresei, N.; Lazic, P.; Caciuc, V.; Pauly, C.; Georgi, A.; Busse, C.; Liebmann, M.; Blugel, S.; et al. Absence of Edge States in Covalently Bonded Zigzag Edges of Graphene on Ir(111). Adv. Mater. 2013, 25, 1967−1972. (30) Ploigt, H.-C.; Brun, C.; Pivetta, M.; Patthey, F.; Schneider, W.D. Local Work Function Changes Determined by Field Emission Resonances: NaCl/Ag(100). Phys. Rev. B 2007, 76, 195404. (31) Blum, V.; Gehrke, R.; Hanke, F.; Havu, P.; Havu, V.; Ren, X.; Reuter, K.; Scheffler, M. Ab Initio Molecular Simulations with Numeric Atom-Centered Orbitals. Comput. Phys. Commun. 2009, 180, 2175−2196. (32) Liu, Y.; Wu, X.; Zhao, Y.; Zeng, X. C.; Yang, J. Half-Metallicity in Hybrid Graphene/Boron Nitride Nanoribbons with Dihydrogenated Edges. J. Phys. Chem. C 2011, 115, 9442−9450. (33) Rutter, G. M.; Crain, J. N.; Guisinger, N. P.; Li, T.; First, P. N.; Stroscio, J. A. Scattering and Interference in Epitaxial Graphene. Science 2007, 317, 219−222. (34) Hancock, Y.; Uppstu, A.; Saloriutta, K.; Harju, A.; Puska, M. J. Generalized Tight-Binding Transport Model for Graphene Nanoribbon-Based Systems. Phys. Rev. B 2010, 81, 245402. (35) Jung, J.; Qiao, Z.; Niu, Q.; MacDonald, A. H. Transport Properties of Graphene Nanoroads in Boron Nitride Sheets. Nano Lett. 2012, 12, 2936−2940. (36) Ijäs, M.; Ervasti, M.; Uppstu, A.; Liljeroth, P.; van der Lit, J.; Swart, I.; Harju, A. Electronic States in Finite Graphene Nanoribbons: Effect of Charging and Defects. Phys. Rev. B 2013, 88, 075429. (37) Radzig, A. A.; Smirnov, B. M. Reference Data on Atoms, Molecules, and Ions; Springer Series in Chemical Physics; Springer: BerlinHeidelberg, 1985; Vol. 31.
5132
dx.doi.org/10.1021/nl501895h | Nano Lett. 2014, 14, 5128−5132
Electronic States at the Graphene−Hexagonal Boron Nitride Zigzag Interface Robert Drost,† Andreas Uppstu,‡ Fabian Schulz,† Sampsa K. Ham ̈ al̈ aï nen,† Mikko Ervasti,‡ Ari Harju,‡ ,† and Peter Liljeroth* †
Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, 00076 Aalto, Finland COMP Centre of Excellence and Helsinki Institute of Physics, Department of Applied Physics, Aalto University School of Science, P.O. Box 11100, 00076 Aalto, Finland
‡
S Supporting Information *
ABSTRACT: The electronic properties of graphene edges have been predicted to depend on their crystallographic orientation. The so-called zigzag (ZZ) edges haven been extensively explored theoretically and proposed for various electronic applications. However, their experimental study remains challenging due to the difficulty in realizing clean ZZ edges without disorder, reconstructions, or the presence of chemical functional groups. Here, we propose the ZZterminated, atomically sharp interfaces between graphene and hexagonal boron nitride (BN) as experimentally realizable, chemically stable model systems for graphene ZZ edges. Combining scanning tunneling microscopy and numerical methods, we explore the structure of graphene−BN interfaces and show them to host localized electronic states similar to those on the pristine graphene ZZ edge. KEYWORDS: Graphene, hexagonal boron nitride, interface, zigzag, scanning tunneling microscopy (STM)
T
The problematic edge chemistry can be circumvented by passivating the graphene edge with a 2D insulator, thus preserving any edge states lying within the band gap of the insulating material. Hexagonal boron nitride (BN), a wide band gap insulator isostructural to graphene, is well-suited to stabilize graphene edges.15−20 Here, we have used graphene islands with ZZ edges as templates for BN growth19 to obtain atomically sharp and chemically stable ZZ oriented graphene−hexagonal boron nitride (G−BN) interfaces. We study their electronic structure using low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS) and demonstrate the presence of interface states. These experimental results, together with density functional theory (DFT) and tight binding (TB) calculations, show that the interface state has very similar electronic properties to pristine graphene ZZ edge states.6 We grew ZZ-oriented G−BN interfaces in ultrahigh vacuum (UHV) using a combination of temperature-programmed growth (TPG) of epitaxial graphene on a (111)-terminated iridium single crystal,21−23 followed by deposition of BN.24,25 In order to decouple the heterolayer from the substrate and to reduce the interface reconstruction, we intercalated the G−BN layer with 5−10 monolayers of gold. Details of the sample
he electronic properties of graphene edges depend on their crystallographic orientation and the so-called zigzag (ZZ) edges are expected to host one-dimensional states with a flat dispersion.1−5 These edge states have been extensively explored theoretically and proposed for various electronic applications including devices based on spintronics and valleytronics: using the spin degree of freedom of the electron or the valley degree of freedom inherent to the band structure of honeycomb crystals to transmit and process information.2,6−8 The half-metallic ZZ edge state resides on a single sublattice of the crystal1−3,5 and should be susceptible to spinpolarization at suitable doping levels. Furthermore, in contrast to armchair-edged ribbons, the band structure of ZZ-edged ribbons contains two independent momentum valleys close to the charge neutrality point, a prerequisite for valleytronics.6 Despite strong theoretical attention, experimental realization of clean ZZ edges without disorder, reconstructions, or chemical functional groups that could cause scattering between the different spin and valley channels remains challenging.2,4,6,9−14 Pioneering studies on unzipped carbon nanotubes have shown that the chemical edge termination can be controlled, but the crystallographic direction of the edge cannot be a priori selected.10,12,14 In addition, the transfer techniques involved in producing graphene-based devices rely on solution-based chemistry that may in general cause unknown and uncontrollable changes to the chemistry of the graphene edges. © 2014 American Chemical Society
Received: May 21, 2014 Revised: July 16, 2014 Published: July 31, 2014 5128
dx.doi.org/10.1021/nl501895h | Nano Lett. 2014, 14, 5128−5132
Nano Letters
Letter
Figure 1. Overview of the epitaxial G−BN sample. (a) Large scale topography of the intercalated G−BN sample with an overlaid color scale indicating the clean gold surface (yellow), graphene (red), and BN (blue) islands (feedback parameters 0.5 V, 0.1 nA). (b) Low-bias spectroscopy showing the Au(111) surface state on bare gold (black line) and graphene (red) and BN (blue) covered surfaces. (c) Field-emission resonance spectroscopy allowing us to identify the different surface regions based on their work functions.
reconstruction of the gold surface. BN on the other hand retains a corrugated moiré-like structure even on top of the gold thin film. While some interface reconstruction prevails on the intercalated sample, the overall length and quality of the interfaces is significantly improved compared to the nonintercalated G−BN directly on the Ir(111) surface (see Figure S1 in the Supporting Information). Finally, the surface state of Au(111) only shifts slightly under graphene and BN (Figure 1b) again indicating weak interaction between the G−BN layer and the substrate. In the following, we will focus our investigation on highquality ZZ-terminated interfaces between graphene and BN. We observe a distinct lobe structure in the STM images at low bias on the ZZ oriented parts of the interfaces, which is not visible on interfaces with other terminations. An example of the lobe structure is shown in Figure 2a. The slight variation of the lobe intensity along the interface is due to the herringbone reconstruction of the underlying gold substrate. STS performed on the lobes of the G−BN interfaces shows a clear peak in the local density of states (LDOS, see black lines in Figure 2b,c). The sets of spectra shown in Figures 2b and 22c were acquired with different microtips causing slight variations in the background signal. The peak, close to zero bias, is completely absent in the spectra taken next to the interface on either graphene or BN (red and blue lines in Figure 2b,c). The energetic position of the peak is similar to the earlier experiments on free graphene edges resulting from unzipped carbon nanotubes or chemically synthesized graphene nanoribbons.12,26 G−BN interfaces can be formed with either nitrogen- or boron-terminated BN and it is not directly possible to discern the different elements from the STM images. Yet, the atomic structure of the interface is important in terms of, for example, charge transfer to or from the graphene edge state. We have studied the effect of B and N termination on the interface by DFT using the FHI-aims package31 (details given in the Supporting Information). Simulated tunneling current maps, evaluated for periodic graphene ZZ ribbons embedded in BN,
preparation can be found in the Supporting Information. Graphene and passivated graphene edges have been demonstrated to be only weakly coupled to gold surfaces.26−28 The resulting G−BN layer was characterized by low-temperature STM at T = 4.2 K. STM experiments on the sample reveal that graphene and BN connect along the ZZ high symmetry direction (see Figures S1 and S2 in the Supporting Information). Graphene grown on Ir(111) by the TPG method exposes only ZZ terminated edges. As a result of the graphene moiré pattern on Ir(111), small kinks appear in the edges of graphene islands.29 This limits the length of atomically perfect G−BN interfaces to that of the moiré period, ca. 2.4 nm, even in the absence of any additional strain or reconstruction. Because of the strong modulation of the BN to Ir(111) interaction,25 the G−BN interface exhibits strong reconstruction on this surface, which further limits the length of high quality interfaces. We reduce the G−BN to surface interaction by intercalating gold underneath the samples. The reduced interaction upon intercalation results in higher quality interfaces, some of which exceed the length of the graphene moiré on Ir(111). Figure 1a shows an overview of the gold-intercalated G−BN layer. After intercalation, most of the graphene and BN domains are embedded within the first Au layer. The Au adlayer exhibits the well-known Au(111) herringbone reconstruction and shows a surface state at ca. −500 mV bias (Figure 1b), demonstrating the bulklike quality of the gold thin film. Tunneling spectroscopy in the field emission regime,30 shown in Figure 1c, reveals resonances related to the local work function of the surface. Graphene (first resonance at 4.7 V) and BN (4.7 and 5.0 V) show a lower work function than clean gold (5.2 V) and can be distinguished from each other by the characteristic split peak resonance of BN.25 The position and shape of the first field emission resonance are spectroscopic fingerprints that allow for the clear identification of gold, graphene, and BN regions on the sample. Graphene forms a smooth adlayer without any discernible superstructure on the Au thin film, its corrugation following the herringbone 5129
dx.doi.org/10.1021/nl501895h | Nano Lett. 2014, 14, 5128−5132
Nano Letters
Letter
Figure 3. Scattering at graphene zigzag edges and comparison between theory and experiment. (a) High-resolution STM image of the G−BN interface along the ZZ high symmetry direction. Scale bar 2 nm, feedback parameters 0.1 V, 1 nA. (b) Calculated band structure for a BN-terminated graphene nanoribbon. The interface bands are indicated by the red and blue lines. The bending of the interface state is indicated by ΔE and the bulk bandgap by ΔEc. (c) STM image showing the G−BN interface state with an overlaid model of the atomic structure (0.1 V, 1 nA). (d) Local density of states (LDOS) map calculated by TB on the G−BN interface with the same atomic structure as in the experimental image shown in panel (c).
Figure 2. Geometric and electronic structure of the interface between graphene and BN. (a) STM image of the G−BN interface showing the interface state local density of states. Scale bar 1 nm, feedback parameters −1 V, 3 nA. (b,c) Wide energy range (b) and highresolution (c) tunneling spectra measured on graphene (red), BN (blue), and at the interface (black). (d) Simulated tunneling current maps of G−BN interfaces based on DFT calculations with either nitrogen- (left) or boron (right) terminated BN edge. The maps have been calculated at the bias corresponding to the maximum LDOS of the interface state (0.1 V for nitrogen and −0.2 V for boronterminated BN edges, respectively).
that the localized states observed at the interface are a property of the interface itself and do not arise from, for example, interaction of the G−BN layer with the gold surface state. We have developed a TB model that allows us to treat large G−BN structures numerically (see Supporting Information for details).34−37 Results are in good agreement with DFT based on LDOS maps and band structures for smaller systems (Figure S4 in the Supporting Information). Figure 3b shows the calculated band structure for a narrow graphene ribbon forming a C−B interface with BN with the TB model. Quantum confinement opens a gap in the graphene band structure at the K and K′ points (bulk bands indicated by gray lines). The red and blue lines in Figure 3b show the dispersion of the interface state. The downward bending between the K and K′ points (energy shift of ΔE w.r.t to the Dirac point) is caused by the edge potential resulting from bonding with the boron atoms.5,35 For a nitrogen-terminated G−BN interface, our model predicts a corresponding bending to higher energies, which is in agreement with earlier DFT calculations.35 The interface state is only fully localized at the edge of the first Brillouin zone (BZ) and propagates throughout the graphene bulk for states between k = 2π/(3a) and k = 0. Theoretically, a dispersive interface state will lead to the formation of localized standing waves along finite interface segments. Here, the standing waves have an additional modulation of π, because the edge band is centered at k = π/ a. The standing waves occur at different energies depending also on the length of the segment, akin to states found in a onedimensional quantum well. For short segments, there are only a few possible modes between the allowed interval of edge states with k values between 2π/(3a) and 4π/(3a). Therefore, this model predicts standing wave states for which in the STM spectra the number of peaks and their energies depend on the length of the segment and ΔE. Our STS measurements, however, show only a single peak that is always located close to the Fermi level. This statement holds for both the different lobes on a single interface as well as
are shown in Figure 2d. The results indicate that a C−B termination is not only energetically favorable (on the order of an electronvolt per edge carbon atom)32 but also reproduces the experimental lobe structure far better than a C−N connection. The lobes at the C−B interface are elongated, which is consistent with the experimental image shown in Figure 2a. In addition, the energetic position of the main interface state peak in simulated tunneling spectra (Figure S3 in the Supporting Information) agrees well with the experimental results considering the known doping of graphene by the gold substrate. Our results suggest that the G−BN interfaces are formed between graphene- and boron-terminated BN with the interface state arising from C−B bonding states. An atomically resolved STM image of a G−BN interface is shown in Figure 3a. The ZZ high symmetry direction of the graphene sheet is extracted from the atomic positions far from the interface region and highlighted in the figure, demonstrating that the G−BN interface is aligned along the ZZ direction. The ZZ interface state appears as a series of bright lobes in lowbias STM scans that are entirely confined to within one atomic row of the interface. The fact that the state is attenuated on the short armchair sections of the interface is further evidence that it is derived from the ZZ symmetry at the graphene edge. The ZZ interface results in a characteristic scattering pattern close to the interface, where one of the graphene sublattices is imaged with significantly higher intensity than the other (indicated by a black arrow in Figure 3a). This type of scattering pattern results from broken sublattice symmetry in the absence of intervalley scattering in graphene, suggesting that the interface state could carry valley-polarized currents.11,12,14 On the other hand, defects in the graphene lattice (lower right-hand corner of Figure 3a) are surrounded by the well-known (√3 × √3)R30° pattern (indicated with a white arrow), which results from intervalley scattering.33 Finally, no scattering pattern is found on the BN side of the interface as the ZZ interface state lies within the BN bandgap. This shows 5130
dx.doi.org/10.1021/nl501895h | Nano Lett. 2014, 14, 5128−5132
Nano Letters
■
for separate interfaces of different lengths. Thus, based on our experiments, ΔE is small, i.e. the dispersion of the interface state is low. This may be partly due to screening caused by the substrate, which may result in an increase of the effective edge potential on the graphene flake and subsequently a reduced dispersion of the interface state.5 We validate the TB model by comparing the G−BN interface state structure measured experimentally (Figure 3c with an overlaid atomic model of the interface) with the result of the TB calculation (Figure 3d) on the same atomic structure. The excellent correspondence between theory and experiment further evidences the C−B bonding and absence of intervalley scattering at the G−BN interfaces. Furthermore, the short armchair segments do not significantly affect the interface state properties, which is important for potential applications. Theory predicts the pure graphene ZZ edge state to be spinpolarized with opposite spin ground states on opposite sublattices. The spin polarization is a result of the nearly flat dispersion of the ZZ edge state that occurs exactly at the charge neutrality point. While it is not clear if the G−BN interface states are spin-polarized, the sharpness of the peak observed in our experiments indicates a highly degenerate electronic state that should be susceptible to spin polarization with appropriate gating or doping. In conclusion, we prepared atomically sharp and well-defined ZZ G−BN interfaces and showed the existence of an interfacelocalized state near zero bias using STS. The G−BN ZZ interface is an experimentally realizable, chemically stable model system to study the fundamental properties of the graphene ZZ edge state. Our results show that the electronic structure of the ZZ G−BN interface is similar to that of the free graphene ZZ edge state and many important properties of the graphene edge state are preserved. Most notably, the distinct valley channels persist at the G−BN interface and our results suggest the possibility of graphene valleytronics in experimentally realizable structures.
■
REFERENCES
(1) Nakada, K.; Fujita, M.; Dresselhaus, G.; Dresselhaus, M. S. Edge State in Graphene Ribbons: Nanometer Size Effect and Edge Shape Dependence. Phys. Rev. B 1996, 54, 17954−17961. (2) Son, Y.-W.; Cohen, M. L.; Louie, S. G. Half-Metallic Graphene Nanoribbons. Nature 2006, 444, 347−349. (3) Akhmerov, A. R.; Beenakker, C. W. J. Boundary Conditions for Dirac Fermions on a Terminated Honeycomb Lattice. Phys. Rev. B 2008, 77, 10. (4) 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. (5) Yazyev, O. V. A Guide to the Design of Electronic Properties of Graphene Nanoribbons. Acc. Chem. Res. 2013, 46, 2319−2328. (6) Rycerz, A.; Tworzydlo, J.; Beenakker, C. W. J. Valley Filter and Valley Valve in Graphene. Nat. Phys. 2007, 3, 172−175. (7) Yazyev, O. V.; Katsnelson, M. I. Magnetic Correlations at Graphene Edges: Basis for Novel Spintronics Devices. Phys. Rev. Lett. 2008, 100, 047209. (8) Gunlycke, D.; White, C. Graphene Valley Filter Using a Line Defect. Phys. Rev. Lett. 2011, 106, 136806. (9) Wassmann, T.; Seitsonen, A. P.; Saitta, A. M.; Lazzeri, M.; Mauri, F. Structure, Stability, Edge States, and Aromaticity of Graphene Ribbons. Phys. Rev. Lett. 2008, 101, 096402. (10) Li, X. L.; Wang, X. R.; Zhang, L.; Lee, S. W.; Dai, H. J. Chemically Derived, Ultrasmooth Graphene Nanoribbon Semiconductors. Science 2008, 319, 1229−1232. (11) Koskinen, P.; Malola, S.; Häkkinen, H. Self-Passivating Edge Reconstructions of Graphene. Phys. Rev. Lett. 2008, 101, 115502. (12) Tao, C.; Jiao, L.; Yazyev, O. V.; Chen, Y.-C.; Feng, J.; Zhang, X.; Capaz, R. B.; Tour, J. M.; Zettl, A.; Louie, S. G.; et al. Spatially Resolving Edge States of Chiral Graphene nanoribbons. Nat. Phys. 2011, 7, 616−620. (13) Kim, K.; Coh, S.; Kisielowski, C.; Crommie, M. F.; Louie, S. G.; Cohen, M. L.; Zettl, A. Atomically Perfect Torn Graphene Edges and Their Reversible Reconstruction. Nat. Commun. 2013, 4, 6. (14) Zhang, X.; Yazyev, O. V.; Feng, J.; Xie, L.; Tao, C.; Chen, Y.-C.; Jiao, L.; Pedramrazi, Z.; Zettl, A.; Louie, S. G.; et al. Experimentally Engineering the Edge Termination of Graphene Nanoribbons. ACS Nano 2012, 7, 198−202. (15) Sutter, P.; Cortes, R.; Lahiri, J.; Sutter, E. Interface Formation in Monolayer Graphene-Boron Nitride Heterostructures. Nano Lett. 2012, 12, 4869−4874. (16) Levendorf, M. P.; Kim, C.-J.; Brown, L.; Huang, P. Y.; Havener, R. W.; Muller, D. A.; Park, J. Graphene and Boron Nitride Lateral Heterostructures for Atomically Thin Circuitry. Nature 2012, 488, 627−632. (17) Liu, Z.; Ma, L.; Shi, G.; Zhou, W.; Gong, Y.; Lei, S.; Yang, X.; Zhang, J.; Yu, J.; Hackenberg, K. P.; et al. In-Plane Heterostructures of Graphene and Hexagonal Boron Nitride with Controlled Domain Sizes. Nat. Nanotechnol. 2013, 8, 119−124. (18) Gao, Y.; Zhang, Y.; Chen, P.; Li, Y.; Liu, M.; Gao, T.; Ma, D.; Chen, Y.; Cheng, Z.; Qiu, X.; et al. Toward Single-Layer Uniform Hexagonal Boron Nitride−Graphene Patchworks with Zigzag Linking Edges. Nano Lett. 2013, 13, 3439−3443. (19) Liu, L.; Park, J.; Siegel, D. A.; McCarty, K. F.; Clark, K. W.; Deng, W.; Basile, L.; Idrobo, J. C.; Li, A.-P.; Gu, G. Heteroepitaxial Growth of Two-Dimensional Hexagonal Boron Nitride Templated by Graphene Edges. Science 2014, 343, 163−167. (20) Kim, S. M.; Hsu, A.; Araujo, P. T.; Lee, Y.-H.; Palacios, T.; Dresselhaus, M.; Idrobo, J.-C.; Kim, K. K.; Kong, J. Synthesis of Patched or Stacked Graphene and hBN Flakes: A Route to Hybrid Structure Discovery. Nano Lett. 2013, 13, 933−941. (21) Coraux, J.; N’Diaye, A. T.; Engler, M.; Busse, C.; Wall, D.; Buckanie, N.; Meyer zu Heringdorf, F.-J.; van Gastel, R.; Poelsema, B.; Michely, T. Growth of Graphene on Ir(111). New J. Phys. 2009, 11, 023006. (22) Hämäläinen, S. K.; Sun, Z.; Boneschanscher, M. P.; Uppstu, A.; Ijäs, M.; Harju, A.; Vanmaekelbergh, D.; Liljeroth, P. Quantum-
ASSOCIATED CONTENT
S Supporting Information *
Details on the experimental and computational methods and additional results. This material is available free of charge via the Internet at http://pubs.acs.org.
■
Letter
AUTHOR INFORMATION
Corresponding Author
*E-mail: peter.liljeroth@aalto.fi. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This research made use of the Aalto Nanomicroscopy Center (Aalto NMC) facilities and was supported by the European Research Council (ERC-2011-StG No. 278698 “PRECISENANO”), the Finnish Academy of Science and Letters and the Academy of Finland (Centres of Excellence in Low Temperature Quantum Phenomena and Devices No. 250280 and in Computational Nanoscience No. 251748). We acknowledge the computational resources provided by Aalto Science-IT project and Finland’s IT Center for Science (CSC). 5131
dx.doi.org/10.1021/nl501895h | Nano Lett. 2014, 14, 5128−5132
Nano Letters
Letter
Confined Electronic States in Atomically Well-Defined Graphene Nanostructures. Phys. Rev. Lett. 2011, 107, 236803. (23) Subramaniam, D.; Libisch, F.; Li, Y.; Pauly, C.; Geringer, V.; Reiter, R.; Mashoff, T.; Liebmann, M.; Burgdörfer, J.; Busse, C.; et al. Wave-Function Mapping of Graphene Quantum Dots with Soft Confinement. Phys. Rev. Lett. 2012, 108, 046801. (24) Corso, M.; Auwärter, W.; Muntwiler, M.; Tamai, A.; Greber, T.; Osterwalder, J. Boron Nitride Nanomesh. Science 2004, 303, 217−220. (25) Schulz, F.; Drost, R.; Hämäläinen, S. K.; Demonchaux, T.; Seitsonen, A. P.; Liljeroth, P. Epitaxial Hexagonal Boron Nitride on Ir(111): A Work Function Template. Phys. Rev. B 2014, 89, 235429. (26) van der Lit, J.; Boneschanscher, M. P.; Vanmaekelbergh, D.; Ijäs, M.; Uppstu, A.; Ervasti, M.; Harju, A.; Liljeroth, P.; Swart, I. Suppression of Electron−Vibron Coupling in Graphene Nanoribbons Contacted Via a Single Atom. Nat. Commun. 2013, 4, 2023. (27) Leicht, P.; Zielke, L.; Bouvron, S.; Moroni, R.; Voloshina, E.; Hammerschmidt, L.; Dedkov, Y. S.; Fonin, M. In Situ Fabrication of Quasi-Free-Standing Epitaxial Graphene Nanoflakes on Gold. ACS Nano 2014, 8, 3735−3742. (28) Li, Y.; Zhang, W.; Morgenstern, M.; Mazzarello, R. Electronic and Magnetic Properties of Zigzag Graphene Nanoribbons on the (111) Surface of Cu, Ag, and Au. Phys. Rev. Lett. 2013, 110, 216804. (29) Li, Y.; Subramaniam, D.; Atodiresei, N.; Lazic, P.; Caciuc, V.; Pauly, C.; Georgi, A.; Busse, C.; Liebmann, M.; Blugel, S.; et al. Absence of Edge States in Covalently Bonded Zigzag Edges of Graphene on Ir(111). Adv. Mater. 2013, 25, 1967−1972. (30) Ploigt, H.-C.; Brun, C.; Pivetta, M.; Patthey, F.; Schneider, W.D. Local Work Function Changes Determined by Field Emission Resonances: NaCl/Ag(100). Phys. Rev. B 2007, 76, 195404. (31) Blum, V.; Gehrke, R.; Hanke, F.; Havu, P.; Havu, V.; Ren, X.; Reuter, K.; Scheffler, M. Ab Initio Molecular Simulations with Numeric Atom-Centered Orbitals. Comput. Phys. Commun. 2009, 180, 2175−2196. (32) Liu, Y.; Wu, X.; Zhao, Y.; Zeng, X. C.; Yang, J. Half-Metallicity in Hybrid Graphene/Boron Nitride Nanoribbons with Dihydrogenated Edges. J. Phys. Chem. C 2011, 115, 9442−9450. (33) Rutter, G. M.; Crain, J. N.; Guisinger, N. P.; Li, T.; First, P. N.; Stroscio, J. A. Scattering and Interference in Epitaxial Graphene. Science 2007, 317, 219−222. (34) Hancock, Y.; Uppstu, A.; Saloriutta, K.; Harju, A.; Puska, M. J. Generalized Tight-Binding Transport Model for Graphene Nanoribbon-Based Systems. Phys. Rev. B 2010, 81, 245402. (35) Jung, J.; Qiao, Z.; Niu, Q.; MacDonald, A. H. Transport Properties of Graphene Nanoroads in Boron Nitride Sheets. Nano Lett. 2012, 12, 2936−2940. (36) Ijäs, M.; Ervasti, M.; Uppstu, A.; Liljeroth, P.; van der Lit, J.; Swart, I.; Harju, A. Electronic States in Finite Graphene Nanoribbons: Effect of Charging and Defects. Phys. Rev. B 2013, 88, 075429. (37) Radzig, A. A.; Smirnov, B. M. Reference Data on Atoms, Molecules, and Ions; Springer Series in Chemical Physics; Springer: BerlinHeidelberg, 1985; Vol. 31.
5132
dx.doi.org/10.1021/nl501895h | Nano Lett. 2014, 14, 5128−5132
