J. Phys. Chem. C 2008, 112, 12683–12686
12683
Asymmetric Spin Gap Opening of Graphene on Cubic Boron Nitride (111) Substrate Y. H. Lu,† P. M. He,*,† and Y. P. Feng*,‡ Department of Physics, Zhejiang UniVersity, Hangzhou, China, and Department of Physics, National UniVersity of Singapore, 2 Science DriVe 3, Singapore, 117542 ReceiVed: March 23, 2008; ReVised Manuscript ReceiVed: June 24, 2008
Graphene grown on cubic BN (111) is studied using the first-principles method based on density functional theory. Results of our calculations reveal that spin polarized surface states break the equivalence of the A and B sublattices and lead to spin polarized graphene bands with finite energy gaps. As a result, spin polarized carriers can be generated by shifting the Fermi-level inside the band gap of minority (majority) spin but inside the conduction (valence) band of majority (minority) spin. The spin state of the injected electrons can be manipulated by an external electric field alone. Active control and manipulation of spin degrees of freedom in solid-state systems have attracted much attention in recent years due to its potential applications in spintronic devices or spin-based quantum computing. One of the crucial questions related to spintronics is how long can a system remain spin polarized?1 Typical time scales for spin relaxation in electronic systems are measured in nanoseconds. Several mechanisms, most involving spin-orbit coupling, have been proposed to understand spin-dependent dynamics and spin relaxation. Recent studies suggest that graphene2 can be an excellent material for spintronics applications. This is because spin-orbit coupling is weak in carbon owing to its relatively low atomic weight, and because natural carbon consists predominantly of the zerospin isotope 12 C, for which the hyperfine interaction is absent. Spin transport over micrometer-scale distances has been observed in a single graphene layer at room temperature3 and supercurrent transport in graphene has also been observed.4 Although the intrinsic properties of graphene ensure a very long spin relaxation length and relaxation time, it is difficult to manipulate the spin of the injected electrons via application of an electrical field only, without a magnetic field. In addition, graphene is a zero-gap semiconductor and its Fermi level exactly crosses the Dirac point. Several attempts have been made to lift the degeneracy of the two bands at the Dirac point, such as using suitable transverse states in graphene ribbons to confine electrons,5 combining single and bilayer regions of graphene,6 or achieving confinement by using inhomogeneous magnetic fields.7 Recently, Zhou et al.8 showed that a gap can be easily induced by growing graphene on a suitable substrate, because the interaction with the substrate breaks the equivalence of the A and B sublattices. Thus, choosing a proper substrate can be a key to modify the properties of graphene to satisfy the application requirement. In this work, we investigate properties of graphene grown on cubic boron nitride (cBN) (111) surface using first-principles calculations based on the density function theory (DFT). We demonstrate that the substrate not only breaks the equivalence of the A and B sublattices, but further the effect is spin dependent. The conduction and valence band edges of the * Corresponding authors. † Zhejiang University. Y.H.L.: e-mail
[email protected]. P.M.H.: e-mail
[email protected]. ‡ National University of Singapore. E-mail:
[email protected].
majority spin are shifted relative to those of the minority spin. Therefore, spin-polarized carriers can be generated by moving the Fermi level inside the band gap of one spin but in the conduction or valence bands of the other spin. This provides a means to directly control the electron spin in devices based on a graphene layer, a potentially useful property for spintronics. First-principles calculations were performed with the VASP code.9-12 The projector augmented wave potentials13 were used for electron-ion interactions while the local spin density approximation (LSDA) was used for exchange-correlation function. For the Brillouin-zone integrations, we used a 15 × 15 × 1 grid of Monkhorst-Pack special points14 together with a Gaussian smearing of 0.1 eV for the one-electron eigenvalues. The plane wave basis set was restricted by a cutoff energy of 400 eV. The in-plane lattice constant of the heteroepitaxial graphene/cBN (111) structure was set to 2.52 Å, which is the lattice parameter of cBN (111) determined from our firstprinciples calculation within LSDA. Eight atomic layers (four BN double layers) were used to model the substrate. Dangling bonds of atoms in the bottom layer are saturated by pseudohydrogen and graphene is adsorbed on the top surface. Upon hydrogenation, forces on atoms in the bulk-terminated surface are very small except in the first couple of layers. Atoms from the third layer downward remain essentially in their ideal bulk positions after structural relaxation. A vacuum region of at least 18 Å was used to avoid interaction between the top and bottom surfaces. The different polarities of the two surfaces together with the periodic boundary conditions introduce a spurious field in the vacuum region. We found that this field has little effect on the force but it causes errors in total energy. To avoid this, a dipole plane in the vacuum region is added to remove the total dipole moment of the cell. All structures were fully relaxed, and the force acting on an atom is e0.01 eV/Å in the relaxed structures. cBN is a wide band gap crystalline compound and it is easy to grow cBN with (111) surface by chemical vapor deposition (CVD).15 The (111) surface is the most stable surface among the three low-index surfaces16 of cBN although reconstructions may occur.17 The experimental lattice constant of cBN (111) surface is 2.55 Å, which is very close to that of graphene (2.46 Å). It is noted that in the growth of graphene directly on SiC, the excess carbon atoms self-organize to form the honeycomb structure, which overwhelms the covalent bonding with sub-
10.1021/jp802525v CCC: $40.75 2008 American Chemical Society Published on Web 07/26/2008
12684 J. Phys. Chem. C, Vol. 112, No. 33, 2008
Lu et al.
Figure 1. (a) Side view of the optimized structure of N-terminated cBN (111) with intralayer distance and interplane distance indicated, where nitrogen and boron atoms are represented by big blue and small pink spheres, respectively. The little white spheres represent pseudohydrogen. (b) Spin charge density projected on the (100) plane shown by a dash line in part a with a unit of charge density of 10-2 e/Å3. (c) Band structure of part a with majority spin (dashdotted line) and minority spin (solid line) band. The Fermi level is indicated by a dashed line.
strate.18 The cBN (111) planes consist of alternate B- and N-layers and we consider only the N-terminated (111) surface here, which has lower surface energy than the B-terminated (111) surface (by about 1 eV per surface unit cell according to our calculation). The length of the B-N bond in our optimized bulk cBN is 1.545 Å, which is very close to the experimental value of 1.569 Å. Compared to bulk cBN, significant atomic relaxations were found in the top two layers of the optimized N-terminated cBN (111) surface. N atoms in the surface layer relax inward by 0.04 Å but B atoms in the next layer move outward by 0.20 Å, resulting in a flatter first double layer and elongation of the perpendicular B-N bonds connecting the second and third layer. Bonds in the first double layer are reduced to 1.48 Å, 3.9% shorter than that in bulk cBN, but 3.5% larger than the in-plane bond length of hexagonal boron nitride (hBN) within LSDA calculation. At the same time, B-N bonds normal to the surface between the second and third atomic layer are increased by 13% compared to the bond length in bulk cBN, to 1.745 Å. It is noted that the result of our spin-polarized calculation is different from that of a previous non-spin-polarized calculation17where the corresponding B-N bond length was found increased by 25% compared to that in bulk cBN and therefore the surface double layer essentally breaks off from the underneath double layer. Smaller atomic relaxations were found in the second double layer. The bond length in the second double layer is 1.530 Å, slightly shorter than the bulk value, and the double layer becomes a little flatter. Essentially no change was found in the third double layer after structural optimization. cBN is an sp3-bonded structure in which each atom forms four covalent bonds with its four nearest neighboring atoms of a differnt type. In a bulk truncated (111) surface, however, each N atom in the top layer has only three nearest neighbor B atoms and therefore one unsaturated dangling bond, which may induce surface states in the band gap of bulk cBN. The surface states were found mainly localized on the surface N atoms (unsaturated N-2p orbitals) and are highly dispersive around the Fermi level (Figure 1b,c), which is in agreement with results of a previous non-spin-polarized calculation.19 However, results of our spinpolarized calcualtions reveal that these states split around the Fermi level, with fully occupied majority spin surface bands
and essentially empty minority spin surface bands, leading to a half-metallic cBN (111) surface. This is an example of flatband ferromagnetism, which was predicted to occur under certain conditions, especially in hexagonally bonded honeycomb heterosheets, based on the Hubbard model.20 As mentioned above, in the relaxed cBN (111) surface, the first double layer becomes so flat that the separation between the boron and nitrogen layers is only 0.276 Å. Therefore, the double layer can be viewed as a distorted hBN sheet with boron atoms occupying one sublattice (A) and nitrogen atoms the other (B). Atoms in the two sublattices were found spin-polarized in opposite directions, with each nitrogen atom carrying a magnetic moment of 0.321 µB and a boron atom -0.025 µB. These values are similar to the moments in a hexagonally bonded sheet, which is due to the edge states resulting from a delicate balance of electron transfer among the π orbitals.20,21 The spin density is mainly localized on the outmost N atoms with pz-like orbitals (Figure 1b) and decreases rapidly from the surface double layer to bulk, and becomes essentially zero in the third double layer where the B-N bond length also recovers its bulk value. To find the stable structure of graphene on the N-terminated cBN (111) surface, self-consistent calculations were performed for a number of possible configurations. Relative to the flattered surface double layer of cBN (111) surface, the carbon atoms of graphene can be placed directly over the B and N atoms. Two other possible structures were obtained by placing one carbon atom above the hexagonal hollow site of the surface double layer of cBN (111) and the other either above a boron or a nitrogen atom, respectively. Results of our calculations indicate that all three structures are stable and their total energies differ by less than 15 meV. Therefore, it is possible for the three structures to coexist at room temperature. Figure 2a shows the optimized structure with carbon atoms of the graphene directly over the boron and nitrogen atoms of the surface double layer of cBN (111). The graphene layer floats above the cBN (111) surface at a distance of 2.95 Å from the outmost nitrogen layer. It is noted that this separation between the graphene layer and the cBN (111) surface is smaller than that of graphene on hBN (0001) substrate,22 which may be due to stronger interaction between carbon atoms in the graphene and the dangling bonds on the cBN (111) surface. Upon graphene adsorption, the
Asymmetric Spin Gap Opening of Graphene
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Figure 2. (a) Side view of the optimized structure of graphene grown directly on B and N atoms of N-terminated cBN (111) with intralayer distance and interplane distance indicated, where nitrogen and boron atoms are represented by big blue and small pink spheres, respectively. The medium sized dark spheres represent carbon atoms and the little white spheres represent pseudohydrogen.(b) Partial spin charge density at K around the Fermi level projected on the (100) plane shown by a dash line in part a with a unit of charge density of 102e/Å3. (c) Band structure of part a with majority spin (dash-dotted line) and minority spin (solid line) band. The Fermi level is indicated by a dashed line.
Figure 3. K-resolved DOS of the graphene layer. The upper panels show K-resolved DOS of carbon atop B (A-sublattice) along the Γ-K path in reciprocal space for majority and minority spin, respectively. The lower panels show K-resolved DOS of carbon atop N (B-sublattice) along the same path in reciprocal space for majority and minority spin, respectively. CBM or VBM is indicated for each spin band.
structure of the N-terminated cBN (111) surface changes little. The only noticeable change is the inward relaxation of 0.02 Å of the boron atom in the surface double layer. The structure of graphene also maintains its pristine geometry without apparent distortion due to its strong C-C bonds. Its electronic structure, however, is significantly modified by the cBN (111) substrate. There is a charge transfer of ∼0.036e per unit cell, based on the Bader23 partition scheme, from graphene to the substrate, which results in a p-type graphene. Furthermore, more valence charges (0.475e on the Bader scheme) are found localized on carbon atoms occuping the B sublattice site, which is over the nitrogen atom of the cBN (111) surface, than that on the A sublattice site. This is expected since the surface nitrogen atoms
have a dangling bond. Therefore the equivalence between the A and B sublattices is broken by the substrate and a band gap of ∼0.13 eV opens at the Dirac cone for both spins (Figure 2c). In addition, the spin polarized surface states of the substrate induce spin polarized states of graphene around the Dirac cone, as seen in the projected spin density shown in Figure 2b. The spin density around the Dirac cone is mainly localized at the hollow site of graphene. Figure 2c shows the band structure of graphene on the N-terminated cBN (111). Energy bands characteristic of graphene appear above the Fermi level in the band gap of the substrate. The fully occupied majority spin band and almost empty minority spin band of cBN (111) around the Fermi level remain
12686 J. Phys. Chem. C, Vol. 112, No. 33, 2008 unchanged. However, these surface states now hybridize with bands of graphene around the K point, leading to a band splitting. The minority spin band of the substrate, which has higher energy than the majority spin band, hybridizes with the minority spin band of graphene, resulting in the energy of the minority spin band of graphene being higher than that of the majority spin band. To further investigate the electronic properties around the Dirac cone of graphene on cBN (111), we plot the K-resolved DOS of the A and B sublattices along the Γ-K line in the reciprocal space in Figure 3 The K-resolved DOS is equivalent to what an angle-resolved ultraviolet photoemission spectrum (ARUPS) experiment measures. It is apparant that in the energy range of 1.0-4.5 eV, which corresponds to the energy gap of cBN (111), the energy band of graphene remains the same as that of pristine graphene. However, the band below the Fermi level is significantly distorted due to hybridization with 2p orbitals of the surface nitrogen atoms of the substrate. Nevertheless, the unique linear character of the graphene energy band is almost maintained around the K point for both majority and minority spin. The Fermi level is about 0.5 eV lower than the Dirac cone, which indicates that the graphene is hole doped. Since the two sublattices are no longer equivalent, the degeneracy between the conduction band minimum (CBM) and the valence band maximum (VBM) at the Direc point is lifted. The CBM is dominated by carbon orbitals of the B-sublattice while the VBM consists of mainly carbon orbitals of the A-sublattice (Figure 3). An energy gap is open for both majority and minority spin band, which can be used to tune conductivity in graphene-based electronics. The most interesting observation is that the CBM of the minority spin band is about 0.13 eV higher than that of the majority spin band while the VBM of the minority spin band is 0.07 eV higher than that of the majority spin band. It is thus possible to generate spin polarized carriers by shifting the Fermi level inside the band gap of minority (majority) spin but inside the conducting (valence) band of majority (minority) spin. In such an all-carbon system, spin-orbit coupling is negligible, and by proper tuning of the Fermi level with an external electronic field only, switching between majority spin and minority spin carriers can be realized. It is noted, however, that the transport of the system considered will be dominated by the spin-polarized electron bands which come from the surface states of BN. Similar calculations and analysis were carried out for the other configurations of graphene on N-terminated cBN (111) surface. It was found that their electronic structures have essentially the same properties as that of the configuration discussed above, except for the size of the energy gap around the K point. We also investigated the properties of graphene on B-terminated cBN (111) surface but its electronic properties were found quite
Lu et al. different. The energies of the surface states of B-terminated cBN (111) are much higher than that of the Fermi level and have very little effect on the graphene states. In summary, we investigated graphene grown on cBN (111) surface using the first-principles method based on DFT. The equivalence between A and B sublattices of graphene is broken by interaction with the substrate and a band gap of 0.13 eV opens when graphene is grown on the N-terminated cBN (111) surface. Hybridization between graphene states and the spin polarized surface states of the substrate results in splitting of the majority and minority spin bands, especially around the Dirac point. It is thus possible to generate spin polarized carriers by shifting the Fermi level inside the band gap of one spin but in the conducting or valence band of the other spin. An allgraphene system can be realized. A mechanism that allows switching between majority and minority spin carriers can be achieved by tuning the Fermi level with an external electronic field only. Therefore, the electronic properties of graphene grown on cBN (111) surface can be tuned by the Fermi level,which makes the graphene/N-cBN (111) an interesting system for spintronics applications. ¨ zyilmaz Acknowledgment. The authors wish to thank B. O for useful discussion and valuable input to this manuscript. References and Notes (1) Zutic, I.; Fabian, J.; Sarma, S. D. ReV. Mod. Phys. 2004, 76, 323. (2) Novoselov, K. S.; et al. Science 2004, 306, 666. (3) (a) Tombros, N.; Jozsa, C.; Popinciuc, M.; Jonkman, H. T.; Wees, B. J. Nature 2007, 448, 571. (b) Hill, E. W.; Geim, A. K.; Novoselov, K.; Schedin, F.; Blake, P. IEEE Trans. Magn. 2006, 42, 2694. (4) Heersche, H. B.; et al. Nature 2007, 446, 56. (5) Silvestrov, P. G.; Efetov, K. B. Phys. ReV. Lett. 2007, 98, 016802. (6) Nilsson, J.; Neto, A. H. C.; Guinea, F; et al. Phys. ReV. B 2007, 76, 165416. (7) Martino, A. D.; Anna, L. D.; Egger, R. Phys. ReV. Lett. 2007, 98, 066802. (8) Zhou, S. Y.; et al. Nat. Mater. 2007, 6, 770. (9) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 47, 558. (10) Kresse, G., Ph.D. Thesis, Technische University Wien, Austria, 1993. (11) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B. 1996, 54, 11169. (12) Kresse, G.; Furthmu¨ller, J. Comput. Mater. Sci. 1996, 6, 15. (13) Kresse, G.; Joubert, D. Phys. ReV. B 1999, 59, 1758. (14) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (15) Zhang, W. J.; Jiang, X.; Matsumoto, S. Appl. Phys. Lett. 2001, 79, 4530. (16) Ruuska, H.; Larsson, K. Diamond Relat. Mater. 2007, 16, 118. (17) Kadas, K.; Kern, G.; Hafner, J. Phys. ReV. B 1998, 58, 15636. (18) Chen, W. Surf. Sci. 2005, 596, 176. (19) Kadas, K.; Kern, G.; Hafner, J. Phys. ReV. B 1999, 60, 8719. (20) Okada, S.; Oshiyama, A. Phys. ReV. Lett. 2001, 87, 146803. (21) Okada, S.; et al. Phys. ReV. B 2000, 62, 9896. (22) Giovannetti, G.; et al. Phys. ReV. B 2007, 76, 073103. (23) Henkelman, G.; Arnaldsson, A.; Jnsson, H. Comput. Mater. Sci. 2006, 36, 254.
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