Home
Search
Collections
Journals
About
Contact us
My IOPscience
The design of d-character Dirac cones based on graphene
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 385501 (http://iopscience.iop.org/0953-8984/26/38/385501) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 192.236.36.29 This content was downloaded on 14/06/2017 at 00:33 Please note that terms and conditions apply.
You may also be interested in: Aluminene as highly hole doped graphene C Kamal, Aparna Chakrabarti and Motohiko Ezawa Germanene: the germanium analogue of graphene A Acun, L Zhang, P Bampoulis et al. Conetronics in 2D Metal-Organic Frameworks: Double/Half Dirac Cones and Quantum Anomalous Hall Effect Menghao Wu, Zhijun Wang, Junwei Liu et al. Dirac fermions in blue-phosphorus Yuanchang Li and Xiaobin Chen Quasiparticle interference in unconventional 2D systems Lan Chen, Peng Cheng and Kehui Wu 1D graphene-like silicon systems: silicene nano-ribbons Paola De Padova, Paolo Perfetti, Bruno Olivieri et al. Topological phases in two-dimensional materials: a review Yafei Ren, Zhenhua Qiao and Qian Niu DFT and TB study of the geometry of hydrogen adsorbed on graphynes Hunpyo Lee, Jahyun Koo, Massimo Capone et al.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 385501 (4pp)
doi:10.1088/0953-8984/26/38/385501
The design of d -character Dirac cones based on graphene Yuanchang Li and Ying Fang National Center for Nanoscience and Technology, Beijing 100190, People’s Republic of China E-mail: [email protected] and [email protected] Received 13 June 2014, revised 28 July 2014 Accepted for publication 5 August 2014 Published 2 September 2014 Abstract
We introduce a new framework for designing a transition metal (TM) d-electrons dominant Dirac cone spectrum based on the hybridization between graphene and a modulated TM d impurity band. The obtained Dirac cone behaves like a ‘copy’ from graphene, insensitive to the TM coverage and order. First-principles calculations reveal such a system of Mn intercalated epitaxial graphene on SiC(0 0 0 1), dubbed manganosine. The robustness of the Dirac cone is discussed in terms of the possible imperfection of Mn atoms. The mechanism at work is expected to be rather general and may open the door to designing new d- or f -character Dirac systems. Keywords: d-character Dirac cone, graphene, DFT, intercalation (Some figures may appear in colour only in the online journal)
Dirac materials, characterized by a linear band dispersion, continue to be the hot topics in condensed matter physics from graphene [1] to topological insulators [2, 3]. Unlike the conventional matters with quadratic dispersions, the low-energy excitations in Dirac materials are described by the relativistic Dirac equation, behaving like massless fermions. Such a unique band structure leads to many fascinating properties, for example, the extremely high free carrier mobility and conductivity [1, 4], Klein tunnelling [5], anomalous half-integer quantum Hall effects [6] and fractional quantum Hall effect [7]. Apart from the celebrated Dirac cones in graphene and topological insulators, another two typical materials have also been found to exhibit their own Dirac cones, namely, tilted Dirac cones in a layered organic conductor α-(BEDT-TTF)2 I3 at high pressures [8, 9] and anisotropic Dirac fermions in SrMnBi2 [10, 11]. Above all, most of the theoretically predicted or experimentally confirmed Dirac materials are composed of the sp-electrons. Compared to the sp-character Dirac materials, not only the investigations but also the material species are limited for those based on d-electrons and the exploration [12, 13] has just started very recently. With respect to their sp-counterparts, d-character Dirac materials can have the magnetic moment, larger spin–orbit interaction and more significant electron correlation effect, which may intrinsically yield the novel physics like a spin-polarized Dirac cone, quantum spin Hall state and Mott effect, and so on. Thus, prediction 0953-8984/14/385501+04$33.00
of a new d-character Dirac material is desirable, especially, an experimentally potential material design method. In this paper, we introduce a proposal to design d-character Dirac materials through the hybridization between transition metal (TM) and graphene. The idea is to use the delocalized graphene π state connecting the dispersively distributed TM d orbitals. We first illustrate our notion by a schematic tight-binding calculation based on the TM-graphene system. Then by using the first-principles calculations, we reveal that Mn intercalated epitaxial graphene on SiC(0 0 0 1), dubbed manganosine, is such a system. Furthermore, we discuss the robustness of the Dirac cone spectrum from two viewpoints, i.e. an Mn intercalated coverage and distributed order. We show that Mn atoms prefer to distribute uniformly rather than cluster together. Moreover, the Dirac cone remains intact when the intercalated Mn coverage is lower than 1/3 monolayer, and almost insensitive to Mn order. The d-character Dirac cone system offers a new platform and opportunities for the investigations of unconventional electronic properties based on Dirac electrons. The Hamiltonian used to illustrate the design notion is (1) H = HG + HTM + Hpd † where HG =−t rr (cr† cr )+H.c., HTM = m r εm (dmr dmr ) mrr † and Hpd = m rr tpd (dmr cr )+H.c., respectively. The HG 1
© 2014 IOP Publishing Ltd
Printed in the UK
J. Phys.: Condens. Matter 26 (2014) 385501
Y Li and Y Fang
Figure 1. (a) A transition metal atom adsorption on the hexagonal center of the 2 × 2 graphene lattice. (b) Corresponding tight-binding band structures calculated with graphene hopping strength t = 2.5 eV and adatom on-site energy m = 0.2 eV. The adatom-graphene hopping tpd =0 (left) and tpd = 1.8 eV (right).
Figure 2. (a) Optimized geometries for the graphene/Mn/SiC(0 0 0 1) sandwich structure with the Mn intercalation coverage of 1/3 monolayer, dubbed manganosine. (b) Corresponding band structure and (c) local density of states from first-principles calculations.
describes the nearest-neighbor hopping of the graphene lattice, where cr† and cr are the creation and annihilation operators of carbon pz orbitals at the site r and t is the nearest-neighbor hopping parameter. The HTM describes the on-site energy of the intercalated TM d orbitals, where m is the orbital-dependent energy of the mth d orbital. The Hpd denotes the hybridization between TM d and C pz orbitals, which is generally demonstrated by two parameters of tpdπ and tpdσ [14]. The first-principles calculations are conducted by using the Vienna ab initio simulation package [15] with the local density approximation (LDA) [16]. The projector augmented wave [17] method is employed and the energy cut-off is set to 400 eV. The sandwiched structure is modeled by intercalating √ one √ Mn ◦atom between a 2×2 graphene overlayer and the 3× 3R30 reconstructed 6H -SiC. The SiC substrate consists of six SiC bilayers and the bottom three are fixed during the geometric optimization. The vacuum layer is larger than 10 Å. In figure 1, we show the schematic diagram of designing a d-character Dirac cone through the hybridization between graphene and TM. We consider a TM atom adsorption on the hexagonal center of the graphene honeycomb lattice with a very d orbitals splitting. For simplicity, only the dxy and dx 2 −y 2 orbitals with angular momentum m = ±2 are taken into account accurately while the other three d orbitals are assumed to lie far away in energy from these two. Note that this is highly reasonable provided that TM atom endures a C3v local environment as shown in figure 1(a). Consequently, only one parameter tpd is necessary to characterize the hybridization between graphene π and TM d states in the Hpd [14, 18]. Figure 1(b) gives the band structures without (left) and with (right) the pd coupling. Under the non-spin-split situation, the originally two-fold degenerate flat band (highlighted by the blue dot in the left panel),
contributed by TM dxy and dx 2 −y 2 orbitals, becomes highly dispersive through the pd hybridization. More importantly, two Dirac points (red circles in the right panel) emerge at the K point in the band after coupling. At no matter which point the Fermi level passes through, it will be a Dirac system in analogy to the graphene. Because the states between the two Dirac points originate from the TM d orbitals, the new Dirac system has to be characterized by the d-electrons unlike the pure p-electrons in graphene [19] or silicene [20]. This can open up the possibility of combining the strong correlation physics with those of Dirac cones. [21–24] It is worthwhile to mention that the crossing (green circle in the right panel) at the Γ point seems largely like a parabolic rather than linear. Following such a notion, we try to find an experimentally accessible system. Two preconditions should be considered. On the one hand, the TM atoms are required to distribute separately rather than cluster to avoid the direct coupling between them. On the other hand, a C3v local environment is maintained so as to allow the emergence of the two-fold degenerate flat band before coupling. And simultaneously, the states belonging to |m| = 0, 1 and 2 had better separate each other sufficiently in energy to realize the coupling as illustrated in figure 1(b). To this end, we select the TM as Mn and passivate it with SiC from the other side opposite to graphene. Figure 2(a) shows the optimized geometry. Hereafter we call such sandwich systems metallosine in analogy with metallocene for different TM species. Thus it is manganosine for Mn. The corresponding band structure and local density of states are plotted in figures 2(b) and (c), respectively. Obviously, manganosine forms a Dirac system characterized by Mn d-electrons. The Fermi level passes through the ‘upper’ Dirac point and thus the topmost valence band consists of dominant d orbitals; whereas 2
J. Phys.: Condens. Matter 26 (2014) 385501
Y Li and Y Fang
Figure 3. Configurations of the intercalated Mn atoms with (a) isolated distribution versus (b) paired Mn dimer.
the bottommost conduction band retains relatively more of the C p feature. Next, we turn to illustrate the robustness of the obtained Dirac cone spectrum. In the tight-binding model, there is no direct hopping between the neighboring Mn atoms. This requires the Mn atoms to exist in isolated form. As is well known, however, TM atoms on the extended aromatic carbon complexes such as fullerene, graphene and nanotube easily cluster owing to their relatively large bulk cohesive energy with respect to the small moving barrier [25–27]. Herein, not only is the Mn immobilization remarkably enhanced by the two-sided strong bonding, its movement is also heavily hindered kinetically due to the reduced space between the graphene and SiC. To further reveal this, we compare the energetics between two configurations, namely, an isolated Mn form and paired Mn dimers as shown in figure 3. We find the separately distributed configuration is about 3.0 eV in energy more favorable than that of the Mn dimer one. It is the dangling-bond state of the surface Si that provides the large driving force, thereby the good stability. This means no Mn dimer will appear unless all the surface Si dangling-bonds are saturated, corresponding to Mn intercalated coverage of 1/3 monolayer (ML)1 . Trapping a TM atom by the dangling-bond state was also used in other systems like graphene [28] and boron nitride [29]. In addition, we calculate the Mn intercalation energy2 at the 1/3 ML. The obtained value of 5.6 eV is even larger than the Mn bulk cohesive energy of 5.2 eV [30]. Thus, the notion demonstrated in figure 1(b) will work well and hence the robust Dirac cone spectrum. Below we consider the effect of Mn intercalated coverage and distributed order.‘First, we discuss the coverage dependence. We remove one Mn atom from every 2 × 2 supercell as shown in the left panel of figure 4(a), and now the Mn coverage is reduced to 3/12 ML. It is obvious that the Dirac cone remains intact at K point as demonstrated in the right panel of figure 4(a). In the calculation, we have passivated the three Si dangling-bonds around Mn vacancy by hydrogen atoms to eliminate the defect states. These states, even if not passivated, will have no intrinsic effect on the presence of the Dirac cone, except that they will shift the position of the system Fermi level. On the other hand, the d-character Dirac cone spectrum arises from the pd coupling and the graphene Dirac cone is the base, thereby in principle insensitive to the Mn order in the intercalated layer. Under the Slater– Koster approximation [14], the Slater–Koster matrix element is
Figure 4. Robustness of the d-character Dirac cone. (a) Missing 1/4 Mn atom geometry and corresponding band structure. (b) Two Mn atoms missing out of a 2 × 3 superlattice and corresponding electronic structure. Note that the intercalated Mn layer does not form any unique lattice now.
invariant with the inversion operation for pz coupling with dxy and dx 2 −y 2 orbitals, which indicates the interaction is graphene AB symmetry preserved, hence the intact Dirac cone of graphene. It is thus not the consequence of a special Mn lattice although the Mn indeed forms a hexagonal lattice at 1/3 ML. To progress our study one step further, we show the calculated results for a defective 2 × 3 supercell with only 4 metal atoms in figure 4(b). Since the symmetry is greatly reduced here (the hexagonal symmetry is removed in the Mn sublayer), density of states is used to assess the linearly dispersive Dirac cone spectrum. This shows strongly that the formation of the Dirac cone has nothing to do with the lattice symmetry in the intercalated metal layer. Particularly, it does not require the existence of a hexagonal lattice congruent to that of graphene. Our above demonstrations reinforce that the d-character Dirac cone is robust against the degree of Mn order and coverage. Finally, we discuss the experimental feasibility of the metallosine system. We find the experiment of reference [31] has realized the intercalation of atomic Mn or Ni layer into the interface between graphene and SiC. The large nuclear can penetrate the compact graphene honeycomb lattice through the defects under the high temperature [32]. Although the direct image of the Mn layer pattern was hardly obtained, the experiment confirms that Mn is definitely a single layer and distributes individually. Because of the contrast due to the Pauli repulsion rather than the tunnelling current, we expect to see a better and unambiguous Mn pattern using the noncontact atomic force microscopy technique which has achieved some success in detecting and identifying the atomic structure of bad conducting √ √ materials. Another important issue is the adopted 3 × 3R30◦ reconstructed model of graphene on
1
The monolayer is defined as the atom number ratio of Mn and surface Si. The Mn intercalation energy with epitaxial graphene on SiC(0 0 0 1) is defined as: E = EMn + EG/SiC − EG/Mn/SiC , where EMn , EG/SiC and EG/Mn/SiC are the total energies of isolate Mn, G/SiC, and the intercalated sandwich structure, respectively. 2
3
J. Phys.: Condens. Matter 26 (2014) 385501
Y Li and Y Fang
√ √ SiC. In fact, it is a 6 3 × 6 3R30◦ reconstruction accommodating a 13 × 13 graphene layer. In that case, Mn will be no longer at the hexagonal center exactly with respect to graphene, thus inducing the corrugation. Alternatively, the corrugation may be generated by the uneven distribution of Mn atoms when the coverage is much lower than 1/3 ML. Nevertheless, we expect the Dirac cone would be preserved largely but with the Dirac point shifted away from the high symmetry line of the Brillouin zone. In summary, the notion of designing d-character Dirac cone spectra based on graphene is verified in manganosine by the band structure calculations. The Dirac cone is originated from the coupling between the TM d orbitals and graphene π orbitals, insensitive to the Mn coverage and distribution. We call for further experimental progress in this field.
[7] Apalkov V M and Chakraborty T 2006 Phys. Rev. Lett. 97 126801 [8] Katayama S, Kobayashi A and Suzumura Y 2006 J. Phys. Soc. Japan 75 054705 [9] Himura T, Morinari T and Tohyama T 2011 J. Phys.: Condens. Matter 23 464202 [10] Park J et al 2011 Phys. Rev. Lett. 107 126402 [11] Farhan M A, Lee G and Shim J H 2014 J. Phys.: Condens. Matter 26 042201 [12] Li Y C, Chen P C, Zhou G, Li J, Wu J, Gu B-L, Zhang S B and Duan W H 2012 Phys. Rev. Lett. 109 206802 [13] Miyamoto K, Kimura A, Kuroda K, Okuda T, Shimada K, Namatame H, Taniguchi M and Donath M 2012 Phys. Rev. Lett. 108 066808 [14] Slater J and Koster G 1954 Phys. Rev. 94 1498 [15] Kresse G and Furthm¨uller J 1996 Phys. Rev. B 54 11169 [16] Ceperley D M and Alder B J 1980 Phys. Rev. Lett. 45 566 [17] Bl¨ochl P E 1994 Phys. Rev. B 50 17953 Kresse G and Joubert D 1999 Phys. Rev. B 59 1758 [18] Li Y C et al 2013 Phys. Rev. B 87 245127 [19] Wallace P R 1947 Phys. Rev. 71 622 [20] Aufray B, Kara A, Vizzini S, Oughaddou H, L´eandri C, Ealet B and Le Lay G 2010 Appl. Phys. Lett. 96 183102 [21] Jafari S A 2009 Eur. Phys. J. B 68 537 [22] Ebrahimkhas M and Jafari S A 2012 Eur. Phys. Lett. 98 27009 [23] Jafari S A and Baskaran G 2012 J. Phys.: Condens. Matter 24 095601 [24] Jafari S A 2012 J. Phys.: Condens. Matter 24 305601 [25] Yang S Y, Yoon M, Wang E G and Zhang Z Y 2008 J. Chem. Phys. 129 134707 [26] Reunchan P and Jhi S-H 2011 Appl. Phys. Lett. 98 093103 [27] Krasnov P O, Ding F, Singh A K and Yakobson B I 2007 J. Phys. Chem. C 111 17977 [28] Krasheninnikov A V, Lehtinen P O, Foster A S, Pyykko P and Nieminen R M 2009 Phys. Rev. Lett. 102 126807 [29] Lu Y, Zuo X, Feng M and Zhou T G 2013 J. Appl. Phys. 113 17C304 [30] Philipsen P H T and Baerends E J 1996 Phys. Rev. B 54 5326 [31] Gao T et al 2012 ACS Nano 6 6562 [32] Li Y C, Zhou G, Li J, Wu J, Gu B-L and Duan W H 2011 J. Phys. Chem. C 115 23992
Acknowledgments
We thank P C Chen, W H Duan and S B Zhang for helpful discussions. We acknowledge the support of the National Natural Science Foundation of China (Grant Nos. 11304053). References [1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V and Firsov A A 2004 Science 306 666-9 [2] Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 226801 [3] Ko¨nig M, Wiedmann S, Brune C, Roth A, Buhmann H, Molenkamp L W, Qi X L and Zhang S C 2007 Science 318 766 [4] Bolotin K I, Sikes K J, Jiang Z, Klima M, Fudenberg G, Hone J, Kim P and Stormer H L 2008 Solid State Commun. 146 351 [5] Katsnelson M I, Novoselov K S and Geim A K 2006 Nat. Phys. 2 620 [6] Zhang Y B, Tan Y W, Stormer H L and Kim P 2005 Nature 438 201
4
Search
Collections
Journals
About
Contact us
My IOPscience
The design of d-character Dirac cones based on graphene
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 385501 (http://iopscience.iop.org/0953-8984/26/38/385501) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 192.236.36.29 This content was downloaded on 14/06/2017 at 00:33 Please note that terms and conditions apply.
You may also be interested in: Aluminene as highly hole doped graphene C Kamal, Aparna Chakrabarti and Motohiko Ezawa Germanene: the germanium analogue of graphene A Acun, L Zhang, P Bampoulis et al. Conetronics in 2D Metal-Organic Frameworks: Double/Half Dirac Cones and Quantum Anomalous Hall Effect Menghao Wu, Zhijun Wang, Junwei Liu et al. Dirac fermions in blue-phosphorus Yuanchang Li and Xiaobin Chen Quasiparticle interference in unconventional 2D systems Lan Chen, Peng Cheng and Kehui Wu 1D graphene-like silicon systems: silicene nano-ribbons Paola De Padova, Paolo Perfetti, Bruno Olivieri et al. Topological phases in two-dimensional materials: a review Yafei Ren, Zhenhua Qiao and Qian Niu DFT and TB study of the geometry of hydrogen adsorbed on graphynes Hunpyo Lee, Jahyun Koo, Massimo Capone et al.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 385501 (4pp)
doi:10.1088/0953-8984/26/38/385501
The design of d -character Dirac cones based on graphene Yuanchang Li and Ying Fang National Center for Nanoscience and Technology, Beijing 100190, People’s Republic of China E-mail: [email protected] and [email protected] Received 13 June 2014, revised 28 July 2014 Accepted for publication 5 August 2014 Published 2 September 2014 Abstract
We introduce a new framework for designing a transition metal (TM) d-electrons dominant Dirac cone spectrum based on the hybridization between graphene and a modulated TM d impurity band. The obtained Dirac cone behaves like a ‘copy’ from graphene, insensitive to the TM coverage and order. First-principles calculations reveal such a system of Mn intercalated epitaxial graphene on SiC(0 0 0 1), dubbed manganosine. The robustness of the Dirac cone is discussed in terms of the possible imperfection of Mn atoms. The mechanism at work is expected to be rather general and may open the door to designing new d- or f -character Dirac systems. Keywords: d-character Dirac cone, graphene, DFT, intercalation (Some figures may appear in colour only in the online journal)
Dirac materials, characterized by a linear band dispersion, continue to be the hot topics in condensed matter physics from graphene [1] to topological insulators [2, 3]. Unlike the conventional matters with quadratic dispersions, the low-energy excitations in Dirac materials are described by the relativistic Dirac equation, behaving like massless fermions. Such a unique band structure leads to many fascinating properties, for example, the extremely high free carrier mobility and conductivity [1, 4], Klein tunnelling [5], anomalous half-integer quantum Hall effects [6] and fractional quantum Hall effect [7]. Apart from the celebrated Dirac cones in graphene and topological insulators, another two typical materials have also been found to exhibit their own Dirac cones, namely, tilted Dirac cones in a layered organic conductor α-(BEDT-TTF)2 I3 at high pressures [8, 9] and anisotropic Dirac fermions in SrMnBi2 [10, 11]. Above all, most of the theoretically predicted or experimentally confirmed Dirac materials are composed of the sp-electrons. Compared to the sp-character Dirac materials, not only the investigations but also the material species are limited for those based on d-electrons and the exploration [12, 13] has just started very recently. With respect to their sp-counterparts, d-character Dirac materials can have the magnetic moment, larger spin–orbit interaction and more significant electron correlation effect, which may intrinsically yield the novel physics like a spin-polarized Dirac cone, quantum spin Hall state and Mott effect, and so on. Thus, prediction 0953-8984/14/385501+04$33.00
of a new d-character Dirac material is desirable, especially, an experimentally potential material design method. In this paper, we introduce a proposal to design d-character Dirac materials through the hybridization between transition metal (TM) and graphene. The idea is to use the delocalized graphene π state connecting the dispersively distributed TM d orbitals. We first illustrate our notion by a schematic tight-binding calculation based on the TM-graphene system. Then by using the first-principles calculations, we reveal that Mn intercalated epitaxial graphene on SiC(0 0 0 1), dubbed manganosine, is such a system. Furthermore, we discuss the robustness of the Dirac cone spectrum from two viewpoints, i.e. an Mn intercalated coverage and distributed order. We show that Mn atoms prefer to distribute uniformly rather than cluster together. Moreover, the Dirac cone remains intact when the intercalated Mn coverage is lower than 1/3 monolayer, and almost insensitive to Mn order. The d-character Dirac cone system offers a new platform and opportunities for the investigations of unconventional electronic properties based on Dirac electrons. The Hamiltonian used to illustrate the design notion is (1) H = HG + HTM + Hpd † where HG =−t rr (cr† cr )+H.c., HTM = m r εm (dmr dmr ) mrr † and Hpd = m rr tpd (dmr cr )+H.c., respectively. The HG 1
© 2014 IOP Publishing Ltd
Printed in the UK
J. Phys.: Condens. Matter 26 (2014) 385501
Y Li and Y Fang
Figure 1. (a) A transition metal atom adsorption on the hexagonal center of the 2 × 2 graphene lattice. (b) Corresponding tight-binding band structures calculated with graphene hopping strength t = 2.5 eV and adatom on-site energy m = 0.2 eV. The adatom-graphene hopping tpd =0 (left) and tpd = 1.8 eV (right).
Figure 2. (a) Optimized geometries for the graphene/Mn/SiC(0 0 0 1) sandwich structure with the Mn intercalation coverage of 1/3 monolayer, dubbed manganosine. (b) Corresponding band structure and (c) local density of states from first-principles calculations.
describes the nearest-neighbor hopping of the graphene lattice, where cr† and cr are the creation and annihilation operators of carbon pz orbitals at the site r and t is the nearest-neighbor hopping parameter. The HTM describes the on-site energy of the intercalated TM d orbitals, where m is the orbital-dependent energy of the mth d orbital. The Hpd denotes the hybridization between TM d and C pz orbitals, which is generally demonstrated by two parameters of tpdπ and tpdσ [14]. The first-principles calculations are conducted by using the Vienna ab initio simulation package [15] with the local density approximation (LDA) [16]. The projector augmented wave [17] method is employed and the energy cut-off is set to 400 eV. The sandwiched structure is modeled by intercalating √ one √ Mn ◦atom between a 2×2 graphene overlayer and the 3× 3R30 reconstructed 6H -SiC. The SiC substrate consists of six SiC bilayers and the bottom three are fixed during the geometric optimization. The vacuum layer is larger than 10 Å. In figure 1, we show the schematic diagram of designing a d-character Dirac cone through the hybridization between graphene and TM. We consider a TM atom adsorption on the hexagonal center of the graphene honeycomb lattice with a very d orbitals splitting. For simplicity, only the dxy and dx 2 −y 2 orbitals with angular momentum m = ±2 are taken into account accurately while the other three d orbitals are assumed to lie far away in energy from these two. Note that this is highly reasonable provided that TM atom endures a C3v local environment as shown in figure 1(a). Consequently, only one parameter tpd is necessary to characterize the hybridization between graphene π and TM d states in the Hpd [14, 18]. Figure 1(b) gives the band structures without (left) and with (right) the pd coupling. Under the non-spin-split situation, the originally two-fold degenerate flat band (highlighted by the blue dot in the left panel),
contributed by TM dxy and dx 2 −y 2 orbitals, becomes highly dispersive through the pd hybridization. More importantly, two Dirac points (red circles in the right panel) emerge at the K point in the band after coupling. At no matter which point the Fermi level passes through, it will be a Dirac system in analogy to the graphene. Because the states between the two Dirac points originate from the TM d orbitals, the new Dirac system has to be characterized by the d-electrons unlike the pure p-electrons in graphene [19] or silicene [20]. This can open up the possibility of combining the strong correlation physics with those of Dirac cones. [21–24] It is worthwhile to mention that the crossing (green circle in the right panel) at the Γ point seems largely like a parabolic rather than linear. Following such a notion, we try to find an experimentally accessible system. Two preconditions should be considered. On the one hand, the TM atoms are required to distribute separately rather than cluster to avoid the direct coupling between them. On the other hand, a C3v local environment is maintained so as to allow the emergence of the two-fold degenerate flat band before coupling. And simultaneously, the states belonging to |m| = 0, 1 and 2 had better separate each other sufficiently in energy to realize the coupling as illustrated in figure 1(b). To this end, we select the TM as Mn and passivate it with SiC from the other side opposite to graphene. Figure 2(a) shows the optimized geometry. Hereafter we call such sandwich systems metallosine in analogy with metallocene for different TM species. Thus it is manganosine for Mn. The corresponding band structure and local density of states are plotted in figures 2(b) and (c), respectively. Obviously, manganosine forms a Dirac system characterized by Mn d-electrons. The Fermi level passes through the ‘upper’ Dirac point and thus the topmost valence band consists of dominant d orbitals; whereas 2
J. Phys.: Condens. Matter 26 (2014) 385501
Y Li and Y Fang
Figure 3. Configurations of the intercalated Mn atoms with (a) isolated distribution versus (b) paired Mn dimer.
the bottommost conduction band retains relatively more of the C p feature. Next, we turn to illustrate the robustness of the obtained Dirac cone spectrum. In the tight-binding model, there is no direct hopping between the neighboring Mn atoms. This requires the Mn atoms to exist in isolated form. As is well known, however, TM atoms on the extended aromatic carbon complexes such as fullerene, graphene and nanotube easily cluster owing to their relatively large bulk cohesive energy with respect to the small moving barrier [25–27]. Herein, not only is the Mn immobilization remarkably enhanced by the two-sided strong bonding, its movement is also heavily hindered kinetically due to the reduced space between the graphene and SiC. To further reveal this, we compare the energetics between two configurations, namely, an isolated Mn form and paired Mn dimers as shown in figure 3. We find the separately distributed configuration is about 3.0 eV in energy more favorable than that of the Mn dimer one. It is the dangling-bond state of the surface Si that provides the large driving force, thereby the good stability. This means no Mn dimer will appear unless all the surface Si dangling-bonds are saturated, corresponding to Mn intercalated coverage of 1/3 monolayer (ML)1 . Trapping a TM atom by the dangling-bond state was also used in other systems like graphene [28] and boron nitride [29]. In addition, we calculate the Mn intercalation energy2 at the 1/3 ML. The obtained value of 5.6 eV is even larger than the Mn bulk cohesive energy of 5.2 eV [30]. Thus, the notion demonstrated in figure 1(b) will work well and hence the robust Dirac cone spectrum. Below we consider the effect of Mn intercalated coverage and distributed order.‘First, we discuss the coverage dependence. We remove one Mn atom from every 2 × 2 supercell as shown in the left panel of figure 4(a), and now the Mn coverage is reduced to 3/12 ML. It is obvious that the Dirac cone remains intact at K point as demonstrated in the right panel of figure 4(a). In the calculation, we have passivated the three Si dangling-bonds around Mn vacancy by hydrogen atoms to eliminate the defect states. These states, even if not passivated, will have no intrinsic effect on the presence of the Dirac cone, except that they will shift the position of the system Fermi level. On the other hand, the d-character Dirac cone spectrum arises from the pd coupling and the graphene Dirac cone is the base, thereby in principle insensitive to the Mn order in the intercalated layer. Under the Slater– Koster approximation [14], the Slater–Koster matrix element is
Figure 4. Robustness of the d-character Dirac cone. (a) Missing 1/4 Mn atom geometry and corresponding band structure. (b) Two Mn atoms missing out of a 2 × 3 superlattice and corresponding electronic structure. Note that the intercalated Mn layer does not form any unique lattice now.
invariant with the inversion operation for pz coupling with dxy and dx 2 −y 2 orbitals, which indicates the interaction is graphene AB symmetry preserved, hence the intact Dirac cone of graphene. It is thus not the consequence of a special Mn lattice although the Mn indeed forms a hexagonal lattice at 1/3 ML. To progress our study one step further, we show the calculated results for a defective 2 × 3 supercell with only 4 metal atoms in figure 4(b). Since the symmetry is greatly reduced here (the hexagonal symmetry is removed in the Mn sublayer), density of states is used to assess the linearly dispersive Dirac cone spectrum. This shows strongly that the formation of the Dirac cone has nothing to do with the lattice symmetry in the intercalated metal layer. Particularly, it does not require the existence of a hexagonal lattice congruent to that of graphene. Our above demonstrations reinforce that the d-character Dirac cone is robust against the degree of Mn order and coverage. Finally, we discuss the experimental feasibility of the metallosine system. We find the experiment of reference [31] has realized the intercalation of atomic Mn or Ni layer into the interface between graphene and SiC. The large nuclear can penetrate the compact graphene honeycomb lattice through the defects under the high temperature [32]. Although the direct image of the Mn layer pattern was hardly obtained, the experiment confirms that Mn is definitely a single layer and distributes individually. Because of the contrast due to the Pauli repulsion rather than the tunnelling current, we expect to see a better and unambiguous Mn pattern using the noncontact atomic force microscopy technique which has achieved some success in detecting and identifying the atomic structure of bad conducting √ √ materials. Another important issue is the adopted 3 × 3R30◦ reconstructed model of graphene on
1
The monolayer is defined as the atom number ratio of Mn and surface Si. The Mn intercalation energy with epitaxial graphene on SiC(0 0 0 1) is defined as: E = EMn + EG/SiC − EG/Mn/SiC , where EMn , EG/SiC and EG/Mn/SiC are the total energies of isolate Mn, G/SiC, and the intercalated sandwich structure, respectively. 2
3
J. Phys.: Condens. Matter 26 (2014) 385501
Y Li and Y Fang
√ √ SiC. In fact, it is a 6 3 × 6 3R30◦ reconstruction accommodating a 13 × 13 graphene layer. In that case, Mn will be no longer at the hexagonal center exactly with respect to graphene, thus inducing the corrugation. Alternatively, the corrugation may be generated by the uneven distribution of Mn atoms when the coverage is much lower than 1/3 ML. Nevertheless, we expect the Dirac cone would be preserved largely but with the Dirac point shifted away from the high symmetry line of the Brillouin zone. In summary, the notion of designing d-character Dirac cone spectra based on graphene is verified in manganosine by the band structure calculations. The Dirac cone is originated from the coupling between the TM d orbitals and graphene π orbitals, insensitive to the Mn coverage and distribution. We call for further experimental progress in this field.
[7] Apalkov V M and Chakraborty T 2006 Phys. Rev. Lett. 97 126801 [8] Katayama S, Kobayashi A and Suzumura Y 2006 J. Phys. Soc. Japan 75 054705 [9] Himura T, Morinari T and Tohyama T 2011 J. Phys.: Condens. Matter 23 464202 [10] Park J et al 2011 Phys. Rev. Lett. 107 126402 [11] Farhan M A, Lee G and Shim J H 2014 J. Phys.: Condens. Matter 26 042201 [12] Li Y C, Chen P C, Zhou G, Li J, Wu J, Gu B-L, Zhang S B and Duan W H 2012 Phys. Rev. Lett. 109 206802 [13] Miyamoto K, Kimura A, Kuroda K, Okuda T, Shimada K, Namatame H, Taniguchi M and Donath M 2012 Phys. Rev. Lett. 108 066808 [14] Slater J and Koster G 1954 Phys. Rev. 94 1498 [15] Kresse G and Furthm¨uller J 1996 Phys. Rev. B 54 11169 [16] Ceperley D M and Alder B J 1980 Phys. Rev. Lett. 45 566 [17] Bl¨ochl P E 1994 Phys. Rev. B 50 17953 Kresse G and Joubert D 1999 Phys. Rev. B 59 1758 [18] Li Y C et al 2013 Phys. Rev. B 87 245127 [19] Wallace P R 1947 Phys. Rev. 71 622 [20] Aufray B, Kara A, Vizzini S, Oughaddou H, L´eandri C, Ealet B and Le Lay G 2010 Appl. Phys. Lett. 96 183102 [21] Jafari S A 2009 Eur. Phys. J. B 68 537 [22] Ebrahimkhas M and Jafari S A 2012 Eur. Phys. Lett. 98 27009 [23] Jafari S A and Baskaran G 2012 J. Phys.: Condens. Matter 24 095601 [24] Jafari S A 2012 J. Phys.: Condens. Matter 24 305601 [25] Yang S Y, Yoon M, Wang E G and Zhang Z Y 2008 J. Chem. Phys. 129 134707 [26] Reunchan P and Jhi S-H 2011 Appl. Phys. Lett. 98 093103 [27] Krasnov P O, Ding F, Singh A K and Yakobson B I 2007 J. Phys. Chem. C 111 17977 [28] Krasheninnikov A V, Lehtinen P O, Foster A S, Pyykko P and Nieminen R M 2009 Phys. Rev. Lett. 102 126807 [29] Lu Y, Zuo X, Feng M and Zhou T G 2013 J. Appl. Phys. 113 17C304 [30] Philipsen P H T and Baerends E J 1996 Phys. Rev. B 54 5326 [31] Gao T et al 2012 ACS Nano 6 6562 [32] Li Y C, Zhou G, Li J, Wu J, Gu B-L and Duan W H 2011 J. Phys. Chem. C 115 23992
Acknowledgments
We thank P C Chen, W H Duan and S B Zhang for helpful discussions. We acknowledge the support of the National Natural Science Foundation of China (Grant Nos. 11304053). References [1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V and Firsov A A 2004 Science 306 666-9 [2] Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 226801 [3] Ko¨nig M, Wiedmann S, Brune C, Roth A, Buhmann H, Molenkamp L W, Qi X L and Zhang S C 2007 Science 318 766 [4] Bolotin K I, Sikes K J, Jiang Z, Klima M, Fudenberg G, Hone J, Kim P and Stormer H L 2008 Solid State Commun. 146 351 [5] Katsnelson M I, Novoselov K S and Geim A K 2006 Nat. Phys. 2 620 [6] Zhang Y B, Tan Y W, Stormer H L and Kim P 2005 Nature 438 201
4
