Abstract
Using first principles calculations, we investigate the electronic structures of semihydrogenated BC_{3}, BC_{5}, BC_{7}, and Bdoped graphone sheets. We find that all the semihydrogenated boroncarbon sheets exhibit halfmetallic behaviors. The magnetism originates from the nonbonding p_{z }orbitals of carbon atoms, which cause the flat bands to satisfy the Stoner criterion. On the other hand, boron atoms weaken the magnetic moments of nearby carbon atoms and act as holes doped in the sheets. It induces the down shift of the Fermi level and the halfmetallicity in semihydrogenated sheets. Our studies demonstrate that the semihydrogenation is an effective route to achieve halfmetallicity in the boroncarbon systems.
Introduction
Since the discovery of graphene [1], twodimensional (2D) nanosheet structures have attracted lots of research in the condensed matter physics. Graphene is a monolayer carbon hexagonal sheet, in which both α and β sites of the hexagon are occupied by carbon atoms [2]. Owing to the equivalence of two carbon sites, the graphene sheet is a semimetal with the massless Diraclike electronic excitation [3]. When the graphene sheet connects with Si monolayer, this Diraclike electronic structure is maintained [4]. While the graphene sheet is epitaxially grown on the SiC substrate, two carbon sites become inequivalent and a band gap is opened [5]. Recently, several chemical methods have been reported for the highyield production of graphene [6,7]. The graphenebased transistors also develop fast, and those carbonbased nanomaterials are considered as candidates for the postsilicon electronics [8,9].
Since the prefect graphene sheet is a semimetal with zero band gap [2], the hydrogenation is used as an effective way for the chemical functionalization of graphene [10]. The fully hydrogenated graphene sheet, called as graphane, is a semiconductor with a band gap of 3.5 eV [1114]. In the experiments, by exposing graphene under hydrogen plasma surroundings, the graphane sheet has already been synthesized [15]. When some hydrogen atoms are removed from the graphane sheet, the magnetism will appear in those hydrogen vacancies [16]. The large area of hydrogen vacancies can even form the graphene nanoroads or quantum dots in the graphane sheets [17,18]. Under the external electric field, hydrogen atoms are pushed away from one side of the graphane sheet, while the others are still retained at the other side, which forms the semihydrogenated graphene sheet [19]. The previous theoretical study has shown that this semihydrogenated graphene, which is referred to graphone, is a ferromagnetic semiconductor with a small band gap [20]. Using the angleresolved photoemission spectroscopy, researchers have found that the patterned oneside hydrogen adsorption can induce a band gap for the graphene sheet on the Ir (111) surface [21].
Besides the graphene sheet, the semihydrogenation can also tune the properties of other graphenelike 2 D sheets. For example, the semihydrogenated BN sheet becomes a ferromagnetic metal [22], and the semihydrogenated SiC sheet becomes an antiferromagnetic semiconductor [23]. By coevaporation of boron and carbon atoms, hexagonallike boron carbides are formed with the boron content being less than 50% [24]. Moreover, the graphenelike BC_{3 }sheet can be grown on the NbB_{2 }(0001) surface by an epitaxial method [25]. In our previous study, we have found that the fully hydrogenation leads to the semiconductormetal transitions in the BC_{3}, BC_{5}, and BC_{7 }sheets [26]. Since the semihydrogenation can cause spin polarization in the 2 D sheets and the ordered boroncarbon compounds have rich electronic properties, the semihydrogenated boroncarbon sheets will be expected to exhibit interesting electronic and magnetic behaviors. It is also promising for the research on the Bdoped effects on the semihydrogenated sheets. Thus, we perform first principles calculations to investigate the electronic structures of semihydrogenated BC_{3 }(HBC_{3}), BC_{5 }(HBC_{5}), BC_{7 }(HBC_{7}), and Bdoped graphone sheets in this article.
Calculation details
First principles calculations are performed by the VASP code [27]. The approach is based on an iterative solution of the KohnSham equation of the density function theory in a planewave set with the projectoraugmented wave pseudopotentials. In our calculations, the PerdewBurkeErnzerhof (PBE) exchangecorrelation (XC) functional of the generalized gradient approximation is adopted. We set the planewave cutoff energy to be 520 eV and the convergence of the force on each atom to be less than 0.01 eV/Å. The optimizations of the lattice constants and the atomic coordinates are made by the minimization of the total energy. The supercells are used to simulate the isolated sheet and the sheets are separated by larger than 12 Å to avoid interlayer interactions. The MonkhorstPack scheme is used for sampling the Brillouin zone. In the calculations, the structures are fully relaxed with a mesh of 5 × 5 × 1, and the mesh of k space is increased to 7 × 7 × 1, in the static calculations. In the spinpolarized calculations, both the ferromagnetic (FM) and antiferromagnetic (AFM) states are constructed for the initial magnetic structures of the HBC_{x }(x = 3, 5, 7) sheets. However, the artificial AFM state always converges to the FM state after optimization.
Results and discussion
Figure 1 shows the structures of the graphone and HBC_{3 }sheets. In the graphone sheet, hydrogen atoms only bond with the carbon atoms at β sites (C_{β}), not the carbon atoms at α sites (C_{α}). After semihydrogenation, the lattice constant of graphone is increased, which is 2.75% larger than that of graphene. The calculated CC and CH bond lengths are 1.50 and 1.16 Å, respectively, which agree well with the previous study [20]. Owing to the inequivalence of C_{α }and C_{β }atoms, graphone is a semiconductor. As shown in Figure 1c, it has an indirect band gap of 0.48 eV, which is also in good accordance with the results by Zhou et al. [20]. In the HBC_{3 }sheet, only the C_{β }atoms are bonding with hydrogen atoms, since under normal chemical potential, the hydrogen atoms prefer to bonding with carbon atoms in the BC_{3 }sheet [26]. We have also calculated the conformation in which all the C_{β }and B_{β }atoms bond with hydrogen atoms. The binding energy of this conformation is  1.40 eV/H, which is 0.13 eV/H less stable than the HBC_{3 }sheet shown in Figure 1b. The calculated BC, CC, and CH bond lengths of the HBC_{3 }sheet are 1.53, 1.49, and 1.14 Å, respectively, and the lattice constant is 6.59% larger than that of graphene. Different from graphone, the CH bonds tilt to the nearby boron atoms in the HBC_{3 }sheet. These tilting CH bonds, together with the elongated lattice constant, decrease the repulsion between the hydrogen atoms and lead to a high binding energy of  1.53 eV/H for the HBC_{3 }sheet.
Figure 1. The structures and energy bands of semihydrogenated sheets. (a,c) the graphone and (b,d) the HBC_{3 }sheets. The calculated units are delineated by dotted lines in (a,b). The Fermi level is indicated as the line at E = 0 eV.
The band structure of the HBC_{3 }sheet is shown in Figure 1d. Different from the semiconducting graphone, the HBC_{3 }sheet exhibits a halfmetallic character. There are two at bands crossing the Fermi level for the spinup electrons. On the other hand, for the spindown electrons, it opens a band gap of 1.76 eV. The halfmetal gap, defined as the difference between the Fermi level and topmost occupied spindown band, is 1.18 eV for the HBC_{3 }sheet. We have also checked the halfmetallicity of the HBC_{3 }sheet with different XC functionals. Figure 2 displays the calculated densities of states (DOSs) by the CeperlyAlder functional form of the local density approximation and the hybrid XC functional of HeydScuseriaErnzerhof. Both calculations confirm the halfmetallic behavior of the HBC_{3 }sheet.
Figure 2. The electronic structures of the HBC_{3 }sheet. (a) The spin density distribution, (b) the total and partial DOSs, (c) the total DOS with different XC functionals of the HBC_{3 }sheet. The Fermi level is indicated as the line at E = 0 eV.
In order to gain more insight into the halfmetallicity, we plot the spin density distribution and partial DOSs of the HBC_{3 }sheet as shown in Figure 2. The figure indicates that the magnetism is mainly from the p_{z }orbitals of C_{α }atoms. The C_{α }atom is not hydrogenated in the HBC_{3 }sheet. It has an unpaired pelectron localized in the nonbonding p_{z }orbital, which contributes to the flat bands near the Fermi level. The at bands lead to large DOSs flat the Fermi level, which are beneficial to satisfy the Stoner criterion, IN(E_{F}) > 1 and induce the ferromagnetism in the semihydrogenated sheet [28]. For the graphone sheet, there are also flat bands near the Fermi level as shown in Figure 1c, which cause spin polarization of those unhydrogenated C_{α }atoms [20]. However, owing to the existence of boron atoms, the magnetism of HBC_{3 }sheet is weakened. For the same calculated units in Figure 1, the graphone sheet has a total magnetic moment of 4μ_{B}, while the HBC_{3 }sheet has only 1μ_{B}. Using the Bader analysis [29], we obtain that the boron atom transfers 1.27 e to the surrounding C_{α }atoms. Each C_{α }atom contributes 0.79μ_{B }in the graphone sheet, while in the HBC_{3 }sheet it decreases to 0.31μ_{B }because of the charge transfers from nearby boron atoms. Considering that the boron element is one electron less than the carbon one, the boron atoms behave like holes doped in the semihydrogenated sheets. It leads to the down shift of the Fermi level, which crosses the spinup bands. Consequently, the HBC_{3 }sheet becomes a halfmetal.
More interestingly, the halfmetallicity appears not only in the HBC_{3 }sheet, but also in other semihydrogenated boroncarbon sheets. Figure 3 shows the electronic structures of the HBC_{5 }and HBC_{7 }sheets. The magnetism is also mainly localized at the C_{α }atoms of those sheets. In the HBC_{5 }sheet, the C_{α }atom has a magnetic moment of 0.31μ_{B}. On the other hand, in the HBC_{7 }sheet, the atomic magnetic moments become 0.34 and 0.72μ_{B}. The two values correspond, respectively, to the C_{α }atoms with and without neighboring boron atoms. Both the HBC_{5 }and HBC_{7 }sheets are halfmetals, the halfmetal gaps of which are 1.12 and 1.50 eV, respectively. To model the Bdoped graphone sheet, one C atom is replaced by the B atom in a 4 × 4 unit cell, yielding a Bdoped concentration of 3.125%. Figure 4a displays that the doped boron atom weakens the magnetism of three neighboring C_{α }atoms. Comparing with the prefect graphone sheet, the total magnetic moment is reduced by 2μ_{B }after boron doping. The Bdoped graphone sheet also presents a halfmetallic behavior as shown in Figure 4b.
Figure 3. The electronic structures of the HBC_{5 }and HBC_{7 }sheets. (Color online) The structures, energy bands, and DOSs of (a,c,e) the HBC_{5 }and (b,d,f) the HBC_{7 }sheets. The calculated units are delineated by dotted lines, and the spin density distributions are shown in (a,b). The Fermi level is indicated as the line at E = 0 eV.
Figure 4. The electronic structures of the Bdoped graphone sheet. (Color online) (a) The structures and (b) DOSs of the Bdoped graphone sheets. The calculated units are delineated by dotted lines and the spin density distributions are shown in (a). The Fermi level is indicated as the line at E = 0 eV.
Table 1 listed the calculated results. All the semihydrogenated boroncarbon sheets are halfmetals. We find that the different boron contents have two effects on the stabilities of halfmetallic sheets: on the one hand, with the increase of the boron contents, the binding energies increase because of the decreased repulsion between hydrogen atoms with the elongated lattice constants. On the other hand, the boron atoms weaken the nearby C_{α }magnetic moments, which decreases the pp interactions between them. Thus, the energy gain of the ferromagnetic state decreases with the increase of the boron contents. Comparing with the normal room temperature (25 meV), the halfmetallicities of the HBC_{3}, HBC_{5}, and HBC_{7 }sheets are still stable.
Table 1. The binding energy , the increasing rate of lattice constant relative to grapheme ϵ_{rare }= (aa_{Graphene})/(a_{Graphene}), the energy gain of the ferromagnetic state E_{M }= E_{FM } E_{NM}, the total magnetic moment m_{total}, the carbon atomic magnetic moment , and the electronic property for each semihydrogenated sheet
Conclusions
In summary, we find that all the semihydrogenated BC_{3}, BC_{5}, BC_{7}, and Bdoped graphone sheets are halfmetals. The magnetism originates from the nonbonding p_{z }orbitals of C_{α }atoms. The boron atoms weaken the nearby C_{α }magnetic moments, and cause the Fermi level to shift into the spinup states. A halfmetal gap is opened in the spindown bands, the value of which is about 12 eV depending on the boron contents. Owing to the promising halfmetallicity, the semihydrogenated boroncarbon sheets have potential applications in spintronics and nanodevices.
Abbreviations
AFM: antiferromagnetic; DoSs: densities of states; FM: ferromagnetic; PBE: PerdewBurkeErnzerhof.
Competing interests
The authors declare that they have no competing interests.
Authors contributions
YD and YW conceived the idea, performed the calculations, analyzed the data, and wrote the manuscript. JN, LS, SS, CL, and WT participated in the study. All authors read and approved the final manuscript.
Acknowledgements
Some of the calculations were performed in the Beijing Computing Center (BCC) of China. Y. Ding acknowledges the support from Hangzhou Normal University (HZNU), and BCC. Y. Wang acknowledges the support from the Science Foundation of Zhejiang SciTech University (ZSTU) (Grant No. 0913847Y). J. Ni acknowledges the support from the National Science Foundation of China (NSFC) (Grant No. 10974107). Y. Ding would like to thank Dr. Baoxing Li, Dr. Chao Cao, and the HZNU College of Science HPC Center for their assistance.
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