Boron Nitride Nanoribbons with

ARTICLE pubs.acs.org/JPCC

Half-Metallicity in Hybrid Graphene/Boron Nitride Nanoribbons with Dihydrogenated Edges Yuling Liu,† Xiaojun Wu,*,‡ Yu Zhao,§ Xiao Cheng Zeng,*,§ and Jinlong Yang*,† †

Department of Chemical Physics and Hefei National Laboratory for Physical Science at the Microscale, University of Science and Technology of China, Hefei, Anhui, 230026, China ‡ Department of Material Science and Engineering, Hefei National Laboratory for Physical Science at the Microscale and CAS Key Lab of Materials for Energy Conversion, University of Science and Technology of China, Hefei, Anhui, 230026, China § Department of Chemistry and Nebraska Center for Materials and Nanoscience, University of Nebraska—Lincoln, Lincoln, Nebraska 68588, United States

bS Supporting Information ABSTRACT: Motivated by successful fabrication of monolayer materials consisting of hybrid graphene and boron nitride domains (Ci, L.; et al. Nat. Mater. 2010, 9, 430 435), we report a first-principles study of hybrid graphene/boron nitride (C-BN) nanoribbons with dihydrogenated edge(s). The firstprinciples study suggests that hybrid C-BN nanoribbons can possess half-metallicity with a certain range of widths for the graphene and BN sections. In general, the hybrid C-BN nanoribbons, either in HC1HB2 (C2)m(BN)n or HC2HB2 (C2)m(BN)n form, can undergo the semiconductor-to-half-metal-to-metal transitions as the width of both graphene and BN nanoribbons increases. The calculated electronic structures of the hybrid C-BN nanoribbons suggest that dihydrogenation of the boron edge can induce localized edge states around the Fermi level, and the interaction among the localized edge states can lead to the semiconductor-tohalf-metal-to-metal transitions.

’ INTRODUCTION Two-dimensional (2D) monolayer materials, such as the graphene and graphene-like boron nitride (BN) sheet, have received considerable attention due to their intriguing physical properties and their high potential for nanoelectronic applications.1 Graphene is a semimetal with a zero band gap and its charge carriers’ velocity is constant throughout the band edge. The BN monolayer, on the other hand, is a semiconductor with a wide band gap.1 5 When the graphene and BN monolayers are cut into many nanoribbons, using either a physical or chemical method, the electronic properties of the monolayer materials can be tailored for the band gap engineering in low-dimensional materials.6 13 Many previous theoretical studies have also shown that the half-metallicity can be achieved in both the graphene and BN nanoribbons (GNRs and BNNRs), for example, via applying an in-plane electric field,13,14 through chemical functionalizing the edges,15 18 pattering graphene with chemical functional groups,19 and controlling the edge states via doping20,21 or by hydrogenation,24 28 thereby enabling spintronic applications.13 31 Moreover, electronic and magnetic properties of BNNRs and GNRs can be modified by changing the number of hydrogen atoms bonded to every edge atom.24,26 It has been reported that GNRs with dihydrogenated edges can be more stable than those with monohydrogenated edges at room temperature.28 Over the past several years, many theoretical and experimental efforts have been devoted to exploration of synthesizing hybrid r 2011 American Chemical Society

2D materials based on graphene and BN monolayer with new functionalities unavailable in the pristine graphene.32 42 One suggestion based on previous first-principles calculations is to place the graphene on a BN monolayer to form a bilayer structure. A small band gap can be opened in the graphene due to the weak interaction among hybrid layers.32 Another suggestion is to substitute a small fraction of carbon atoms by the boron and nitrogen atoms in the graphene.21,33 42 Previous studies have shown that substitution of carbon atoms with boron or nitrogen atoms may open the possibility for synthesizing p-type or n-type semiconducting graphene.33 By altering the arrangement of boron and nitrogen atoms or the ratio of carbon to boron and nitrogen atoms in the structure, one can tune the electronic, magnetic and half-metallic properties of the graphene nanoribbons (GNRs).35 For example, Okada et al. found that a hybrid BNC sheet with triangle-shaped graphene domains embedded in the BN monolayer is a manifestation of the flat-band ferromagnetism.42 Very recently, the hybrid C-BN monolayer materials consisting of separate BN and graphene domains have been successfully fabricated, implying a possibility of making hybrid C-BN nanoribbons with a more uniform BN and graphene domains by tailoring the hybrid C-BN monolayer materials with some Received: February 10, 2011 Revised: April 13, 2011 Published: April 28, 2011 9442

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The Journal of Physical Chemistry C

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Table 1. Energy Differences per Supercell among Different Magnetic States for Both C-BN Hybrid Nanoribbonsa system

magnetic state

HC1HB1-(C2)4(BN)4

eCvbCV (AFM)

HC1HN1-(C2)4(BN)4

ΔE (meV) 0

eCvbCv (FM) eC0bCv

26.2 71.8

eC0bC0 (NM)

86.8

eCvbCV (AFM)

0

eCvbCv (FM)

23.0

eC0bCv

99.2

eCvbC0 eC0bC0 (NM)

28.0 109.2

The ground state is chosen as the reference state. v denotes spin up, V denotes spin down, 0 denotes zero local magnetic moment, eC denotes carbon atom at the edge, and bC denotes the carbon atom at the graphene/BN boundary. a

Figure 1. The optimized structures of the hybrid (a) HC1HB1-(C2)4(BN)4 and (b) HC1HN1-(C2)4(BN)4 nanoribbons. The white, gray, blue, and pink balls represent hydrogen, carbon, nitrogen, and boron atoms, respectively. The supercell is illustrated with the rectangle (green dashed lines).

physical methods.43 One possible way to fabricate this linear structure is to cut the C-BN hybrid monolayer with the tip of a scanning tunneling microscope, which has been demonstrated for the fabrication of GNRs out of graphene materials.44 In this article, we report a first-principles study of hybrid C-BN nanoribbon structures with a heterojunction formed between the zigzag edges of graphene and BN nanoribbons, and with the open edge(s) dihydrogenated. We find that as the widths of both graphene and BN sections increase the system undergoes semiconductor-to-half-metal-to-metal transitions. We show that dihydrogenation of the edges of the hybrid C-BN nanostructure can induce local edge states around the Fermi level and the coupling among these edge states can induce the semiconductorto-half-metal-to-metal transitions. Our theoretical study shows a prototype of the hybrid C/BN nanoribbons that possess intrinsic half-metallicity.

’ MODELS AND METHODS The first-principles calculations are performed by using VASP package. The frozen-core projector-augmented-wave (PAW) method and spin-polarized density functional method within the generalized gradient approximation (GGA) of the Perdew Burke Ernzerhof (PBE) functional are used.45 47 A kinetic energy cutoff of 400 eV is used in the plane-wave expansion. The energy convergence threshold is set as 1 10 4 eV. To determine the magnetic ground state of hybrid nanoribbons, a supercell containing double unit cells along the ribbon direction is used. Two adjacent nanoribbons are separated by a vacuum region of 15 Å, and the one-dimensional Brillouin zone is sampled by 20 special k-points with the Monkhorst Pack method.48 When the band structure is calculated, 60 special k-points are used to plot the band structure. The conjugate gradient method is used to fully relax both the atomic positions and ribbon periodic lattice constants along the ribbon direction

until the force on each atom is less than 0.01 eV/Å. To confirm that the chosen computational method is sensible, we have performed two additional test calculations with a single-cell hexagonal-BN (h-BN) and graphene systems. The calculations show that the band gaps of the GNR and BNNR with eight zigzag chains are 0.46 and 4.09 eV, respectively, which are consistent with previous theoretical calculations (0.43 and 4.2 eV) using the PW91 functional.21

’ RESULTS AND DISCUSSION The hybrid C-BN nanoribbons are constructed by merging two zigzag edges together (forming a heterojunction), one from the GNR and one from the BNNR. The remaining two open edges of the hybrid C-BN nanoribbons are passivated by hydrogen, with one hydrogen atom per edge atom initially (monohydrogenation). In Figure 1, two C-BN nanoribbons are displayed, namely, the HC1HB1-(C2)4(BN)4 and HC1HN1-(C2)4(BN)4 nanoribbons. Here, HC1HB1 denotes that both carbon edge and boron edge are monohydrogenated with the C N bonds being formed in the heterojunction region, and HC1HN1 denotes that both carbon and nitrogen edges are monohydrogenated with the C B bonds being formed in the heterojunction region. (C2)m(BN)n means that the hybrid nanoribbon contains m zigzag carbon chain(s) and n zigzag BN chain(s). The relative energies among different magnetic states for both HC1HB1-(C2)4(BN)4 and HC1HN1-(C2)4(BN)4 nanoribbons are summarized in Table 1. The ground states for both types of nanoribbons are antiferromagnetic (AFM). The total energy calculation suggests that the HC1HN1-(C2)4(BN)4 nanoribbon is more stable than HC1HB1-(C2)4(BN)4 by ∼1.17 eV per supercell. Spin-charge density distribution shows that the carbon atoms at the open edge and the heterojunction contribute the most to the spin-charge density. A small spin-charge density distribution can be seen on the boron (or nitrogen) atoms at the heterojunction, due to the charge transfer at the interfacial region (see Figure 2a,b). The local magnetic moments for carbon atoms at the edge (eC) or the heterojunction region (bC), nitrogen atom at the heterojunction region (bN), and boron atom at the edge (eB) are 0.113, 0.085, 0.025, and 0 μB, respectively, in the HC1HB1-(C2)4(BN)4 nanoribbon. In the HC1HN1-(C2)4(BN)4 nanoribbon, the local magnetic moments of carbon and boron atom are 0.133 (eC), 0.097 (bC), 0.019 (bB), and 0 (eN) μB, 9443

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Figure 2. Calculated spin-charge density distribution of (a) HC1HB1-(C2)4(BN)4 and (b) HC1HN1-(C2)4(BN)4 nanoribbons, and calculated band structures of (c) HC1HB1-(C2)4(BN)4, (d) HC1HN1(C2)4(BN)4, and (e) a pristine GNR. The isosurface value for the plotted spin charge density profiles is 0.01 au. Blue and red lines in (c) and (d) denote the spin-up and spin-down channel, respectively. The Fermi level is marked by a green dashed line.

respectively. The electronic band structures of the HC1HB1-(C2)4(BN)4 and HC1HN1-(C2)4(BN)4 nanoribbons and a pristine GNR are plotted in Figure 2c e. Both hybrid C-BN nanoribbons are spin-polarized semiconductors with a tiny band gap in one spin channel and a relatively large band gap in another spin channel. For HC1HB1-(C2)4(BN)4, the spin-down channel exhibits an indirect gap of ∼0.06 eV, and the spin-up channel exhibits a direct band gap of 0.58 eV. For HC1HN1-(C2)4(BN)4, the band gaps are 0.08 and 0.58 eV in the two spin channels. Very recently, He et al. reported a similar structure of HC1HN1-(C2)6(BN)6, which is predicted to be metallic.50 Our test calculation shows that the ground state of HC1HN1-(C2)6(BN)6 is AFM and the nanoribbon is also a spin-polarized semiconductor. The metallic FM state is less stable than the AFM state as the latter state is about 8.6 meV per supercell lower than the former state. The partial density of states (PDOS) analysis shows that the bands near the Fermi level are contributed mainly by the carbon atoms at the edge and in the heterojunction region, similar to the case of a pristine GNR when different electric potentials are applied to the two edges.13 Here, the potential difference can be observed within the carbon section due to the formed heterojunction between GNR and BNNR. The contribution from the BN section locates far away from the Fermi level, similar to that in the case of a pristine BNNR. In the ferromagnetic (FM), nonmagnetic (NM), or certain ferrimagnetic state, the hybrid C-BN nanoribbons are all metallic. A test calculation is also performed for the armchair hybrid C-BN nanoribbon by fusing

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two GNR and BNNR at their armchair edges. Our calculations show that the hybrid armchair nanoribbon is a NM semiconductor with a similar band gap as that of a pristine armchair GNR (see Figure S1, Support Information). Next, we consider the hybrid C-BN nanoribbons by attaching two hydrogen atoms to each edge atom at one or both edges. It has been reported that GNRs with dihydrogenated edges can be more stable than those with monohydrogenated edges at room temperature.28 Moreover, one can modify the electronic and magnetic properties of BNNRs and GNRs by changing the number of hydrogen atoms attached to every edge atom.24,26 Six hybrid nanoribbon systems with dihydrogenated edge(s) are considered, namely, HC2HB1-(C2)4(BN)4, HC2HN1-(C2)4(BN)4, HC1HN2-(C2)4(BN)4, HC1HB2-(C2)4(BN)4, HC2HB2-(C2)4(BN)4, and HC2HN2-(C2)4(BN)4. Among the six, HC2HB1-(C2)4(BN)4, HC2HN1-(C2)4(BN)4, HC1HN2-(C2)4(BN)4, and HC1HB2-(C2)4(BN)4 have only one edge entirely dihydrogenated, while in HC2HB2-(C2)4(BN)4 and HC2HN2-(C2)4(BN)4, both edges are entirely dihydrogenated (see Figure 3). After geometric optimization of all six nanoribbon systems, we find that the lattice constants of the hybrid nanoribbons are little affected by changing the number of hydrogen atoms at the edge. Moreover, most systems maintain their planar structures, except for HC1HN2-(C2)4(BN)4 and HC2HN2-(C2)4(BN)4. However, dihydrogenation of N atoms induces small distortion at the nitrogen edge. In Table 2, energy differences among different magnetic states for every nanoribbon system are summarized. It turns out that their ground states are either AFM or FM. Interestingly, the spincharge density distribution exhibits a significant change compared to that of the hybrid nanoribbons with monohydrogenated edges, as shown in Figure 4. Dihydrogenation at the carbon and boron edges induces denser spin-charge density distribution in the hybrid nanoribbons than monohydrogenation at the same edges. As a result, those atoms near the dihydrogenated edge(s) possess larger local magnetic moments (see Table S2, Supporting Information). The spin-charge density distribution decreases gradually from the edge to the heterojunction region in the carbon section but decreases very sharply in the BN section due to the localization of electrons in the BNNR. The dihydrogenation of nitrogen edge does not induce notable spin-charge density in the BN section. In addition, we calculate the formation energy of dihydrogenation at the edge(s), which is defined as Eform = E(hybrid nanoribbon with dihydrogenated edges) E(hybrid nanoribbon with momohydrogenated edges) (difference in the number of H atom at the edge per supercell) E(H). As shown in Table 2, the dihydrogenation of the edge atoms is energetically favorable if starting from the corresponding monohydrogenated system. As shown in Figure 4, the computed band structures of the hybrid nanoribbons with dihydrogenated edges are sensitive to the heterojunction and edge structures. Three types of band structures can be identified. The HC2HB1-(C2)4(BN)4 and HC2HN1-(C2)4(BN)4 hybrid nanoribbons (see Figure 4a,b) are predicted to be a spin-polarized semiconductor or possibly a halfmetal since either the valence or conduction band edge is very close to or even touches the Fermi level. The HC1HN2-(C2)4(BN)4 and HC2HN2-(C2)4(BN)4 hybrid nanoribbons (Figure 4d,f) are metallic, and the HC1HB2-(C2)4(BN)4 and HC2HB2-(C2)4(BN)4 hybrid nanoribbons (Figure 4c,e) are half-metallic because there are two bands crossing the Fermi energy level in one spin channel, whereas an indirect band gap >0.2 eV appears in the other spin channel. It is known that a semilocal functional like 9444



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Figure 3. The top and side views of the optimized hybrid C-BN nanoribbons: with one dihydrogenated edge, (a) HC2HB1-(C2)4(BN)4, (b) HC2HN1-(C2)4(BN)4, (c) HC1HB2-(C2)4(BN)4, and (d) HC1HN2-(C2)4(BN)4; with two dihydrogenated edges, (e) HC2HB2-(C2)4(BN)4 and (f) HC2HN2-(C2)4(BN)4.

Table 2. Energy Differences Per Supercell among Different Magnetic States and the Formation Energy (Eform) for the Edge Dihydrogenation of the Six C-BN Hybrid Nanoribbon Systemsa system HC2HB1-(C2)4(BN)4

0

217.6

HC2HN1-(C2)4(BN)4

0

162.4

3.892

0

185.2

1.370

51.6

0.012

15.6

333.2

5.236

0

160.6

3.856

HC1HB2-(C2)4(BN)4

2.8

HC1HN2-(C2)4(BN)4

0

HC2HB2-(C2)4(BN)4

0

HC2HN2-(C2)4(BN)4 a

AFM (meV) FM (meV) NM (meV) Eform (eV) 3.838

The energy of the ground state is set as the zero for each system.

PBE tends to underestimate the band gap of semiconductors due to its limitation in describing the conducting band, whereas several hybrid density functionals containing nonlocal Hartree Fock exchange can provide more accurate value of the band gap, such as the Heyd Scuseria Ernzerhof (HSE) functional.14,16,49 We perform a test calculation with the HSE06 functional and find that the HC2HN1-(C2)4(BN)4 hybrid nanoribbon turns out to be a spin-polarized semiconductor and its conducting band edge is above the Fermi energy level by about 0.4 eV, while the HC1HB2-(C2)4(BN)4 and HC2HB2-(C2)4(BN)4 hybrid nanoribbons are still half-metallic (see Figure S3, Support Information). Note that the energy differences between AFM and FM states in HC2HB2-(C2)4(BN)4 and HC1HB2-(C2)4(BN)4 systems are small (Table 2), implying that both systems may exhibit paramagnetic behavior at room temperature. PDOS analysis shows that the DOS near the Fermi level is mainly contributed by the carbon section in HC2HB1-(C2)4(BN)4 and HC2HN1-(C2)4(BN)4. In the other four systems, the BN sections give significant contribution around the Fermi level and relatively stronger coupling can be found between carbon and BN sections (see Figure S4, Support Information).

We further examine possible half-metallic properties of HC2HB2-(C2)m(BN)n by varying the width of carbon section (m = 1 13) and the BN section (n = 1 15) separately. The ground states of these hybrid nanoribbons are either NM or AFM, depending on the m and n values (see Table S5, Supporting Information). Some ultranarrow hybrid nanoribbons exhibit the NM ground states, such as the HC2HB2-(C2)1(BN)1, HC2HB2-(C2)1(BN)2, HC2HB2-(C2)2(BN)1 and HC2HB2-(C2)2(BN)2 systems. Wider hybrid nanoribbons tend to possess the AFM ground state. In Figure 5, the band gaps for both spin-up and spin-down channels are plotted as a function of n or m. We find that the HC2HB2-(C2)m(BN)n system is half-metallic when the width of BN section n g 4 and the width of carbon section m < 10. The band gap for the spin-up channel decreases quickly to zero when n increases to 4, regardless of m, while the band gap for the spindown channel decreases slowly with increasing n and converges to a nonzero value (∼0.50 eV for m = 1, and 0.16 eV for m = 5). Meanwhile, the band gap for the spin-down channel also decreases with increasing m and vanishes when m = 10. The narrowest half-metallic nanoribbon is the HC2HB2-(C2)1(BN)4 whose width is ∼11.0 Å. The widest half-metallic hybrid nanoribbon we predict is the HC2HB2-(C2)5(BN)15 whose width is ∼39.2 Å, which has an indirect band gap of 0.16 eV for the spindown channel and a zero band gap for the spin-up channel. Thus, the half-metallic properties of HC2HB2-(C2)m(BN)n can sustain over a wide range of widths (from 11 to 39 Å). Another examination of the HC1HB2-(C2)m(BN)n system gives similar results. All HC1HB2-(C2)m(BN)n hybrid nanoribbons are predicted to be half-metallic when n g 4 and m < 7 (see Figure S6, Supporting Information). Note in passing that here we only consider the perfect hybrid nanoribbon structures. The existence of defects within the hybrid nanoribbons may significantly change the predicted semiconductor half-metal transition behavior, which will be studied in the future. 9445



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Figure 4. Calculated band structures and spin-charge distributions of (a) HC2HB1-(C2)4(BN)4, (b) HC2HN1-(C2)4(BN)4, (c) HC1HB2-(C2)4(BN)4, (d) HC1HN2-(C2)4(BN)4, (e) HC2HB2-(C2)4(BN)4, and (f) HC2HN2-(C2)4(BN)4. The Fermi level is set as zero and marked by a green dashed line. The isosurface value for the spin-charge profiles is 0.01 au.

Figure 5. Calculated band gaps for the HC2HB2-(C2)m(BN)n systems with various m and n: for (a) the HC2HB2-(C2)m(BN)n system with m = 1 5 and n = 2 15; (b) for the HC2HB2-(C2)m(BN)5 system with m = 1 10.

To gain more insights into the relationship between the calculated band gap and values of m and n, we plot the band structures of the HC2HB2-(C2)m(BN)n (m = 3, n = 2 5, and n = 5, m = 3 5) systems in Figure 6. As n increases, the lowest conducting band (LCB) and the highest valence band (HVB) in the spin-up channel move toward each other, and the band gap vanishes when the LCB crosses the Fermi level for n = 4 (Figure 6a d). In the spin-down channel, the HVB moves upward toward the Fermi level and the LCB shifts downward slightly as n increases, resulting in the shrinking of the band gap with increasing n (Figure 6a d). However, the band gap does not vanish even for n = 15, and the hybrid nanoribbons undergoes a transition from a semiconductor to a half-metal as n reaches 4. As m increases, the HVB for both spin channels and the LCB for the spin-up channel do not change with m, but the LCB for the spin-down channel exhibits a significant change in its dispersion (Figure 6e h). Hence, when the width (m) of carbon section increases, the LCB edge is relocated from the Γ k-point to (0,0,0.36) k-point along the Γ X band line, as shown in Figure 6h (Γ and X refer to (0,0,0) and (0,0,0.5) k-point, respectively), and the LCB edge moves downward and eventually reaches the Fermi level when m reaches 10, resulting in the transition from halfmetallic to metallic. Here, we use a simple model to understand the band structures and half-metallic properties of the HC2HB2-(C2)m(BN)n systems. In Figure 7, the band structures and charge density distributions for several bands around the Fermi level are plotted for a pristine GNR with one edge dihydrogenated and the other monohydrogenated (HC2HC1-(C2)3), a pristine BNNR with the nitrogen edge monohydrogenated and the boron edge 9446



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Figure 6. Calculated band structures of HC2HB2-(C2)m(BN)n (m = 3, n = 2 5, and n = 5, m = 3 5). The Fermi level is set as zero and is marked with a green dashed line. The spin-up and spin-down band structures are plotted with blue and red solid lines, respectively.

Figure 7. Calculated band structures of (a) a pristine GNR with one dihydrogenated edge and one monohydrogenated edge, (b) a pristine BNNR with the nitrogen edge monohydrogenated and the boron edge dihydrogenated, and (c) the HC2HB2-(C2)3(BN)5 system. The Fermi level is set as zero and is marked with a green dashed line. The spin-up and spin-down band structures are plotted with blue and red lines, respectively. The width of the pristine GNR in (a) and the BNNR in (b) is same as that of the carbon and BN section in the HC2HB2-(C2)3(BN)5 system. The charge density distributions in (a c) are plotted with a isosurface value of 0.01 au. The golden and green colors represent the charge distribution for the band in spin-up and spin-down channels, respectively.

dihydrogenated (HN1HB2-(BN)5), and a HC2HB2-(C2)3(BN)5 system, respectively. The GNR and BNNR have the same structures as the carbon and BN sections in the HC2HB2-(C2)3(BN)5. As shown in Figure 7, the band structures and

charge density distribution around the Fermi level for the HC2HB2-(C2)3(BN)5 system can be viewed as a combination of those of the pristine GNR and BNNR. The HC2HC1-(C2)3 GNR is a spin polarized semiconductor with a wide band gap in 9447



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Figure 8. Calculated band structures and charge density distribution profiles for the (a) HC2HB2-(C2)3(BN)3 and (b) HC2HB2-(C2)7(BN)5. The Fermi energy is set as zero and marked with a green dashed line.

both spin channels, and the HN1HB2-(BN)5 BNNR is metallic, distinctly different from those of BNNRs with monohydrogenated edges. Clearly, the dihydrogenation of the pristine GNR or BNNR induces new edge states around the Fermi level, which are delocalized in HC2HC1-(C2)3, but localized at the edges of HN1HB2-(BN)5 due to the strong ionicity of the B N bonds.24,26 In the HC2HC1-(C2)3 GNR, two spin-polarized bands around the Fermi level give similar charge density distribution profiles. In the HN1HB2-(BN)5 BNNR, the band that crosses the Fermi level in the spin-up channel (blue line) is mainly contributed by the atoms at the dihydrogenated edge while the other one in the spindown channel is mainly contributed by atoms from both edges. Hence, when HC2HC1-(C2)3 and HN1HB2-(BN)5 nanoribbons are merged together to form the HC2HB2-(C2)3(BN)5 nanoribbon, the newly formed heterojunction results in different modifications on the edge states, depending on their charge density distribution profiles, which leads to the half-metallicty in the hybrid nanoribbon. For the HC2HC1-(C2)3 GNR, the band edges at the X k-point shift upward, whereas those at the Γ k-point shift downward slightly, resulting in the band crossing through the Fermi level (band 4 in Figure 7c) and appearance of a new valley at (0, 0, 0.34) k-point in the band 2 in Figure 7c. Meanwhile, modifications of the edge states of the BNNR are minor due to the localization of the edge states. The band for the spin-down channel of the HN1HB2-(BN)5 BNNR moves away from the Fermi level (band 3 in Figure 7c) so that the hybrid structure becomes half-metallic. The charge density distribution of this band also shows that the origin charge density at the monohydrogenated edge of the BNNR vanishes in the hybrid nanoribbon (band 3 in Figure 7c). The localization of the edges states also explains why the HC2HB2-(C2)m(BN)n becomes half-metallic when n reaches 4 and undergoes a transition from a half-metal to a metal when m reaches 10. In Figure 8, we plot the band structures and charge density distributions around the Fermi level for HC2HB2-(C2)3(BN)3 and HC2HB2-(C2)7(BN)5 nanoribbons, respectively. The bands from pristine GNR and BNNR cross each other near the Fermi level for the spin-up channel. When the BN section in the hybrid nanoribbon is very narrow (n < 4), the strong interaction between two crossing bands induces a wide gap and the system

becomes a spin-polarized semiconductor, as shown in Figure 8a. As the width of BN section increases, the induced band gap decreases due to the weakened interaction between localized edge state from the BN section and delocalized edge state from the graphene section, resulting in the “semiconductor-to-halfmetal transition”, as shown in Figure 6a d. On the other hand, the interaction among the edges states that belong to dihydrogenated carbon edge and the edge states due to the heterojunction region pushes the bands of the spin-down channel away from the Fermi level (as band 2 in Figure 7c). The strongest interaction can be seen in the HC2HB2-(C2)1(BN)4, for which the band gap in the spin-down channel is ∼0.55 eV (calculated at the PBE level, and 2.34 eV at the HSE06 level). As the width of the carbon section increases, the band due to the heterojunction region moves toward the Fermi level (the circled region in Figure 8b) and the hybrid nanoribbon becomes a metal when m reaches 10.

’ CONCLUSION In conclusion, we have shown a new design of 1D half-metallic materials, that is, the hybrid C-BN nanoribbons with dihydrogenated edge(s). The onset of the half-metallicity depends on the width of both carbon and BN sections, as well as the heterojunction type between the graphene and BN section. As the width of carbon and BN sections increases, semiconductor-to-halfmetal-to-metal transitions can occur in both HC1HB2-(C2)m(BN)n and HC2HB2-(C2)m(BN)n hybrid nanoribbons. Electronic structure calculations suggest that dihydrogenation of the boron edge in the BN section induces localized edge states around the Fermi level. The interaction among the edge states from the carbon and BN sections leads to the semiconductor-tohalf-metal-to-metal transitions in the hybrid nanoribbons with dihydrogenated boron edge. The hybrid nanoribbons can become half-metallic when n reaches 4 and the half-metallicity can sustain as long as the m < 10 for HC2HB2-(C2)m(BN)n, and m < 7 for HC1HB2-(C2)m(BN)n. Successful fabrication of the hybrid C-BN nanoribbons with half-metallicity has implications for the development of novel low-dimensional spintronic materials. 9448



’ ASSOCIATED CONTENT

bS

Supporting Information. Geometry and band structure of a hybrid nanoribbon with the armchair edges, magnetic moment distribution in the hybrid nanoribbons with dihydrogenated edge(s), the HSE06 band structures of three hybrid nanoribbons, DOS and PDOS analysis of the hybrid nanoribbons with dihydrogenated edge(s), the ground state of the hybrid nanoribbons with dihydrogenated edge(s) and different widths of graphene and BN sections, and band gaps of HC1HB2 (C2)m(BN)n. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected], [email protected], and xjwu @ustc.edu.cn.

’ ACKNOWLEDGMENT This work is partially supported by National Science Foundation of China (Grant No. 20873129, 11004180) and by National Key Basic Research Program (Grant No. 2011CB921400). X.C.Z. is supported by grants from the ONR (N00014-09-1-0943), ARL (W911NF1020099), NSF (CMMI-0709333), and the Nebraska Research Initiative. Calculations were performed in the Shanghai Supercomputer Center and the USTC-HP computer. ’ REFERENCES (1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Twodimensional gas of massless Dirac fermions in graphene. Nature 2005, 438, 197. (2) Zhang, Y. B.; Tan, Y. W.; Stormer, H. L.; Kim, P. Experimental Observation of Quantum Hall Effect and Berry’s Phase in Graphene. Nature 2005, 438, 201. (3) Berger, C.; Song, Z. M.; Li, X. B.; Wu, X. S.; Brown, N.; Naud, C.; Mayou, D.; Li, t. B.; Hass, J.; Marchenkov, A. N.; Conrad, E. H.; First, P. N.; de Heer, W. A. Electronic Confinement and Coherence in Patterned Epitaxial Graphene. Science 2006, 312, 1191. (4) Novoselov, K. S.; Geim, A. K.; Morozov, S. V. Two-dimensional Atomic Crystals. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 10451. (5) Nag, A.; Raidongia, K.; Hembram, K. P. S. S.; Datta, R.; Waghmare, U. V.; Rao, C. N. R. Graphene analogues of BN: novel synthesis and properties. ACS Nano 2010, 4, 1539. (6) Li, X. L.; Wang, X. R.; Zhang, L.; Lee, S.; Dai, H. J. Chemically Derived, Ultrasmooth Graphene Nanoribbon Semiconductors. Science 2008, 319, 1229. (7) Pisani, L.; Chan, J. A.; Montanari, B.; Harrison, N. M. Electronic structure and magnetic properties of graphitic ribbons. Phys. Rev. B 2007, 75, 64418. (8) Okada, S. Energetics of nanoscale graphene ribbons: Edge geometries and electronic structures. Phys. Rev. B 2008, 77, 41408. € (9) Han, M. Y.; Ozyilmaz, B.; Zhang, Y.; Kim, P. Energy band-gap engineering of graphene nanoribbons. Phys. Rev. Lett. 2007, 98, 206805. (10) Son, Y. W.; Cohen, M. L.; Louie, S. G. Energy gaps in graphene nanoribbons. Phys. Rev. Lett. 2006, 97, 216803. (11) Wu, X. J.; Zeng, X. C. Sawtooth-like Graphene Nanoribbons. Nano Res. 2008, 8, 241. (12) Xiang, H. J.; Kan, E. J.; Wei, S. H.; Whangbo, M. H.; Yang, J. L. “Narrow” Graphene Nanoribbons Made Easier by Partial Hydrogenation. Nano Lett. 2009, 9, 4025. (13) Son, Y. W.; Cohen, M. L.; Louie, S. G. Half-metallic graphene nanoribbons. Nature 2006, 444, 347.

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