Boron Nitride Nanoribbons Become Metallic - Nano Letters (ACS

LETTER pubs.acs.org/NanoLett

Boron Nitride Nanoribbons Become Metallic Alejandro Lopez-Bezanilla,* Jingsong Huang, Humberto Terrones, and Bobby G. Sumpter Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, Tennessee 37831-6493, United States

bS Supporting Information ABSTRACT: Standard spin-polarized density functional theory calculations have been conducted to study the electronic structures and magnetic properties of O and S functionalized zigzag boron nitride nanoribbons (zBNNRs). Unlike the semiconducting and nonmagnetic H edge-terminated zBNNRs, the O edge-terminated zBNNRs have two energetically degenerate magnetic ground states with a ferrimagnetic character on the B edge, both of which are metallic. In contrast, the S edge-terminated zBNNRs are nonmagnetic albeit still metallic. An intriguing coexistence of two different Peierls-like distortions is observed for S edge-termination that manifests as a strong S dimerization at the B zigzag edge and a weak S trimerization at the N zigzag edge, dictated by the band fillings at the vicinity of the Fermi level. Nevertheless, metallicity is retained along the S wire on the N edge due to the partial filling of the band derived from the pz orbital of S. A second type of functionalization with O or S atoms embedded in the center of zBNNRs yields semiconducting features. Detailed examination of both types of functionalized zBNNRs reveals that the p orbitals on O or S play a crucial role in mediating the electronic structures of the ribbons. We suggest that O and S functionalization of zBNNRs may open new routes toward practical electronic devices based on boron nitride materials. KEYWORDS: Boron nitride, nanoribbon, edge functionalization, Peierls-like distortion, magnetic moment, DFT

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round-breaking experiments with graphene have stimulated a revolution in materials science related with one-atomthick layered materials.1 Monolayer materials such as BN, MoS2, NbSe2, and graphene remain planar as separated from the native 3D stacked crystals by means of simple techniques such as the scotch tape method.2 Thin films of some of these materials could provide a cheap replacement for the current oxide electrodes used in organic solar cells3 and also for the silicon-based transistors widely used in electronic devices.4 Nanoribbons, a quasi 1D version of the above 2D materials, have also been the subject of extensive experimental and theoretical research. Graphene nanoribbons (GNRs) can be made by cutting a graphene sheet or by longitudinally unzipping carbon nanotubes.5 Fujita and co-workers were the first to investigate planar GNRs and they showed that, at a tight binding level of theory, zigzag graphene nanoribbons (zGNRs) display interesting electronic edge effects which are potentially important for various applications.6 Depending on the width and edge orientation, H edgeterminated GNRs exhibit semiconducting behavior with different bandgaps.7 GNRs edge-terminated with O, S, or F have also been theoretically studied.8 Along with GNRs, studies of nanoribbons based on other materials such as BN9 and ZnO10 are also attracting interest. A hexagonal boron nitride (h-BN) sheet is analogous to graphene since it is isoelectronic and isomorphic to the graphene honeycomb lattice. Specifically, h-BN is a one-atom-thick material composed of a hexagonal network with an equal number of alternating B and N atoms in sp2 hybridization that are bonded covalently and yet with a remarkable ionic character. While r 2011 American Chemical Society

graphene is a zero gap semimetal, h-BN is a wide bandgap semiconductor.11 Because of these features, h-BN has also attracted significant attention of the science community.11
13 Jin et al. have synthesized a free-standing layer of h-BN inside a high-resolution electron microscope, making possible the identification of triangularly shaped vacancies.14 Shi et al. have reported a method to synthesize films with a variable number of h-BN layers on Ni substrates and derived by optical measurements a bandgap of 5.92 eV.11 This wide bandgap allows for the integration of BN derivatives as dielectric gate substrates and UV light emitting films in optoelectronic applications but prevent their utilization as conductive electronic channels in future electronic devices. Similar to GNRs, boron nitride nanoribbons (BNNRs) can be obtained by cutting a h-BN sheet or unzipping a BN nanotube.12 Barone and Peralta studied the electronic and magnetic properties of BNNR with bare edges and provided theoretical evidence that these ribbons are magnetic semiconductors with bandgaps decreasing with ribbon width.9 When only the B edge in a zigzag boron nitride nanoribbon (zBNNR) is terminated with H atoms, half-metallicity was found.15 Half-metallicity has also been reported theoretically in zBNNRs edge-terminated with F atoms.16 Nakamura et al. have analyzed the electronic properties of a zBNNR with both B and N edges terminated with H atoms and found that the zBNNR becomes an insulator in which the Received: May 13, 2011 Revised: June 17, 2011 Published: July 07, 2011 3267

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Figure 1. (a) Nonspin-polarized band structure of the nonmagnetic ground state of H-[BN]20-H(1) ribbon. (b) Spin-resolved band structure of one of the two degenerate magnetic ground states of the O-[BN]20-O(1) ribbon with a total magnetic moment of 0.24 μB. For this ribbon, the projected density of states (PDoS) of O atoms attached to B (O@B) and N (O@N) are shown in (c) and (d), respectively. The total density of states (TDoS) of the same ribbon is plotted in (e). (f) depicts the geometry of the fully relaxed ribbon and (g) shows the spin densities of this magnetic ground state at an isosurface value of 10
4 e/Å3. Compared to (a), the energy band diagram of O-[BN]20-O(1) displays two outstanding differences in terms of spin polarization and metallic features which arise from the pz orbital derived band of O@N and the px orbital derived bands of O on both edges. Horizontal dashed lines indicate the Fermi energy level.

bandgap is determined by two edge states localized at the B and N sites.17 On the experimental side, the conductivity of BNNRs has recently been explored by Zeng et al. where BNNRs produced by unwrapping BN nanotubes through argon plasma etching of multiwalled BN nanotubes were shown to exhibit semiconducting behavior.12 The observed enhanced conductivity of the resulting nanoribbons over that of the primal nanotubes was ascribed to the electrically conductive properties of bare zigzag edges and to the vacancy defects that introduce dopinglike states into the ribbons. In this Letter, we report a first-principles study of the electronic and magnetic properties of O and S functionalized zBNNRs. We show that the O and S edge functionalization on both B and N zigzag edges gives rise to metallic states, despite a Peierls-like distortion in the case of S edge functionalization. Such a distortion is very unusual in that two different distortions in the form of double and triple periods coexist in the same ribbon and, to our best knowledge, they have never been observed before for any functionalized nanoribbons. A second type of functionalization with O or S atoms embedded in the center of zBNNRs forming a central nanowire is also studied in order to compare with the edge-functionalized ribbons. This leads to semiconducting ribbons that display a different type of distortion due to van der Waals repulsion between closecontacting atoms. Thus we highlight the importance of edge

functionalization versus an embedded wire as a route toward achieving metallic states in zBNNRs. The two types of functionalized nanoribbons are shown in Figures 1, 2 (edge functionlization), and 3 (embedded wire). Ribbons grow in the x axis and the surface vector points in the z direction. Edge-functionalized nanoribbons are denoted as X-[BN]m-X(n), where [BN]m indicates m boron-nitride dimers in each row characterizing the ribbon width, X is H, O, or S atoms attached to both zigzag edges, and n indicates the number of rows in the unit cell along the ribbon axis. Embedded-wire nanoribbons are denoted as H-[NB]m-X-[BN]m-H(n). Note that O and S atoms are embedded in the center through two B atoms between two identical zBNNRs that are H terminated on the N zigzag edges. The geometry optimizations and electronic structure calculations are performed using the SIESTA DFT-based code.18 We use a double-ζ basis set with additional polarization orbitals. The spin-dependent local density approximation (LSDA) is adopted for the exchange correlation functional and the Troullier-Martins scheme is used for the norm-conserving pseudopotentials. This level of theory has been broadly employed to study the electronic and geometric properties of BNNRs.16,19 zBNNRs are modeled within a supercell with at least 10 Å of vacuum between noninteracting neighboring cells. All atoms are relaxed with a force tolerance of 0.01 eV/Å and unit cell vectors are relaxed with the 3268

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Figure 2. (a) Nonspin-polarized band structure of the nonmagnetic ground state S-[BN]6-S(1) nanoribbon depicted in (f) is similar to that of the O edge-terminated nanoribbon in terms of the four dispersive bands (cf. Figure 1b) at the vicinity of the Fermi level (horizontal dashed lines). The green, black, and red dot symbols are located at 1/3, 1/2, and 5/6 of the irreducible Brillouin zone. The band fillings of the three bands crossing the Fermi level suggest Peierls distortion in a way of dimerization of S atoms attached to the B edge (S@B) and trimerization of S atoms attached to the N edge (S@N), which are verified by a S-[BN]6-S(6) nanoribbon (b
e and g). The Peierls distortion of S-[BN]6-S(6) leads to an intradimer distance of d1 = 2.13 Å and an interdimer distance of d2 = 2.83 Å for the S@B wire, and intratrimer distance of d3 = 2.36 Å and intertrimer distance of d4 = 2.72 Å for the S@N wire. Going from (f) to (g), the band structure of S-[BN]6-S(6) becomes six-folded (b). The projected density of states (PDoS) of S@B (c) shows that the dimerization opens a gap of 3.17 eV on the px derived bands of S@B at the X point. Correspondingly, the PDoS of S@N (d) shows that trimerization opens a gap of 1.14 eV on the px derived bands of S@N at the Γ point. However, the pz derived band of S@N shows no gap, as can be seen in the PDoS (d) and total density of states (TDoS) in (e). A side view of a S-[BN]6-S(12) nanoribbon (h) shows that further inclusion of van der Waals repulsion between neighboring S dimers causes deviations of the dimer pairs from the ribbon plane by d5/2=0.22 Å and slightly elongated intradimer distance of d0 1 = 2.14 Å and interdimer distance of d0 2 = 2.85 Å. On the N edge, the trimer pairs only deviate negligibly from the ribbon plane by 0.02 Å.

maximum stress component being smaller than 0.02 GPa. During geometry optimizations, we adopt a 128  1  1 Monkhorst sampling in the Brillouin zone for ribbons with one row of atoms (n = 1) but reduce the number of k-points along the ribbon direction to 64, 16, and 8 for n = 2, 6, and 12, respectively. The numerical integrals are performed on a real space grid with an equivalent cutoff of 300 Ry. In addition, a number of calculations based on the generalized gradient approximation (GGA) are also performed using the ab initio simulation package VASP20 for the most interesting S edge-terminated zBNNRs. The Kohn
Sham equations are solved using the projector augmented wave approach21 within the frozen core approximation, a k-mesh sampling of 22  1  1, and a plane wave basis set with a 600 eV kinetic energy cutoff. The electronic self-consistent field is converged to 10
5 eV per cell and all atoms are relaxed with a force tolerance of 0.005 eV/Å. Before addressing the O and S edge-terminated nanoribbons, we revisit the primitive H edge-terminated ribbon H-[BN]20H(1) in order to use its electronic band structure as a frame of reference. Table 1 lists the energy of H-[BN]20-H(1) at its nonmagnetic ground state relative to a bare zBNNR ribbon [BN]20 and H2. The negative functionalization energy of
11.07 eV indicates that the bare ribbon is stabilized by passivating the dangling bonds at both zigzag edges with H atoms. Figure 1a

shows the energy band diagram of a H-[BN]20-H(1). The band structure is nonspin-polarized and exhibits an indirect bandgap of 3.72 eV. DFT-LDA bandgaps are known to be underestimated with respect to experimental values but this discrepancy inherent to DFT calculations does not affect our general conclusions about the metallic features in zBNNRs. The valence electronic structure consists of four groups of twenty bands plus a single band crossing the uppermost group. The lower three groups are associated with the σ-bonds of the BN-network arising from the three valence atomic orbitals on each B or N atom in sp2 hybridization. In contrast, the uppermost group has a π-symmetry and is associated with the perpendicular pz valence atomic orbitals on B and N atoms. In addition, the last group of bands is crossed by a single band which can be ascribed to the s orbitals of H atoms that passivate the dangling bonds of the B and N edges. Unlike the nonmagnetic H edge-terminated zBNNRs, the O-[BN]20-O(1) ribbon has two energetically degenerate magnetic ground states with a total magnetic moment of 0.24 and 0.61 μB, respectively. O edge-termination stabilizes the magnetic ground states by
5.98 eV relative to the bare zBNNR ribbon and a triplet O2 (Table 1). For the two solutions, the O
B and O
N distances are 1.32 and 1.28 Å, respectively, and the lattice vector along the ribbon is 2.48 Å, which is the same as that of H-[BN]20-H(1). Figure 1b
e shows the spin-resolved band structure 3269

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Figure 3. Nonspin-polarized band structure (a) and projected density of states (PDoS) (b) for embedded-wire nanoribbon H-[NB]10-O-[BN]10-H(2). Side view (e) and top view (f) of the ribbon. (e) shows that sp-hybridized O atoms on the central wire deviate slightly from the planar structure to reduce the van der Waals repulsion. Band structure (c) and PDoS (d) for the embedded-wire nanoribbon H-[NB]10-S-[BN]10-H(2). Side view (g) and top view (h) of the ribbon. The van der Waals interaction between neighboring sp2-hybridized S atoms is reduced through alternating deviations of S atoms by 1.13 Å above and below the ribbon plane. Unlike the edge functionalizations, both of these nanoribbons are semiconductors with a direct bandgap of 3.81 eV for O functionalization and 1.83 eV for S functionalization at the Γ point. Horizontal dashed lines indicate the Fermi energy level.

and accompanying projected density of states (PDoS) of O atoms attached to B and N (denoted as O@B and O@N, respectively) and total density of states (TDoS) for the first solution with a total magnetic moment of 0.24 μB. The results for the other solution of 0.61 μB are provided in Figure S1 (Supporting Information). The existence of two energetically degenerate solutions can be rationalized as follows. Figure 1g shows the spin densities of the first solution where the cyan and orange isosurfaces correspond to net spin-up and spin-down electron densities, respectively. These isosurfaces show that spin densities are localized primarily on the edges whereas the middle part of the ribbon is nonmagnetic. Comparing both solutions shown in Figure 1g and Figure S1f (Supporting Information), we observe that spin orientations on the B edge flip over in Figure S1f (Supporting Information) while those on the N edge remain unchanged. Nevertheless, a common feature on the two edges is that the local magnetic moments decay quickly from the edge atoms to the interior. For a wide ribbon, the spin densities vanish in the center and consequently, the spins on the two edges do not interact with one another, leading to two energetically degenerate solutions. Decreasing the ribbon width to m = 8, we still obtain the same conclusion. Although the primitive H edge-terminated ribbon has a large bandgap, the O-[BN]20-O(1) ribbon exhibits metallic features, as

can be seen from Figure 1b
e. Comparing the spin-up component of O-[BN]20-O(1) with the band structure of H-[BN]20H(1), one may recognize that the main differences arise from the four bands at the vicinity of the Fermi level. This can be understood from the hybridization of the O atoms. Each O atom undergoes an sp hybridization yielding two hybrid orbitals along the y direction. One sp orbital points toward the B (N) atom forming a O
B (O
N) σ-bond, whereas the other sp orbital is a lone pair pointing outward. The other two mutually perpendicular px and pz orbitals on each O atom are nearly degenerate and accommodate a total of three electrons. The near degeneracy of px and pz can be partly removed by their symmetry-allowed mixings with the σ- or π-bands on the BN network, respectively, which add additional π-bond character to the O
B and O
N bonds. A detailed analysis of the PDoS shown in Figure 1c,d allows assigning the origins of the four bands at the vicinity of the Fermi level without ambiguity. The band derived from the pz orbital of O@B runs up from Γ to X, and then descends when it meets the Fermi level, as verified by Figure 1c. The band derived from the pz orbital of O@N ascends monotonically from Γ to X, crossing the Fermi level, as verified by Figure 1d. Both bands derived from the px orbitals of O@B and O@N descend nearly in parallel from Γ to X crossing the Fermi level. Note that the energy of the px derived band of O@N is lower in energy than 3270

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Table 1. Functionalization and Distortion Energies of Zigzag Boron-Nitride Nanoribbons at Their Ground States magnetic moment

functionalization

distortion

(μB)

E (eV)a

E (meV)b

nanoribbon H-[BN]20-H(1)


11.07c

0

O-[BN]20-O(1)

0.24, 0.61


5.98e

S-[BN]6-S(1)

0


5.73f

S-[BN]6-S(6)

0

S-[BN]6-S(12)

0

d


482g
25h

S-[BN]20-S(1)

0


5.38

H-[NB]10-O-[BN]10-H(2)

0


19.49j

H-[NB]10-S-[BN]10-H(2)

0


10.90k

i

a

The energy difference between functionalized nanoribbons and their corresponding bare ribbons and singlet H2, triplet O2, or singlet S8 ring. b The energy gain with Peierls distortion or deviation of functionalizing atoms from planar structures. c Relative to a bare [BN]20 ribbon and a singlet H2. d The metastable nonmagnetic state is higher in energy than these two degenerate magnetic ground state by 5 meV. e Relative to a bare [BN]20 ribbon and a triplet O2. f Relative to a bare [BN]6 ribbon and 1/4 of a singlet S8 ring. g Energy of Peierls distorted S-[BN]6-S(6) relative to six times that of S-[BN]6-S(1). h Energy of nonplanar S-[BN]6S(12) relative to two times that of planar S-[BN]6-S(6). i Relative to a bare [BN]20 ribbon and 1/4 of S8 ring. j Relative to four H-[BN]10 ribbons and a O2. k Relative to four H-[BN]10 ribbons and 1/4 of a S8 ring.

that of O@B, which may be ascribed to the larger electronegativity of N. This is also the case for the pz derived bands, as can be seen from the Γ point. Notice the highly delocalized character of ∼3 eV between Γ and X points due to the overlap of in-plane px orbitals along the ribbon edges. It is worthwhile to highlight that the behavior of the PDoS curves corresponds√to the case of an infinite linear chain, with the characteristic 1/ E relation at the critical points.22 Figure 1e presents the spin-resolved TDoS showing peaks matching those in Figure 1c,d and also illustrating the offset in energy between the two spin components. On the basis of these results, it can be concluded that the pz band of O@N and the px bands of O on both edges contribute to the metallic features of O-[BN]20-O(1). No distortion due to Peierls instability toward the formation of oxygen dimers or trimers along the edges is observed when the number of unit cells in the supercell is increased to n = 2 or n = 3. In addition, by doubling the unit cell for a narrower ribbon, that is, O-[BN]8-O(2), we found that the ribbon remains metallic and there are no magnetic configurations with spin-polarized states extended along the edges as found for the bare zBNNRs.9 Functionalization with S atoms at the two zigzag edges leads to a more intriguing behavior. First we examine a S-[BN]6-S(1) nanoribbon for which the unit cell contains only one row of atoms.23 Energetics tabulated in Table 1 also suggests that S functionalization stabilizes the S-[BN]6-S(1) nanoribbon. Compared to the O functionalization, the distances from S to the B and N atoms on the two zigzag edges are elongated to 1.81 and 1.73 Å, respectively, whereas the lattice vector along the ribbon remains at 2.48 Å. Figure 2a shows the band structure of S-[BN]6-S(1) which, unlike the O counterpart, is not spin polarized. However, a noticeable similarity is observed between the two ribbons in terms of the four dispersive bands at the vicinity of the Fermi level. The two bands derived from the pz valence orbital of S run up and then intersect one another while

the two px derived bands run down nearly in parallel from Γ to X points. The dispersions of these four bands are greatly enhanced as a result of the more diffuse valence orbitals on S atoms compared to O atoms. The px derived bands exhibit a highly delocalized character of ∼7 eV and represent infinite atomic wires formed by the overlap of the in-plane px orbitals along the ribbon edges. Similar to the O case, the pz band of S@N and the px bands of S on both edges contribute to the metallic features of S-[BN]6-S(1). Studies on ribbons as wide as S-[BN]20-S(1) give the same conclusion. Starting from the results of S-[BN]6-S(1), we examine other S edge-terminated homologues with the number of rows increased beyond n = 1 in order to scrutinize possible Peierls instability along the ribbon axis. Insights on the number of rows can be obtained from the band filling at the vicinity of the Fermi level. As can be seen from the black dot symbol in the middle of the irreducible Brillouin zone (BZ) in Figure 2a, the px derived band of S@B is slightly more than half-filled, denoted as 1/2 + δ. A half filling should be expected since the pz derived band of S@B is below the Fermi level, implying two electrons on each pz orbital of S@B. Similar to the O edge-terminated ribbons, the px and pz orbitals of each S@B accommodate a total of three electrons. This leaves only one electron on each px orbital of S@B, rendering the px derived band half-filled. As will become clear from below, the extra filling in the amount of δ comes from an interband charge transfer from the S@N wire. The red dot symbol on the right of the irreducible BZ in Figure 3a shows that the pz derived band of S@N is 5/6 filled. The remaining electrons in the 1/6 irreducible BZ are transferred into the px derived band of S@N, filling it from half of the irreducible BZ to 2/3. The charge transfer takes place only on the S@N wire and should not be confused with the interband charge transfer of δ noted above. As a matter of fact, the filling of the px derived band of S@N is slightly under 2/3, that is, 2/3
δ, as can be seen from the green dot symbol in Figure 2a. This shortage of electrons in the amount of δ is the extra charge in the 1/2 + δ filling of the px derived band of S@B. From the ∼1/2 and ∼2/3 band fillings, it is expected that the S@B and the S@N wires may undergo a Peierls-like distortion toward dimerization and trimerization on the B and N edges, respectively. However, such distortions cannot take place unless one condition is satisfied, that is, the interband charge transfer δ must be restored from the px derived band of S@B to the px derived band of S@N, so that the two bands are exactly 1/2 and 2/3 filled and accordingly the Fermi level meets the backfolded bands at the zone edge. Results prove that the band-filling analysis is helpful for choosing the right number of n. We examined a S-[BN]6-S(6) nanoribbon and found that the ribbon dimerizes on the B edge and in the meantime trimerizes on the N edge. Energy comparison confirms that the distortion lowers the energy by 0.48 eV per unit cell with n = 6 (Table 1) and causes negligible changes in bond distances of the S
B and S
N bonds. The bond length alternations manifest in the inter-S distances along the two edges (Figure 2g), yielding an intradimer distance of d1 = 2.13 Å and an interdimer distance of d2 = 2.83 Å for the S@B wire, and intratrimer distance of d3 = 2.36 Å and intertrimer distance of d4 = 2.72 Å for the S@N wire. Wider ribbons up to S-[BN]20-S(6) do not change the observation of dimerization and trimerization. Additional calculations for S-[BN]n-S(6) with n = 2, 4, 6, and 8 using VASP at the level of PBE24 also verified these double and triple period distortions. To our best knowledge, the S-[BN]m-S(6) nanoribbon studied here is the first example to 3271

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Nano Letters exhibit such an intriguing distortion with both dimerization and trimerization manifesting in the same nanoribbon. The band structure for the distorted S-[BN]6-S(6) nanoribbon and its accompanying PDoS on S@B and S@N are shown in Figure 2b
d. Upon lineal distortion the dispersive bands of the S-[BN]6-S(1) ribbon are each back folded into six branches. As a result of the dimerization, the px derived bands of S@B open a gap of 3.17 eV at the X point. Correspondingly, the px derived bands of S@N open a gap of 1.14 eV at the Γ point. On the other hand, the pz derived band of S@N remains 5/6 filled with the energies of the sixth and fifth branches being degenerate at the zone edge and also equal to the Fermi energy. This band filling implies that every six neighboring pz orbitals of S@N lose two electrons from the highest antibonding orbital of a linear hexamer in the unit cell. Accordingly, every three neighboring px orbitals of S@N gains one electron which is filled in the nonbonding orbital of each trimer, and thus each trimer has two px electrons in the nonbonding orbital and two px electrons in the lowest bonding orbital. Note that the two bonding px electrons are shared among three S centers in each trimer, unlike in a dimer where two bonding px electrons are shared between only two S centers, leading to a weaker trimer bond and a stronger dimer bond. The weaker trimer bonds are responsible for the much weaker bond length alternations in trimers compared to dimers, which is in turn responsible for the smaller bandgap opening at the N edge compared to that at the B edge. It should be pointed out that the 5/6 partial filling for the pz derived band of S@N should have driven a Peierls-like distortion toward a hexamerization with a linear 6-fold pz weak bonding interaction. Such a potential hexamerization would open a gap between the sixth and fifth branches of the pz derived bands on S@N wire. However, this hexamerization is overwhelmed by the trimerization, mainly because the pz orbitals only overlap with one another in a weaker side-by-side fashion, whereas the px orbitals overlap in a stronger head-over-head fashion. Consequently, the backfolded sixth and fifth branches remain degenerate at the Fermi energy. The absence of a gap is clearly seen from the TDoS in Figure 2d,e. Therefore, it can be concluded that the distorted S-[BN]6-S(6) nanoribbon remains metallic along the S wire on the N edge even after the Peierls-like distortion on the two edges and that the metallicity comes from the pz derived band of S@N. The analysis of geometry and electronic structure of S edgetermination presented above appears to be thorough but it is still not the end of the story. If we put aside the pz orbitals of S@N and only focus on the px orbitals of S at both edges, the S dimers on the B edge and the S trimers on the N edge can be both considered as closed-shell species. The distances d2 and d4 are both shorter than twice of the van der Waals radius of S atom at 1.8 Å, suggesting that the S dimer and trimer will adopt opposite tilts with respect to the ribbon plane so as to reduce the van der Waals repulsion. To account for both the Peierls-like distortion and alternating tilts, we doubled the unit cell of S-[BN]6-S(6) to twelve rows, as in a S-[BN]6-S(12) nanoribbon. The optimized structure for the nanoribbon is shown in Figure 2h and Figure S3 (Supporting Information). We found that the dimer pairs deviate from the ribbon plane by 0.22 Å, thus giving two S wires on the B edge, 0.43 Å apart. With more space around each dimer, the intradimer and interdimer distances are slightly elongated to 2.14 and 2.85 Å, respectively. On the N edge, the trimer pairs deviate slightly from the ribbon plane by 0.02 Å. The relatively larger tilts for the dimers and the negligible tilts for the trimers imply that the dimers have a greater closed-shell character than the trimers.

LETTER

The small bond length alternations on the N edge could also play a role to suppress the tilts of S trimers. Energy wise, the final structure is more stable than the untilted one by 25 meV (Table 1). The effects of the van der Waals repulsion on the band structure is negligible and therefore the back-folded band structure of S-[BN]6-S(12) is not presented here but provided in Figure S3 (Supporting Information). Next, we turn to the embedded-wire nanoribbons. As can be seen from Table 1, both H-[NB]10-O-[BN]10-H(2) and H-[NB]10-S-[BN]10-H(2) are stabilized by embedded O and S wire functionalization with respect to the H-[BN]10 ribbons and a triplet O2 or S8 ring. The band structures and accompanying PDoS of H-[NB]10-O-[BN]10-H(2) and H-[NB]10-S-[BN]10H(2) are shown in Figure 3a
d. Note that for these embeddedwire nanoribbons, we doubled the cell along the ribbon axis to allow for the distortion of O or S atoms off the ribbon plane, in order to reduce the van der Waals repulsion between closecontacting O or S atoms. As can be seen from the resulting nonplanar geometries of the nanoribbons (Figure 3e,g), each O or S atom deviates above and below the ribbon plane alternately. In contrast to the edge-functionalized nanoribbons presented above, each O or S atom forms two σ-bonds with its neighboring B atoms. For O functionalization, the O atom adopts an sp hybridization and therefore is linearly bonded to its neighboring B atoms. The px orbital of O atom overlaps head-over-head with those of neighboring O atoms along the central wire, leading to a dispersive band close to the Fermi level. The pz orbital of the O atom perpendicular to the ribbon plane overlaps side-by-side with those of neighboring O atoms and the BN network. For S functionalization, each S atom adopts an sp2 hybridization, as verified by the B
S
B bond angle of 117°. Two of the three sp2 orbitals form σ-bonds with B atoms while the third sp2 orbital perpendicular to the ribbon plane is responsible for a doubly occupied band low in energy. The px orbital of S atoms overlaps head-over-head with those of S atoms two rows up and down the central wire, giving a dispersive band close to the Fermi level. Unlike the edge functionalization, these valence structures of O and S give rise to semiconducting nanoribbons with a direct bandgap of 3.81 eV for O functionalization and 1.83 eV for S functionalization at the Γ point. Another effect of these valence structures of O and S is the nonplanar geometries of the nanoribbons. For planar H-[NB]10-O-[BN]10-H(1) and H[NB]10-S-[BN]10-H(1) nanoribbons, the lattice vectors along the ribbons remain close to those of the edge-functionalized ribbons, that is, 2.48 Å. This distance is also the interatomic distance between O atoms and S atoms, which appears to be too short if compared with the van der Waals radii of O and S, which are 1.52 and 1.80 Å, respectively. Despite the constraint from the sp hybridization, the O atoms deviate by 0.19 Å from the plane, giving rise to two O wires down the ribbon, about 0.37 Å apart. Likewise, the S atoms deviate by 1.13 Å above and below the ribbon plane, giving rise to two S wires down the ribbon, 2.26 Å apart. In summary, we have studied the electronic structures and magnetic properties of O and S functionalized zBNNRs. Unlike the semiconducting and nonmagnetic H edge-terminated zBNNRs, we have found that the O edge-terminated zBNNRs have two energetically degenerate magnetic ground states with a ferrimagnetic character on the B edge, both of which are metallic. The delocalization of the pz orbitals on O at the N edge and especially of the px orbitals on O at both the B and N zigzag edges is responsible for the metallic features of O edge terminated zBNNRs. In contrast, the S edge-terminated zBNNRs are nonmagnetic. 3272

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Nano Letters An unusual coexistence of two different Peierls-like distortions has been observed for S edge-termination that manifests as a strong S dimerization at the B zigzag edge and a weak S trimerization at the N zigzag edge, dictated by the ∼1/2 and ∼2/3 electron fillings of the dispersive bands derived from the px oribtals of S at the B and N edges, respectively. Consequently, these two bands showed a bandgap opening of 3.17 and 1.14 eV for the S wires at the B and N edges, respectively. In addition, a third band derived from the pz orbital of S@N also crosses the Fermi level. The partial band filling by 5/6 of the irreducible BZ should have driven a Peierls-like distortion toward a hexamerization of S wire at the N edge, which is however suppressed by the lattice constraint of the trimerization on S@N. As a result, the distorted nanoribbons remain metallic along the S wire on the N zigzag edge and the metallic behavior originates from the band derived from the pz orbitals of S at the N zigzag edge. A second type of functionalization with O or S atoms embedded in the center of zBNNRs forming a nanowire was found to yield semiconducting nanoribbons which also display a distortion toward nonplanar ribbons but in this case as result of van der Waals repulsion between closed shell atoms. As such, the presence of px and pz orbitals on O or S, depending on their occupancy, plays a crucial role in mediating the electronic structures of functionalized zBNNRs. The various geometries analyzed share a common feature: functionalizing atoms create extended nanowires along the growing direction of the zBNNRs with charge densities at the vicinity of Fermi level localized either on the ribbon edge in the case of edge termination, or within a narrow area across the ribbon width in the case of atom lines joining two zBNNRs. Because of the localized character of these “defects”, these results may be extrapolated to arbitrary large zBNNRs without loss of generality. These modeled systems may also shed new fundamental insight into boron nitride materials.

’ ASSOCIATED CONTENT

bS

Supporting Information. Band structure, PDoS, and TDoS of O-[BN]20-O(1) that has a total magnetic moment of 0.61 μB, side views of spin density isosurfaces for O-[BN]20-O(1) showing multiple shells of isosurface on S@N, and band structure, TDoS, and geometrical structure of S-[BN]6-S(12). This material is available free of charge via the Internet at http://pubs. acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This research used computational resources of the National Center for Computational Sciences at Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0500OR22725. We are also grateful for the support from the Center for Nanophase Materials Sciences (CNMS), sponsored at Oak Ridge National Laboratory by the Division of Scientific User Facilities, U.S. Department of Energy. We are indebted to Professor Ashwin Ramasubramaniam and Drs. Paul R. Kent, Eduardo CruzSilva, and Miguel Fuentes-Cabrera for helpful discussions.

LETTER

’ REFERENCES (1) (a) Novoselov, K.; Geim, A.; Morozov, S.; Jiang, D.; Zhang, Y.; Dubonos, S.; Grigorieva, I.; Firsov, A. Science 2004, 306, 666–669. (b) Novoselov, K.; Geim, A.; Morozov, S.; Jiang, D.; Katsnelson, M.; Grigorieva, I.; Dubonos, S.; Firsov, A. Nature 2005, 438, 197–200. (c) Berger, C.; Song, Z.; Li, T.; Li, X.; Ogbazghi, A.; Feng, R.; Dai, Z.; Marchenkov, A.; Conrad, E.; First, P.; de Heer, W. J. Phys. Chem. B 2004, 108, 19912–19916. (2) Novoselov, K. S.; Jiang, D.; Schedin, F.; Booth, T. J.; Khotkevich, V. V.; Morozov, S. V.; Geim, A. K. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 10451–10453. (3) Chen, X. L.; Xu, B. H.; Xue, J. M.; Zhao, Y.; Wei, C. C.; Sun, J.; Wang, Y.; Zhang, X. D.; Geng, X. H. Thin Solid Films 2007, 515, 3753–3759. (4) Radisavljevic, B.; Radenovic, A.; Brivio, J.; Giacometti, V.; Kis, A. Nat. Nanotechnology 2011, 6, 147–150. (5) Kosynkin, D. V.; Higginbotham, A. L.; Sinitskii, A.; Lomeda, J. R.; Dimiev, A.; Price, B. K.; Tour, J. M. Nature 2009, 458, 872–876. (6) (a) Fujita, M.; Wakabayashi, K.; Nakada, K.; Kusakabe, K. J. Phys. Soc. Jpn. 1996, 65, 1920–1923. (b) Nakada, K.; Fujita, M.; Dresselhaus, G.; Dresselhaus, M. S. Phys. Rev. B 1996, 54, 17954–17961. (c) Son, Y.-W.; Cohen, M. L.; Louie, S. G. Nature 2006, 444, 347–349. (7) Son, Y.-W.; Cohen, M. L.; Louie, S. G. Phys. Rev. Lett. 2006, 97, 216803. (8) (a) Cantele, G.; Lee, Y.-S.; Ninno, D.; Marzari, N. Nano Lett. 2009, 9, 3425–3429. (b) Ramasubramaniam, A. Phys. Rev. B 2010, 81, 245413. (c) Gunlycke, D.; Li, J.; Mintmire, J. W.; White, C. T. Appl. Phys. Lett. 2007, 91, 112108. (d) Gunlycke, D.; Li, J.; Mintmire, J. W.; White, C. T. Nano Lett. 2010, 10, 3638–3642. (9) (a) Barone, V.; Peralta, J. E. Nano Lett. 2008, 8, 2210–2214. (b) Park, C.-H.; Louie, S. G. Nano Lett. 2008, 8, 2200–2203. (10) (a) Tu, Z. C.; Hu, X. Phys. Rev. B 2006, 74, 035434. (b) Botello-Mendez, A. R.; Lopez-Urías, F.; Terrones, M.; Terrones, H. Nano Lett. 2008, 8, 1562–1565. (11) Shi, Y.; Hamsen, C.; Jia, X.; Kim, K. K.; Reina, A.; Hofmann, M.; Hsu, A. L.; Zhang, K.; Li, H.; Juang, Z.-Y.; Dresselhaus, M. S.; Li, L.-J.; Kong, J. Nano Lett. 2010, 10, 4134–4139. (12) Zeng, H.; Zhi, C.; Zhang, Z.; Wei, X.; Wang, X.; Guo, W.; Bando, Y.; Golberg, D. Nano Lett. 2010, 10, 5049–5055. (13) (a) Reina, A.; Jia, X.; Ho, J.; Nezich, D.; Son, H.; Bulovic, V.; Dresselhaus, M. S.; Kong, J. Nano Lett. 2009, 9, 30–35. (b) Song, L.; Ci, L.; Lu, H.; Sorokin, P. B.; Jin, C.; Ni, J.; Kvashnin, A. G.; Kvashnin, D. G.; Lou, J.; Yakobson, B. I.; Ajayan, P. M. Nano Lett. 2010, 10, 3209–3215. (c) Gorbachev, R. V.; Riaz, I.; Nair, R. R.; Jalil, R.; Britnell, L.; Belle, B. D.; Hill, E. W.; Novoselov, K. S.; Watanabe, K.; Taniguchi, T.; Geim, A. K.; Blake, P. Small 2011, 7, 465–468. (14) Jin, C.; Lin, F.; Suenaga, K.; Iijima, S. Phys. Rev. Lett. 2009, 102, 195505. (15) Zheng, F.; Zhou, G.; Liu, Z.; Wu, J.; Duan, W.; Gu, B.-L.; Zhang, S. B. Phys. Rev. B 2008, 78, 205415. (16) Wang, Y.; Ding, Y.; Ni, J. Phys. Rev. B 2010, 81, 193407. (17) Nakamura, J.; Nitta, T.; Natori, A. Phys. Rev. B 2005, 72, 205429. (18) (a) Soler, J.; Artacho, E.; Gale, J.; Garcia, A.; Junquera, J.; Ordejon, P.; Sanchez-Portal, D. J. Phys.: Condens. Matter 2002, 14, 2745–2779. (b) Ordejon, P.; Artacho, E.; Soler, J. Phys. Rev. B 1996, 53, 10441–10444. (19) Si, M.; Xue, D. J. Phys. Chem. Solids 2010, 71, 1221–1224. (20) Kresse, G.; Furthmuller, J. Phys. Rev. B 1996, 54, 11169–11186. (21) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758–1775. (22) Grosso, G.; Parravicini, G. P. In Solid State Physics; Press, A., Ed.; Academic Press: New York, 2000. (23) For S-[BN]m-S(n) nanoribbons, as shall be clear later, we need to increase the number of rows to n = 6 and 12. For these ribbons, a smaller m = 6 is justified from the standpoints of computational cost and clarity of band structures which would otherwise be too crowded. (24) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865–3868.

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