Hybrid structures of a BN nanoribbon/single-walled carbon nanotube: ab initio study

Abstract

Hybrid structures of a zigzag edge BN nanoribbon/single-walled carbon nanotube, namely, (i) ZBNNR-B-SWCNT in which only the B-edge of a zigzag edge BN nanoribbon (ZBNNR) is passivated with a single-walled carbon nanotube (SWCNT); (ii) ZBNNR-N-SWCNTs in which only the N-edge of ZBNNR is terminated with a SWCNT; (iii) hydrogenated ZBNNR-B-SWCNT; and (iv) hydrogenated ZBNNR-N-SWCNT, have been studied via standard spin-polarized density functional theory (DFT) calculations as well as ab initio molecular dynamics (MD) simulations. The DFT calculations and ab initio MD simulations results clearly show that all the examined hybrid structures are stable at room temperature. The formation energy, as well as the local DOS and Mulliken charge analysis, reveals that the hybrid structure of ZBNNR-B-SWCNT is more stable than that of ZBNNR-N-SWCNT, since the covalent bond of B–C is stronger than that of N–C owing to the electronegativity difference of the N and C atoms (1.49) being larger than that of the C and B atoms (0.51). Surprisingly, the ZBNNR-B-SWCNTs belong to intrinsic ferromagnetic metals, whereas the ZBNNR-N-SWCNTs belong to intrinsic spin-gapless semiconductors (SGS). Furthermore, in contrast to hydrogenated ZBNNRs, which are nonmagnetic semiconductors, hydrogenated ZBNNR-N-SWCNTs turn into intrinsic spin-semiconductors (hydrogenation induces a SGS–spin-semiconductor transition), whereas hydrogenated ZBNNR-B-SWCNTs remain in the ferromagnetic metallic state, because H-passivation removes the dangling bond states of N-edge or B-edge, but the magnetic properties of the “-SWCNT” edge remain unchanged.

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1 Introduction

It is known that graphene nanoribbons (GNRs) are made by cutting graphene sheets, which have edge carbon atoms that are modified by hydrogen. Notably, the properties of GNRs are sensitive to the crystallographic orientation of the edges, with armchair type nanoribbons (AGNRs) belonging to the non-magnetic semiconductors. In contrast, GNRs that have zigzag edges (ZGNRs) are predicted to be magnetic semiconductors with magnetically ordered edge states, where each edge is ferromagnetically ordered whereas between the edges there is antiferromagnetic coupling.¹ Theoretical studies have revealed that such magnetically ordered edge states have a potential application in spintronics.^2–5 Moreover, if the edges are not straight, the edge magnetic coupling can be a ferromagnetic coupling.^6,7 In addition, owing to the edge’s chemical activity,^8–10 different electronic and magnetic behaviors can be obtained when the two edges are terminated and passivated with different atoms or chemical groups.^11–16

In recent years, BN nanoribbons (BNNRs) have also attracted increasing attention.^17–38 Experimental and theoretical studies have confirmed that pristine BNNRs are magnetic metals.^17,18 In pristine zigzag edge BNNRs with n chains (n-ZBNNRs), the two edges are respectively terminated by B and N atoms, namely one edge is terminated with B atoms (called the B-edge), whereas another edge is terminated with N atoms (called the N-edge, see Fig. 8(a)). Interestingly, when the B-edge is passivated with H atoms, it becomes half-metallic.^19–21 In contrast, hydrogenated n-ZBNNRs, as well as hydrogenated armchair edge BNNRs with n dimer lines, belongs to non-magnetic semiconductors.^22–24 Moreover, a lot of studies have revealed that different electronic and magnetic behaviors can be obtained by various strategies, such as chemical functionalization,^25–28 creating defects, impurities or doping,^29–35 hydrogenation,³⁶ applying an external strain,³⁷ and applying an external electric field.^22,38

On the other hand, a lot of studies have revealed that the hybrid structures of BNNRs/GNRs also show rich electronic and magnetic properties,^39–48 such as that the band gap and edge magnetism of the hybrid BN–C nanoribbons can be regulated by the BN/C ratio.⁴⁵ Recently, Du et al. have studied hybrid C–BN single-walled nanotubes and found that zigzag C_0.5(BN)_0.5 SWNTs belong to narrow gap semiconductors, whereas armchair C_0.5(BN)_0.5 SWNTs belong to gapless semiconductors.⁴⁸

Furthermore, there has been increasing evidence that d and f metal elements are not the sole source in inducing intrinsic magnetism. It is known that metal-free ferromagnetism holds great promise to overcome the limitations of technologies relying on current magnetic materials based on d and f metal elements, as they involve only 2p elements. Moreover, owing to 2p electron systems with weak spin–orbit coupling and a relatively long spin relaxation time, metal-free ferromagnetism would play an important role in constructing future-generation spintronic devices.^49,50 It is hence highly desirable to design and develop ferromagnetic materials based on 2p elements instead of d and f metal elements.

Herein, hybrid structures of n-ZBNNR/(m,m)SWCNT, namely, (i) pristine nZBNNR-B-(m,m)SWCNTs in which the B-edge of pristine ZBNNR is passivated with a (m,m)SWCNT (see Fig. 1(a) and (b)); (ii) pristine nZBNNR-N-(m,m)SWCNTs in which the N-edge of pristine ZBNNR is passivated with a (m,m)SWCNT (see Fig. 1(d) and (e)); (iii) hydrogenated nZBNNR-N-(m,m)SWCNTs (H-nZBNNR-N-(m,m)SWCNTs, see Fig. 3(a)); (iv) hydrogenated nZBNNR-B-(m,m)SWCNTs (H-nZBNNR-B-(m,m)SWCNTs, see Fig. 3(b)), were studied via standard spin-polarized density functional theory (DFT) calculations as well as ab initio molecular dynamics (MD) simulations. The DFT calculations and ab initio MD simulations results clearly show that all the examined hybrid structures are stable at room temperature. The formation energy, local DOS, and Mulliken charge analyses reveal that the hybrid structure of ZBNNR-B-SWCNT is more stable than that of ZBNNR-B-SWCNT. Fascinatingly, we found that pristine nZBNNR-B-(m,m)SWCNTs belong to intrinsic ferromagnetic metals, whereas pristine nZBNNR-N-(m,m)SWCNTs belong to intrinsic spin-gapless semiconductors.^51,52 Moreover, hydrogenation makes the nZBNNR-N-(m,m)SWCNTs become ferromagnetic intrinsic spin-semiconductors,^53–55 whereas hydrogenated nZBNNR-B-(m,m)SWCNTs remain as intrinsic ferromagnetic metals. They are viewed as one of the most ideal materials for constructing metal-free spintronic nanodevices.^51–54

Fig. 1 (a) Top view and (b) side view of 3ZBNNR-B-(6,6)SWCNT, and (c) is the spatial distribution of the spin differences. (d) Top view and (e) side view of a 3ZBNNR-N-(6,6)SWCNT, and (f) is the spatial distribution of the spin differences. C₀, C₁, and C₂ mark the special C sites. Edge-B and B₀ mark the special B sites, whereas edge-N and N₀ mark the special N sites. The red and blue surfaces represent spin-up (↑) and spin-down (↓). The isosurface of 0.003 μ_B Å⁻³ is adopted for spin-up (↑), whereas the isosurface of 0.0015 μ_B Å⁻³ is adopted for spin-down (↓).

2 Computational methods

All full structural optimizations, total energy, and electronic structure calculations are performed in the framework of spin-polarized density functional theory (DFT), as implemented in the numerical atomic orbitals basis-set OPENMX computer code.⁵⁶ DFT within the generalized gradient approximation (GGA)⁵⁷ for the exchange-correlation energy was adopted. Norm-conserving Kleinman–Bylander pseudopotentials⁵⁸ were employed, and the wave functions were expanded by a linear combination of multiple pseudo atomic orbitals (LCPAO)^59,60 with a kinetic energy cutoff of 300 Ry. The basis functions used were B7.0-s²p¹d¹, C7.0-s²p²d¹, N7.0-s²p³d¹, and H7.0-s¹p¹. The first symbol designates the chemical name, followed by the cutoff radius (in Bohr radius) in the confinement scheme and the last set of symbols defines the primitive orbitals applied. We adopted a supercell geometry where the length of the vacuum region along the non-periodic direction (x-, y-directions) was 30 Å, and the lattice constant along the periodic direction (z-direction). 1 × 1 × 121 k-point sampling points in the Brillouin zone integration were used for reliable results.^61–64 Structural optimizations were performed using a conjugate gradient algorithm until the residual forces were smaller than 10⁻⁴ Hartree bohr⁻¹. The convergence in energy was 10⁻⁸ Hartree. We have also increased the size of the supercell to make sure that it does not produce any discernible difference on the results.

On the other hand, ab initio MD simulations were performed by a canonical (NVT) ensemble and carried out with the OPENMX computer code,⁵⁶ in which the heat bath was realized by means of the Nosé–Hoover method^65,66 and the temperature was fixed at 298 K, the time step was 1.0 femtosecond, and the total steps were 10 000.

3 Results and discussion

3.1 Atomic geometries, and electronic and magnetic properties

3.1.1 Atomic geometries and spin distribution. Fig. 1 plots the atomic geometries and spatial distribution of the spin differences for 3ZBNNR-B-(6,6)SWCNT and 3ZBNNR-N-(6,6)SWCNT, respectively. From Fig. 1(a) and (b), one can find that in 3ZBNNR-B-(6,6)SWCNT, via the bonding of C₀ and B₀ atoms, pristine n-ZBNNR and pristine (6,6)SWCNT bonded with each other. From Fig. 1(d) and (e), one can find that in 3ZBNNR-N-(6,6)SWCNT, via the bonding of C₀ and N₀ atoms, pristine n-ZBNNR and pristine (6,6)SWCNT bonded with each other. Note that each C₀ atom has four nearest neighbor atoms and is sp³-hybridized. As a result, in 3ZBNNR-B-(6,6)SWCNT, each C₀ and its four nearest neighbor atoms form one C–B bond and three C–C bonds (C₀–B, C₀–C₂, and two C₀–C₁ bonds), whereas in 3ZBNNR-N-(6,6)SWCNT, each C₀ and its four nearest neighbor atoms form one C–N bond and three C–C bonds (C₀–N, C₀–C₂, and two C₀–C₁ bonds). Clearly, both 3ZBNNR-B-(6,6)SWCNT and 3ZBNNR-N-(6,6)SWCNT possess an sp³-hybridized Y-shape and maintain a stable tube-shaped structure, commonly used for building construction. As a result, 3ZBNNR-B-(6,6)SWCNT, as well as 3ZBNNR-N-(6,6)SWCNT, entails much greater flexural rigidity than 3-ZBNNR. In addition, in Table 1, we have listed the magnetic moments of each C₀, C₁, C₂, B₀, and edge-N atom, as well as per unit cell, for 3ZBNNR-B-(6,6)SWNTs, whereas Table 2 shows the magnetic moments of each C₀, C₁, C₂, N₀ and edge-B atom, as well as per unit cell, for 3ZBNNR-N-(6,6)SWNT. As shown in Table 1, each of the C₁, C₂, and edge-N atoms possess relatively large magnetic moments with the same spin orientation. As a result, 3ZBNNR-B-(6,6)SWCNT has a ferromagnetic ground state with a net magnetic moment of 1.4 μ_B per unit cell. As shown in Table 2, each of the C₁, C₂, and edge-B atoms possess relatively large magnetic moments with the same spin orientation. As a result, 3ZBNNR-N-(6,6)SWCNT possesses a ferromagnetic ground state with a net magnetic moment of 1.9 μ_B per unit cell.

Table 1 The magnetic moments of each C₀, C₁, C₂, B₀, and edge-N atom, and in a unit cell, in the unit of μ_B for pristine and hydrogenated nZBNNR-B-(6,6)SWNT (n = 3 and 6)

nZBNNR-B-(6,6)SWNT	C0	C1	C2	B0	Edge-N	Cell
Pristine
3	−0.02	0.18	0.18	0.02	0.79	1.4
6	−0.02	0.21	0.09	0.02	0.88	1.4
Hydrogenated
3	−0.03	0.23	0.07	0.02	0.00	0.5
6	−0.03	0.25	0.09	0.03	0.00	0.6

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Table 2 The magnetic moments of each C₀, C₁, C₂, N₀, and edge-B atom, and in a unit cell, in the unit of μ_B for pristine and hydrogenated nZBNNR-N-(6,6)SWNT (n = 3 and 6)

nZBNNR-N-(6,6)SWNT	C0	C1	C2	N0	Edge-B	Cell
Pristine
3	−0.06	0.41	0.32	0.04	0.98	1.9
6	−0.06	0.42	0.33	0.04	1.00	2.0
Hydrogenated
3	−0.06	0.42	0.35	0.05	0.00	1.0
6	−0.06	0.42	0.35	0.05	0.00	1.0

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3.1.2 Band structures. The spin-polarized band structures for pristine 6ZBNNR-N-(6,6)SWCNT and 6ZBNNR-B-(6,6)SWCNT (respectively named as 6ZBNNR-N-(6,6)SWCNT and 6ZBNNR-B-(6,6)SWCNT) are shown in Fig. 2 (the relative stability of the ferromagnetic, antiferromagnetic, and non-magnetic states is shown in ESI Fig. 2 and 4†). Clearly, from Fig. 2(a), one can find that in the band structure of 6ZBNNR-N-(6,6)SWCNT, both spin channels are gapped, but the spin-down conduction band minimum and the spin-up valence band maximum touch at the Fermi energy, i.e., “spin-gapless”. Thus, 6ZBNNR-N-(6,6)SWCNT is an intrinsic spin-gapless semiconductor (SGS), in which not only the excited electrons, but also the holes, can be fully spin polarized.⁵¹ On the other hand, in order to reveal the origin of its electronic band structure, we marked the energy bands near the Fermi level via the partial charge densities of the unoccupied band (LΓ) and the occupied band (HΓ) at the Γ point. From Fig. 2(a), one can find that the energy bands marked with ↑HΓ − 0 and ↓LΓ + 0 are contributed to mainly by the atomic orbitals of “-(6,6)SWCNT” which is absent in 6-ZBNNR-NH, whereas the energy band marked with ↑HΓ − 1 is contributed to mainly by the atomic orbitals of the B-edge, which corresponds to the dangling-bond state. Thus, we can conclude that the unique electronic and magnetic properties of 6ZBNNR-N-(6,6)SWCNT are ascribable to the zigzag edge state of “6ZBNNR-N-” as well as the special edge shape of “-(m,m) SWCNT”. However, as shown in Fig. 2(b), 6ZBNNR-B-(6,6)SWCNT is an intrinsic ferromagnetic metal, owing to four bands crossing the Fermi level. On the other hand, the energy bands marked with ↑LΓ + 0 and ↓LΓ + 1 are contributed to mainly by the atomic orbitals of “-(6,6) SWCNT” which is absent in 6-ZBNNR-BH, whereas the energy bands marked with ↓LΓ + 0 and ↓HΓ − 0 are contributed to mainly by the atomic orbitals of the N-edge, which correspond to the dangling-bond state. Thus, we can conclude that the unique electronic and magnetic properties of 6ZBNNR-B-(6,6)SWCNT are ascribable to the zigzag edge state of “6ZBNNR-B-” as well as the special edge shape of “-(m,m)SWCNT”.

Fig. 2 Spin-polarized band structures and partial charge densities of the unoccupied band (LΓ) and the occupied band (HΓ) at the Γ point. (a) Pristine 6ZBNNR-N-(6,6)SWCNT and (b) Pristine 6ZBNNR-B-(6,6)SWCNT. The red solid and blue dash dotted lines denote the spin-up (↑) and spin-down (↓) bands, respectively. The Fermi level is set to zero. The isosurface is 0.05 e Å⁻³.

3.1.3 Hydrogenation effects. The spin-polarized band structures and spatial distribution of the spin differences for hydrogenated 6ZBNNR-B-(6,6)SWCNT and 6ZBNNR-N-(6,6)SWCNT (hereafter referred to as H-6ZBNNR-B-(6,6)SWCNT, H-6ZBNNR-N-(6,6)SWCNT) are shown in Fig. 3 (the relative stability of the ferromagnetic, antiferromagnetic, and non-magnetic states is shown in ESI Fig. 3 and 5†). Clearly, as shown in Fig. 3(b), H-6ZBNNR-B-(6,6)SWCNT can be classed as an intrinsic ferromagnetic metal,⁵⁵ which is ascribable from the energy bands marked with ↑LΓ + 0 and ↓LΓ + 1 as shown in Fig. 2(b). Comparing between Fig. 2(b) and 3(b), one can find that the ↓LΓ + 0 band that appears in 6ZBNNR-B-(6,6)SWCNT disappears in the H-6ZBNNR-B-(6,6)SWCNT, which indicates that the dangling-bond state of the N-edge is removed by H-passivation. Meanwhile, the local spin moment of each edge-N atom vanishes. As a result, the H-6ZBNNR-B-(6,6)SWCNT has a net magnetic moment of 0.6 μ_B per unit cell (see Table 1). Thus, we can conclude that the unique electronic and magnetic properties of H-6ZBNNR-B-(6,6)SWCNT are ascribable to the special edge shape of “-(m,m)SWCNT”. In contrast, H-6ZBNNR-N-(6,6)SWCNT becomes an intrinsic spin-semiconductor,^53,55 in which completely spin-polarized currents can be created and manipulated just by applying a gate voltage. On the other hand, comparing between Fig. 3(a) and 2(a), one can find that the ↑HΓ − 1 band that appears in 6ZBNNR-N-(6,6)SWCNT disappears in H-6ZBNNR-N-(6,6)SWCNT and a spin band gap opens, namely, hydrogenation induces a SGS–spin-semiconductor transition. This is because H-passivation removes the dangling-bond state of the B-edge. Meanwhile, the local spin moment of each edge-B atom vanishes. As a result, H-6ZBNNR-N-(6,6)SWCNT has a net magnetic moment of 1.0 μ_B per unit cell (see Table 2). Thus, we can conclude that the unique electronic and magnetic properties of H-6ZBNNR-N-(6,6)SWCNT originate from the special edge shape of “-(m,m)SWCNT”.

Fig. 3 Spin-polarized band structures and spatial distribution of the spin differences. (a) H-6ZBNNR-N-(6,6)SWCNT and (b) H-6ZBNNR-B-(6,6)SWCNT. The other marks are the same as in Fig. 1 and 2.

Comparing between the results of the pristine and hydrogenated hybrid structures of the ZBNNRs/SWCNTs, we can conclude that the unique electronic and magnetic properties of the pristine hybrid structures originate from the zigzag edge state of “nZBNNR-B-” (“nZBNNR-N-”) and the special edge shape of “-(m,m)SWCNT”. However, the unique electronic and magnetic properties of the hydrogenated hybrid structures are only ascribable to the special edge shape of “-(m,m)SWCNT”.

3.1.4 Analysis of density of states. The above results can be further understood by the analysis of the total density of states (TDOS) and the local density of states (LDOS). Fig. 4(a) and (b) plot the TDOS and LDOS for 6ZBNNR-B-(6,6)SWCNT and H-6ZBNNR-B-(6,6)SWCNT, respectively. From Fig. 4(a), one can find that in 6ZBNNR-B-(6,6)SWCNT, the TDOS near the Fermi level are contributed to not only by the C₁ and C₂ atoms of “-(6,6)SWCNT”, but also by the edge-N atom of “6ZBNNR”. However, as shown in Fig. 4(b), in H-6ZBNNR-B-(6,6)SWCNT, hydrogenation removes the contribution of the edge-N atom of “6ZBNNR” completely. On the other hand, as shown in Fig. 4(a), before hydrogenation, in 6ZBNNR-B-(6,6)SWCNT, for the edge-N, C₁ and C₂ atoms, the peak of the LDOS in the spin-up channel is below the Fermi level, while the peak of the LDOS in the spin-down channel is above the Fermi level. As a result, the edge-N, C₁ and C₂ atoms possess spin-up local magnetic moment. However, as shown in Fig. 4(b), after hydrogenation, in H-6ZBNNR-B-(6,6)SWCNT, the peaks of the LDOS of the C₁ and C₂ atoms remain unchanged, but the peak of the LDOS of the edge-N atom disappears completely. As a result, the C₁ and C₂ atoms still possess spin-up local magnetic moments, whereas, the local magnetic moment of the edge-N atom has been removed completely. In addition, from Fig. 4(a), one can find that in 6ZBNNR-B-(6,6)SWCNT, the LDOS in the spin-up channel of the C₁ atom crosses the Fermi level, the LDOS in the spin-up and spin-down channels of the C₁ atoms cross the Fermi level, whereas the LDOS in the spin-down channel of the edge-N atom crosses the Fermi level, which indicates that the orbitals of the edge-N, C₁ and C₂ atoms take part in electrical conduction, namely, the N edge and “-(6,6)SWCNT” edge undertake electrical conduction responsibility. However, as shown in Fig. 4(a), one can find that after hydrogenation, in H-6ZBNNR-B-(6,6)SWCNT, the orbital of the edge-N atom is no longer taking part in the electrical conduction process, namely, only the “-(6,6)SWCNT” edge undertakes electrical conduction responsibility. It is worth mentioning that because the electrically conductive function and magnetic properties of 6-ZBNNR are undertaken by the dangling-bond states at its B-edge and N-edge, hydrogenation makes it become a non-magnetic semiconductor^19–21 owing to the dangling-bond states having been removed by H-passivation. However, in H-6ZBNNR-B-(6,6)SWCNT, H-passivation removes the dangling-bond states at its N-edge, but the electrically conductive function and magnetic properties of the “-(6,6)SWCNT” edge are retained.

Fig. 4 Total density of states (TDOS) and local DOS (LDOS). (a) 6ZBNNR-B-(6,6)SWCNT and (b) H-6ZBNNR-B-(6,6)SWCNT. The other marks are the same as in Fig. 2.

The TDOS and LDOS for 6ZBNNR-N-(6,6)SWCNT and H-6ZBNNR-N-(6,6)SWCNT are plotted in Fig. 5(a) and (b), respectively. From Fig. 5(a), one can find that in 6ZBNNR-N-(6,6)SWCNT, the TDOS near the Fermi level are contributed to not only by the C₁ and C₂ atoms of “-(6,6)SWCNT”, but also by the edge-B atom of “6ZBNNR”. However, as shown in Fig. 5(b), in H-6ZBNNR-N-(6,6)SWCNT, hydrogenation removes the contribution of the edge-B atom of 6ZBNNR completely. Moreover, as shown in Fig. 5(a), in 6ZBNNR-N-(6,6)SWCNT, for the edge-B, C₁ and C₂ atoms, the peak of the LDOS in the spin-up channel is below the Fermi level, while the peak of LDOS in the spin-down channel is above the Fermi level. As a result, the edge-B, C₁ and C₂ atoms possess spin-up local magnetic moments. However, as shown in Fig. 5(b), in H-6ZBNNR-N-(6,6)SWCNT, namely after hydrogenation, below the Fermi level, the peak of the LDOS of the edge-B atom disappears completely, but the peaks of the LDOS of C₁ and C₂ atoms remain unchanged. As a result, the local magnetic moment of the edge-B atom is removed completely, whereas, the spin-up local magnetic moments of the C₁ and C₂ atoms remain unchanged. On the other hand, that the peak of the LDOS of the edge-B atom disappears leads to a band gap between the spin-up and spin-down channels. As a result, H-6ZBNNR-N-(6,6)SWCNT is a intrinsic spin-semiconductor,⁵³ in which hydrogenation induces a SGS–spin-semiconductor transition.

Fig. 5 TDOS and LDOS. (a) 6ZBNNR-N-(6,6)SWCNT and (b) H-6ZBNNR-N-(6,6)SWCNT. The other marks are the same as in Fig. 2.

3.1.5 Mulliken charge and spin population analysis. In order to further understand the above results, we calculated the Mulliken charge and spin population of the special atoms. For example, the Mulliken charge and spin population on each C₀, C₁, C₂, B₀, and edge-N atom for pristine and hydrogenated 6ZBNNR-B-(6,6)SWNT are listed in Table 3. As shown in Table 3, the local magnetic moments of each C₀, C₁, C₂, B₀, and edge-N atom originate from the difference between the spin-up and spin-down charges. Such as, in 6ZBNNR-B-(6,6)SWNT, the charges on each C₁ atom are 2.028 and 1.824 e for spin-up and spin-down channels, respectively. As a result, each C₁ atom possesses a 0.204 μ_B spin-up local magnetic moment. After hydrogenation, namely in H-6ZBNNR-B-(6,6)SWNT, the charges on each C₁ atom are 2.057 and 1.807e for spin-up and spin-down channels, respectively. As a result, each C₁ atom has a 0.250 μ_B spin-up local magnetic moment. Most notably, after hydrogenation the charge and spin population of the edge-N atom significantly change. As shown in Table 3, in 6ZBNNR-B-(6,6)SWNT, the charges on the edge-N atom are 3.081 and 2.203e for spin-up and spin-down channels, respectively. As a result, each edge-N atom possesses a 0.878 μ_B spin-up local magnetic moment. After hydrogenation, namely in H-6ZBNNR-B-(6,6)SWNT, the charges on each edge-N atom are 2.823 and 2.823e for spin-up and spin-down channels, respectively. As a result, the local magnetic moment on each edge-N atom is 0.000 μ_B, namely, the local magnetic moment of each edge-N atom has been removed.

Table 3 The Mulliken charge and spin population on each C₀, C₁, C₂, B₀, and edge-N atom for pristine and hydrogenated 6ZBNNR-B-(6,6)SWNT

System	Spin-up	Spin-down	Sum	Diff.
	C0
6ZBNNR-B-(6,6)SWNT	1.996	2.018	4.014	−0.022
H-6ZBNNR-B-(6,6)SWNT	1.992	2.019	4.011	−0.027
	C1
6ZBNNR-B-(6,6)SWNT	2.028	1.824	3.852	0.204
H-6ZBNNR-B-(6,6)SWNT	2.057	1.807	3.864	0.250
	C2
6ZBNNR-B-(6,6)SWNT	2.059	1.973	4.032	0.086
H-6ZBNNR-B-(6,6)SWNT	2.063	1.974	4.037	0.089
	B0
6ZBNNR-B-(6,6)SWNT	1.388	1.366	2.754	0.022
H-6ZBNNR-B-(6,6)SWNT	1.390	1.365	2.755	0.025
	Edge-N
6ZBNNR-B-(6,6)SWNT	3.081	2.203	5.284	0.878
H-6ZBNNR-B-(6,6)SWNT	2.823	2.823	5.646	0.000

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Similarly, the Mulliken charge and spin population on each C₀, C₁, C₂, N₀, and edge-B atom for pristine and hydrogenated 6ZBNNR-N-(6,6)SWNT are listed in Table 4. As shown in Table 4, after hydrogenation, except for the charge and spin population of the edge-B atom, there is no significant change in the charge and spin population of the system. Such as, before hydrogenation, namely in 6ZBNNR-N-(6,6)SWNT, the charges on each C₂ atom are 2.165 and 1.835 e for spin-up and spin-down channels, respectively. As a result, each C₂ atom has a 0.330 μ_B spin-up local magnetic moment. After hydrogenation, namely in H-6ZBNNR-N-(6,6)SWNT, the charges on each C₂ atom are 2.172 and 1.827 e for spin-up and spin-down channels, respectively. As a result, each C₂ atom has a 0.345 μ_B spin-up local magnetic moment. Most notably, after hydrogenation the charge and spin population of the edge-B atom significantly change. As shown in Table 4, before hydrogenation, namely in 6ZBNNR-N-(6,6)SWNT, the charges of the edge-B atom are 1.893 and 0.898 e for spin-up and spin-down channels, respectively. As a result, each edge-B atom has a 0.995 μ_B spin-up local magnetic moment. After hydrogenation, namely in H-6ZBNNR-N-(6,6)SWNT, the charges on each edge-B atom are 1.402 and 1.402 e for spin-up and spin-down channels, respectively. As a result, the local magnetic moment on each edge-B atom is 0.000 μ_B, i.e., the local magnetic moment of each edge-B atom vanishes.

Table 4 The Mulliken charge and spin population on each C₀, C₁, C₂, N₀, and edge-B atom for pristine and hydrogenated 6ZBNNR-N-(6,6)SWNT

System	Spin-up	Spin-down	Sum	Diff.
	C0
6ZBNNR-N-(6,6)SWNT	1.832	1.889	3.721	−0.057
H-6ZBNNR-N-(6,6)SWNT	1.829	1.887	3.716	−0.058
	C1
6ZBNNR-N-(6,6)SWNT	2.175	1.757	3.932	0.418
H-6ZBNNR-N-(6,6)SWNT	2.176	1.756	3.932	0.420
	C2
6ZBNNR-N-(6,6)SWNT	2.165	1.835	4.000	0.330
H-6ZBNNR-N-(6,6)SWNT	2.172	1.827	3.999	0.345
	N0
6ZBNNR-N-(6,6)SWNT	2.802	2.759	5.561	0.043
H-6ZBNNR-N-(6,6)SWNT	2.804	2.759	5.563	0.045
	Edge-B
6ZBNNR-N-(6,6)SWNT	1.893	0.898	2.791	0.995
H-6ZBNNR-N-(6,6)SWNT	1.402	1.402	2.804	0.000

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3.1.6 Origin of magnetism. The origin of magnetism in the hybrid structures of the ZBNNR/SWCNT is related to their electronic structures. For example, the spin-unpolarized band structures of the 6ZBNNR-B-(6,6)SWCNT is shown in Fig. 6(a), whereas its corresponding total density of states and LDOS are shown in Fig. 7(a). From Fig. 6(a), one can find that there are three energy bands, marked with LΓ + 0, HΓ − 0, and HΓ − 1 or LX + 0, HX − 0 as well as HX − 1, crossing the Fermi level and are called partial-filled bands. Clearly, the partial charge densities of the unoccupied band and the occupied band plotted in Fig. 6(a) show that the partial-filled bands corresponding to electron states are heavily localized. Indeed, as shown in Fig. 7(a), the LDOS analysis reveals that they are strongly localized on the C₁ and C₂ atoms of “-(6,6)SWCNT” as well as the edge-N atom of “6ZBNNR”. According to Hund’s rule, such partial filling of the localized bands drives spontaneous spin polarization, resulting in exchange splittings between the ↓LΓ + 0 and ↑LΓ + 0 bands, as well as between the ↓LΓ + 0 and ↑HΓ − 0 bands, respectively, as shown in Fig. 2(b). As a result, the total energy of the system is lowered by 124.97 meV from that of the spin-unpolarized state.

Fig. 6 Spin-unresolved band structures and partial charge densities of the unoccupied band (LΓ) and the occupied band (HΓ) at the Γ and X points. (a) 6ZBNNR-B-(6,6)SWCNT and (b) 6ZBNNR-N-(6,6)SWCNT. “○” and “Δ” label special bands (see Fig. 8). The other marks are the same as in Fig. 2.

Fig. 7 TDOS and LDOS. (a) 6ZBNNR-B-(6,6)SWCNT and (b) 6ZBNNR-N-(6,6)SWCNT. The other marks are the same as in Fig. 2.

Similarly, as shown in Fig. 6(b), in 6ZBNNR-N-(6,6)SWCNT, there are two partial-filled bands, marked as HΓ − 0 and HΓ − 1, or LX + 0 and HX − 0, crossing the Fermi level. Clearly, the partial charge densities of the unoccupied band and the occupied band plotted in Fig. 6(b) show that the two partial-filled bands corresponding to electron states are heavily localized. Indeed, as shown in Fig. 7(b), the LDOS analysis reveals that they are strongly localized on the C₁ and C₂ atoms of “-(6,6)SWCNT” as well as the edge-B atom of “6ZBNNR”. According to Hund’s rule, such partial filling of the localized bands drives spontaneous spin polarization, resulting in exchange splittings, as shown in Fig. 2(a), between the ↓LΓ + 0 and ↑HΓ − 0 bands, as well as between the ↓LΓ + 1 and ↑HΓ − 1 bands, respectively. As a result, the total energy of the system is lowered by 460.20 meV from that of the non-magnetic state.

3.2 Stability

3.2.1 Formation energy and covalent bonds. The formation energy of the hybrid structures of ZBNNR/SWCNT, which is usually used to characterize the stability of the system structure, is defined as^67,68

E_f = E_tot − E_n-ZBNNR − E_(m,m)SWCNT (1)

where, E_tot is the total energies of the system, E_n-ZBNNR is the energy of pristine n-ZBNNR, and E_(m,m)SWCNT is the energy of the (m,m)SWCNT. The calculated results for nZBNNR-B-(6,6)SWNT and nZBNNR-N-(6,6)SWNT are listed in Table 5. The negative formation energy for all the systems found in this work indicates that all of the hybrid structures of ZBNNR/SWCNT are not only steady, but also can be spontaneously formed. Moreover, one can notice that nZBNNR-B-(6,6)SWNT is more stable than nZBNNR-N-(6,6)SWNT, such as that the formation energy of 6ZBNNR-B-(6,6)SWNT is −2.56 eV, whereas the formation energy of 6ZBNNR-N-(6,6)SWNT is −2.18 eV. In order to explore the binding nature of the n-ZBNNR and (6,6)SWNT interaction, as shown in Fig. 8, we plotted the band structure, TDOS and the LDOS (edge-B and edge-N atoms) of 6-ZBNNR, as well as the band structure of (6,6)SWCNT. As shown in Fig. 8(a), near the Fermi level of 6-ZBNNR, there are four energy bands. TDOS and LDOS analysis reveals that the energy bands marked with “Δ” mainly originate from the 2p orbitals of the edge-B atoms, whereas the energy bands marked with “○” mainly originate from the 2p orbitals of the edge-N atoms. On the other hand, as shown in Fig. 8(b), near the Fermi level of (6,6)SWCNT, two energy bands originate from the 2p orbitals of the C atoms. After 6-ZBNNR bonding with (6,6)SWCNT via edge-B atoms, as shown in Fig. 6(a), the energy bands marked with “○” remain almost unchanged. However, the energy bands marked with “Δ” disappear, owing to the 2p orbitals of the edge-B atoms strongly coupling with the 2p orbitals of the C atoms forming a covalent band labeled as LΓ + 0 and HX − 0 in Fig. 6(a), namely, the B₀–C₀ band in 6ZBNNR-B-(6,6)SWNT is the covalent band. In contrast, after 6-ZBNNR bonding with (6,6)SWCNT via edge-N atoms, as shown in Fig. 6(b), the energy bands marked with “Δ” remain almost unchanged. Whereas, the energy bands marked with “○” disappear, due to the 2p orbitals of the edge-N atoms strongly coupling with the 2p orbitals of the C atoms forming a covalent band labeled as HΓ − 0 and HX − 0 in Fig. 6(b), namely the N₀–C₀ band in 6ZBNNR-N-(6,6)SWNT belongs to a covalent bond.

Table 5 The formation energy in the unit of eV for pristine nZBNNR-B-(6,6)SWNT and nZBNNR-N-(6,6)SWNT

System	n = 3	n = 4	n = 5	n = 6	n = 7	n = 8
nZBNNR-B-(6,6)SWNT	−2.28	−2.48	−2.51	−2.56	−2.58	−2.59
nZBNNR-N-(6,6)SWNT	−1.80	−2.08	−2.15	−2.18	−2.21	−2.25

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Fig. 8 (a) Geometric structure, band structure, and TDOS as well as the LDOS of the edge-B and edge-N atoms for 6ZBNNR. (b) Geometric structure and band structure of (6,6)SWCNT. “○” and “Δ” label special bands (see Fig. 6). The other marks are the same as in Fig. 2.

In order to gain further insight into the B₀–C₀ band and the N₀–C₀ band, the LDOS of the B₀ and C₀ atoms for 6ZBNNR-B-(6,6)SWCNT, as well as the LDOS of the N₀ and C₀ atoms for 6ZBNNR-N-(6,6)SWCNT, are plotted in Fig. 9. From Fig. 9(a), one can find that the strong hybridization of the B₀ and C₀ states demonstrates the formation of covalent bonds. Similarly, as shown in Fig. 9(b), the strong hybridization of N₀ and C₀ states demonstrates the formation of covalent bonds. However, the formation energy difference between 6ZBNNR-B-(6,6)SWNT and 6ZBNNR-N-(6,6)SWNT originates from the electronegativity of the N, C, and B atoms. It is known that electronegativity is the intrinsic property measuring the escaping tendency of electrons from atomic species. The larger the value of the electronegativity, the greater the atom’s strength to attract a bonding pair of electrons. The electronegativity values for N, C, and B atoms are 3.04, 2.55, and 2.04, respectively. We note that the electronegativity difference of the N and C atoms (1.49) is larger than that of the C and B atoms (0.51). Thus, the N₀–C₀ band in 6ZBNNR-N-(6,6)SWNT approaches an ionic bond, which can be demonstrated by the Mulliken charge analysis before and after 6-ZBNNR bonding with (6,6)SWCNT. As listed in Table 6, before 6-ZBNNR bonding with (6,6)SWCNT, the Mulliken charge analysis shows a charge of 2.766, 5.275, and 4.000 e on each edge-B, edge-N, and C₀ atom, respectively. After 6-ZBNNR bonding with (6,6)SWCNT via edge-B atoms, the Mulliken charge analysis shows a charge of 2.754, 5.295, and 4.014 e on each B₀, edge-N atom, and C₀, respectively, namely there is no obvious transfer of electrons from the B₀ atoms to the C₀ atoms. However, after 6-ZBNNR bonding with (6,6)SWCNT via edge-N atoms, the Mulliken charge analysis shows a charge of 2.807, 5.559, and 3.719 e on each edge-B, N₀, and C₀ atom, respectively, namely there is obvious transfer of electrons from the C₀ atoms to the N₀ atoms, showing that the N₀–C₀ band in 6ZBNNR-N-(6,6)SWNT approaches an ionic bond. As a result, nZBNNR-B-(6,6)SWNT is more stable than nZBNNR-N-(6,6)SWNT.

Fig. 9 (a) LDOS of the B₀ and C₀ atoms for 6ZBNNR-B-(6,6)SWCNT and (b) LDOS of the N₀ and C₀ atoms for 6ZBNNR-N-(6,6)SWCNT. The other marks are the same as in Fig. 2.

Table 6 The Mulliken charges on specific atoms in 6ZBNNR, (6,6)SWCNT, 6ZBNNR-B-(6,6)SWCNT and 6ZBNNR-N-(6,6)SWCNT

Atoms	Edge-B(B0)	Edge-N(N0)	C0	C1	C2
6ZBNNR	2.766	5.275
(6,6)SWCNT			4.000	4.000	4.000
6ZBNNR-B-(6,6)SWCNT	2.754	5.295	4.014	3.848	4.033
6ZBNNR-N-(6,6)SWCNT	2.807	5.559	3.719	3.946	4.008

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3.2.2 Hydrogen adsorption energy. On the other hand, the hydrogen adsorption energy per edge atom, which quantifies the gain in energy from the hydrogenation of hybrid structures of ZBNNR/SWCNT as compared to a pristine system and molecular hydrogen, is given by⁶⁸where, E_tot is the total energies of the hydrogenation system where the dangling bonds associated with edge C atoms are saturated with single H atoms and n_H is the total number of such H atoms. E_H2 is the energy of the hydrogen molecule and the factor of 2 in the last term accounts for the fact that each H₂ molecule only contributes one H atom to each initially unsaturated bond. E_pristine is the total energies of the pristine system, whereas, N_edge is the number of edge C atoms per unit cell. The calculated results for nZBNNR-B-(6,6)SWNT and nZBNNR-N-(6,6)SWNT are listed in Table 7. We note that negative hydrogen adsorption energies for all hybrid structures of ZBNNR/SWCNT are found in this work, which indicates that hydrogenation leads to an increase in the binding energy, namely hydrogen adsorption is favored.

Table 7 The hydrogen adsorption energy per edge atom in the unit of eV for H-nZBNNR-B-(6,6)SWNT and H-nZBNNR-N-(6,6)SWNT

System	n = 3	n = 4	n = 5	n = 6	n = 7	n = 8
H-nZBNNR-B-(6,6)SWNT	−2.95	−2.98	−2.84	−2.80	−2.79	−2.79
H-nZBNNR-N-(6,6)SWNT	−2.80	−2.80	−2.80	−2.81	−2.80	−2.80

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3.2.3 Ab initio MD simulations. In order to further examine whether hybrid structures of ZBNNR/SWCNT are stable at room temperature, ab initio MD simulations are performed. For example, at a simulation time of 6.0 ps, snapshots of the structures of 6ZBNNR-B-(6,6)SWNT, 6ZBNNR-N-(6,6)SWNT, H-6ZBNNR-B-(6,6)SWNT, and H-6ZBNNR-N-(6,6)SWNT are shown in Fig. 10. Clearly, although a small distortion is found at the B-edge or N-edge, the essential structures of 6ZBNNR-B-(6,6)SWNT, 6ZBNNR-N-(6,6)SWNT, H-6ZBNNR-B-(6,6)SWNT, and H-6ZBNNR-N-(6,6)SWNT are intact, namely, they are quite stable at room temperature. This is ascribable to their sp³-hybridized Y-shape and remaining tube-shape stability structures commonly used for building construction. On the other hand, comparing between Fig. 10(a) and (c), as well as Fig. 10(b) and (d), one can find that the distortion of the hydrogenation edge is less than that of the pristine edge, owing to H-passivation releasing the edge energy.

Fig. 10 At a simulation time of 6.0 ps, the top view and side view of the snapshots. (a) 6ZBNNR-B-(6,6)SWCNT, (b) 6ZBNNR-N-(6,6)SWCNT, (c) H-6ZBNNR-B-(6,6)SWCNT and (d) H-6ZBNNR-N-(6,6)SWCNT. The other marks are the same as in Fig. 1 and 3.

3.2.4 Fully spin polarized controlling by carrier doping. It is known that the Fermi level can be shifted up and down by altering the sign of the gate voltages (the well-known field-effect transistor (FET) doping technique). Therefore, in order to demonstrate that in 2ZBNNR-N-(6,6)SWCNT FET not only the excited electrons but also the holes can be fully spin polarized,⁵¹ we calculated the TDOS of 2ZBNNR-N-(6,6)SWCNT with x electrons added or removed per unit cell (x < 0 for electron doping, x = 0 for undoped, and x > 0 for hole doping). As shown in Fig. 11(b), when x = 0.0, both the electron and hole spins are not spin polarized. However, as shown in Fig. 11(a), when x = −0.4 (electron doping), the electrons are fully spin polarized. In contrast, as shown in Fig. 11(c), when x = 0.4 (hole doping), the holes are fully spin polarized. Clearly, such a novel phenomenon originates from the unique band structures of nZBNNR-N-(m,m)SWCNTs. In order to check the unique band structure of nZBNNR-N-(m,m)SWCNTs, an additional ab initio Heyd–Scuseria–Ernzerhof screened hybrid functional (HSE06 (ref. 69)) calculation has been carried out using the Quantum-ESPRESSO package.⁷⁰ The result shows that the unique band structure is robust with respect to the different treatments of electronic exchange and correlation even though the different treatments of electronic exchange and correlation lead to a quantitative difference in band structure (ESI Fig. 1†).

Fig. 11 TDOS of 2ZBNNR-N-(6,6)SWCNT with x electrons added or removed per unit cell (x < 0 for electron doping, x = 0 for undoped, and x > 0 for hole doping). The other marks are the same as in Fig. 2.

4 Conclusions

In summary, we have studied the hybrid structures of ZBNNR/SWCNT by using standard spin-polarized density functional theory calculations as well as ab initio molecular dynamics simulations. Several important results are summarized as follows:

1. All the examined hybrid structures are stable at room temperature.

2. The structure of ZBNNR-B-SWCNT is more stable than that of ZBNNR-N-SWCNT.

3. ZBNNR-B-SWCNT belongs to intrinsic ferromagnetic metals.

4. ZBNNR-N-SWCNT belongs to ferromagnetic intrinsic SGSs.

5. In H-ZBNNR-B-SWCNT, hydrogenation removes the dangling-bond states at its N-edge, whereas the electrically conductive function and magnetic properties of the “-SWCNT” edge remain unchanged. However, in H-ZBNNR-N-SWCNT, hydrogenation removes the dangling-bond states at its B-edge, but only the magnetic properties of the “-SWCNT” edge remain unchanged.

6. Hydrogenation induces a SGS–spin-semiconductor transition in the H-ZBNNR-N-SWCNT.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (grant no. 11174003) and the 211 Project of Anhui University.

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Footnote

† Electronic supplementary information (ESI) available: Supporting Fig. 1 showing the band structure of 2ZBNNR-N-(4,4)SWCNT calculated with the PBE functional and HSE06 hybrid functional, supporting Fig. 2 showing the relative energies for 2ZBNNR-N-(6,6)SWCNT in FM, AFM, and NM states, supporting Fig. 3 showing the relative energies for H-2ZBNNR-N-(6,6)SWCNT in FM, AFM, and NM states, supporting Fig. 4 showing the relative energies for 3ZBNNR-B-(6,6)SWCNT in FM, AFM, and NM states, and supporting Fig. 5 showing the relative energies for H-3ZBNNR-B-(6,6)SWCNT in FM and NM states. See DOI: 10.1039/c5ra08331a

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