Article
pubs.acs.org/JPCC
Electronic and Magnetic Engineering in Zigzag Graphene
Nanoribbons Having a Topological Line Defect at Different Positions
with or without Strain
Q. Q. Dai, Y. F. Zhu,* and Q. Jiang*
Key Laboratory of Automobile Materials, Ministry of Education, and Department of Materials Science and Engineering, Jilin
University, Changchun 130022, China
ABSTRACT: Using first-principles calculations, we perform a
comprehensive study of the locations of a topological line
defect (a line defect consisting of alternating pairs of pentagons
and octagons or 585 LD) on the electronic and magnetic
properties of zigzag graphene nanoribbon, with 12 zigzag
chains (12-ZGNR) with or without tensile strain (ε). When ε
= 0, it is found that 585 LD preferably forms near the edge. As
585 LD shifts from the center to the edge, the systems
experience transitions from antiferromagnetic (AFM) semiconductors to an AFM half-metal and then to a ferromagnetic
(FM) metal. As ε increases, the band gaps of the AFM
semiconductors decrease and then the AFM semiconductors change into AFM half-metals. Finally, all the AFM systems turn into
FM metals. The critical ε values of these transitions decrease as 585 LD moves to the edge. A similar behavior can also be found
in 8- and 16-ZGNRs. However, the AFM half-metal region disappears in 8- and 16-ZGNRs due to different variation tendencies
of the critical ε values for the electronic and magnetic phase transitions with the width of ZGNRs. These intriguing electronic and
magnetic modulation behaviors make such defective ZGNRs very useful in nanoelectronic and spintronic devices.
1. INTRODUCTION
Low-dimensional carbon-based nanomaterials, such as graphene and graphene nanoribbons (GNRs), have attracted
considerable attention in recent years due to their extraordinary
physics and promising applications in future nanoelectronics.1,2
Nevertheless, various applications of graphene and GNRs
require that their electronic properties can be properly
modulated at nanoscale. A general method is chemical
functionalization or doping, which has been widely investigated
using various techniques.3−6 Because the electronic properties
of graphene and GNRs originate from their specific structures,
the lattice modification at the atomic level is essentially needed
to tune their electronic structures.1,2 Indeed, introducing
topological defects of nonhexagonal rings in the honeycomb
lattice is an effective way to tailor the local properties of
graphene-based nanomaterials and to achieve new functionalities for suitable applications. Theoretically, such topological
defects are predicted to change not only the electronic
structures, 7−14 but also the chemical activity 15,16 and
thermal17−19 properties. For example, topological defects in
graphene can be used as the centers of chemical activity. Many
transition metal atoms can form covalent bonds with the
defects, which change the electronic properties of graphene by
charge injection from metal atoms and point to a possible
application of such composite structures in catalysis.16
The topological defects are usually characterized by
pentagonal and heptagonal rings in the hexagonal carbon
lattice (for instance, Stone-Wales and 555−777 defects), which
© 2013 American Chemical Society
can appear during growth process and be deliberately
introduced by ion irradiation.20−22 Furthermore, diffusion,
coalescence, and reconstruction of these nonhexagonal rings
have been studied by both theoretical and experimental
techniques.22−25 In addition to the point defects, the extended
line defect (LD) composed of alternating pentagon-heptagon
(5−7) structure has also been observed during chemical vapor
deposition growth on Cu substrate.25−29 And this 5−7 LD has
been confirmed to have enormous influences on the
mechanical29−31 and electronic7−10,32,33 properties of graphene-based materials. In particular, when the linear array of
5−7 rings are embedded in GNRs, the hybrid GNRs consisting
of both armchair- and zigzag-like segments are formed and
predicted to possess unique electronic and transport properties
that differ from the pristine zigzag and armchair GNRs.9−11
Just recently, Lahiri et al. discovered that by using Ni(111)
surface as a substrate, a new LD can be formed when two
graphene sheets with different crystallographic orientations are
translated to each other and then coalesce.34 Differing from the
previous 5−7 LD, this topological defect consists of a line of
alternating pairs of pentagons and octagons (585 LD), which
can act as a conducting metallic wire when embedded in the
perfect graphene.34 By engineering the topological LD,
localized electronic states are introduced at Fermi level (EF)
Received: July 11, 2012
Revised: February 13, 2013
Published: February 15, 2013
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Figure 1. (a−f) Optimized structures of N-585-M systems. The gray and white balls denote carbon and hydrogen atoms, respectively. (g) Total
energies of the N-585-M systems by choosing the energy of 6-585-6 system as a reference. The solid line serves as a guide to the eye.
ZGNRs) are adopted. Here, we mainly present the calculated
results of 12-ZGNR with 585 LD because the other two
defective ZGNRs display the similar behaviors. For 12-ZGNR
with 585 LD, pentagon pairs and octagon are arranged
alternatively along the ribbon axial direction, as shown in
Figure 1a−f. Such defective ZGNR can be considered as two
ZGNR parts connected by C−C dimer lines. As shown in
Figure 1a, when the C−C dimer lines are placed at the middle
part of the 12-ZGNR (6 zigzag chains on both sides of C−C
dimer lines), 585 LD locates at the center of ZGNR. The
position of 585 LD is changed by gradually moving the C−C
dimer lines to the left edge of 12-ZGNR. Figure 1f represents
the limit case. Here we denote the 12-ZGNR with 585 LD as
N-585-M, where N and M are the number of zigzag chains on
the left and right sides of the C−C dimer lines, respectively.
The dangling bonds at both edges are saturated by hydrogen
atoms for all systems.
The first-principles DFT calculations are performed using the
CASTEP package47 with generalized gradient approximation
(GGA) and Perdew−Burke−Ernzerhof (PBE) 48 as the
exchange correlation function. Ultrasoft pseudopotentials49 is
chosen for the spin-unrestricted computations. The Brillouin
zone is sampled by 1 × 6 × 1 (1 × 10 × 1) k-points50 and the
energy cutoff of 400 eV is chosen in the geometry optimization
(electronic) calculations. The nearest distance between nanoribbons in neighboring cells is greater than 18 Å to ensure no
interactions. For geometry optimization, both the cell in the
axial direction and the atomic positions are allowed to fully
relax until the convergence tolerances of energy, maximum
force, and displacement of 1 × 10−5 eV, 3 × 10−2 eV/Å, and 1
× 10−3 Å are reached, respectively. Based on the optimized
structures, the tensile ε along the ribbon axis direction is
realized by modulating the corresponding lattice parameters.
Under different ε, only the atomic positions are relaxed to find
the equilibrium states.
and the charge distribution within the defect regions can be
created and well controlled.35−38 Especially, when 585 LD is
introduced in graphene and carbon nanotubes, these systems
exhibit ferromagnetic ordering consisting solely of 3-fold
coordinated C atoms without carrier doping or network
termination imposed by vacancies or edges.35,36 This suggests
such defective carbon nanomaterials as promising candidates
for applications in future spintronic nanodevices. However, to
our knowledge, there has been hardly any systemic work
studying the influence of 585 LD on GNRs in detail.
On the other hand, graphene samples grown on substrates
are subjected to moderate mechanical strain due to surface
corrugation or lattice mismatch.39−41 This mechanical
deformation can affect the electronic properties of graphene
materials and thus have significant impact on their device
applications. Previous theoretical studies have demonstrated
that the application of external strain provides a simple and
practical method to continuously tune the electronic properties
of graphene-based materials.42−46 For example, the band gap of
armchair GNRs can change in a zigzag manner under uniaxial
strain.42−44 For bilayer graphene, an interlayer electric field can
be generated by applying homogeneous strains with different
strengths, thereby opening a band gap.45 These suggest a
maneuverable approach to fabricate electromechanical devices
based on carbon nanomaterials. Accordingly, it is also
significant to gain physical insight into the effect of external
strain on the electronic structures of GNRs with 585 LD.
In this contribution, we employ first-principles density
functional theory (DFT) calculations to investigate the effects
of the position of 585 LD relative to the edge on the electronic
and magnetic properties of zigzag GNRs (ZGNRs). Meanwhile,
the influences of the defect location on these properties under
tensile strain (ε) have also been considered, which demonstrate
a significantly different characteristic from the pristine ZGNRs.
2. COMPUTATIONAL METHODS
For ZGNR, the ribbon width (W) is defined by the number of
zigzag chains perpendicular to the axial direction. In our
simulation, the ZGNRs with W = 8, 12, and 16 (8-, 12-, and 16-
3. RESULTS AND DISCUSSION
Previous theoretical studies have demonstrated that the pristine
ZGNRs exhibit an antiferromagnetic (AFM) ground state.51,52
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Figure 2. (a−f) Band structures of N-585-M systems. Black and red lines denote spin up and down energy bands, respectively (The color used to
distinguish the spin energy band is also applicable to other figures below). The Fermi level (EF) is set to zero, and the first conduction (valence)
band above (below) the EF is labeled as C1 (V1). The Eg values for the N-585-M systems are given below their corresponding band structures.
Figure 3. (a) Charge density isosurfaces of bands C1 and V1 for spin up and down states for 5-585-7 system. (b) Total DOS and PDOS of 5-585-7
system. Black, blue and red dotted lines denote the total DOS of the whole system, the PDOS of the defect site and the edge atoms, respectively.
The EF is set to zero. (c) Charge density isosurfaces of bands C1 and V1 for spin up and down states for metallic system 1-585-11. The value of the
isosurfaces is 0.02 e/Å3.
However, when 585 LD is introduced, the corresponding
ground state may be influenced. To find the most stable
magnetic configurations, the energies of ferromagnetic (FM)
and AFM states for the 6-585-6, 5-585-7, 4-585-8, 3-585-9, 2585-10, and 1-585-11 systems are calculated. The calculated
energy differences (ΔE = EFM − EAFM) between FM and AFM
states for the six systems are 9.80, 9.37, 6.76, 3.51, 1.83, and
−0.26 meV, respectively. This indicates that the position of 585
LD has a great effect on the magnetic configurations of the N585-M systems. As 585 LD moves from the center to the left
edge, the systems experience a transition from AFM (for 6-5856, 5-585-7, 4-585-8, 3-585-9, and 2-585-10 systems) to FM (for
1-585-11 system) state.
Based on the calculated ground states, the relative stability of
these N-585-M systems is investigated. As shown in Figure 1g,
we compare their total energies by choosing the energy of 6585-6 system as a reference. The result shows that as 585 LD
shifts away from the center to the left edge of 12-ZGNR, the
total energies of these N-585-M systems become more and
more negative. Especially, there is a large drop in energy from
3-585-9 to 1-585-11 system, which indicates that 585 LD
prefers forming near the edge. Furthermore, as 585 LD moves
toward the left edge, the lattice parameters in axial direction
increase gradually, which are 4.9088 Å for 6-585-6, 5-585-7, 4585-8, and 3-585-9 systems, 4.9118 Å for 2-585-10 system, and
4.9178 Å for 1-585-11 system, respectively.
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to the reduction of Eg for the semiconducting N-585-M
systems.
For the metallic system 1-585-11, partial of the electronic
states near the EF exhibit distinct characteristics compared with
other systems. As shown in Figure 3c, the electronic
distribution for the spin down state of C1 is only localized on
the right edge of ZGNR, which differs from the corresponding
electronic states of the other systems that are contributed by
585 LD. It can also be seen from Figure 2f that this energy band
displays an edge state character as that in pristine ZGNR. The
electronic distribution for the spin up state of V1 is
concentrated on both of the defect site and right edge of
ZGNR, which are also different from other systems. For the
spin up state of C1, the electron states distribute on the two
edges and defect site. For the spin down state of V1, the
electron states mainly distribute on the left edge and defect site.
As shown in Figure 2f, the two energy bands show a similar
trend and cross the EF around the Γ point, which lead to a
metallic character of the 1-585-11 system.
Previous theoretical studies have shown that when 585 LD is
embedded in graphene sheet or armchair carbon nanotubes, the
polarized electron spins are strongly localized on the atoms
connected to the C−C dimers and ferromagnetically aligned
along the extended LD.35,36 However, when 585 LD is
introduced in ZGNR, the spin ordering along the defect
exhibits different characteristics. As shown in Figure 4a and b,
Due to the existence of edges, the electronic properties of N585-M systems exhibit unusual features differing from the
metallic character of graphene with 585 LD.34,35 Figure 2a−f
displays the band structures of the six N-585-M systems. It can
be seen that the band structures of N-585-M systems vary with
the different locations of 585 LD in ZGNR. The energy bands
of 6-585-6 system for both spins are degenerate, whereas for
other N-585-M systems, the energy bands near the EF split into
two subbands (spin up and spin down) and exhibit some
deformation. When 585 LD moves gradually to the left edge,
the degree of splitting and deformation becomes stronger. As
shown in Figure 2a−d, the four systems of 6-585-6, 5-585-7, 4585-8, and 3-585-9 are semiconductors with indirect band gaps
(Eg). The conduction band minimum (CBM) for 6-585-6 and
5-585-7 systems locates at gamma (Γ) point, but deviates from
Γ point for 4-585-8 and 3-585-9 systems. In contrast, the
valence band maximum (VBM) keeps unchanged and always
locates at A point. The relevant Eg values of these semiconducting N-585-M systems are given under each diagram.
For 6-585-6 system, Eg = 0.16 eV. As 585 LD shifts away from
the center, the Eg values for the four semiconductors decrease
gradually. Compared with the calculated Eg value of pristine 12ZGNR (0.40 eV), the Eg values for these four semiconducting
systems drop due to the 585 LD introduced impurity states
near the EF (which will be discussed later). When 585 LD
locates near the edge, the electronic properties of the two
systems 2-585-10 and 1-585-11 exhibit interesting behaviors.
The 2-585-10 system displays a half-metallic character, where
the spin up and down states show the semiconducting and
metallic behaviors, respectively, as shown in Figure 2e.
However, for the 1-585-11 system, there is no Eg opening for
both spin up and down states and, thus, it shows a metallic
behavior (see Figure 2f). Moreover, the energy bands of this
system change dramatically near the EF compared to other N585-M systems.
To better understand the electronic states of these systems
near the EF, the charge density isosurfaces of the conduction
band C1 and valence band V1 for both spins have been
analyzed. For the four semiconducting systems and the halfmetallic system 2-585-10, the electronic distributions of bands
C1 and V1 for both spins display similar behaviors. Here, we
take the system 5-585-7 as an example. As shown in Figure 3a,
the spin down state of V1 is contributed by the defect site and
right edge, and the spin up state of C1 is only contributed by
the defect site, where the Eg of this system is determined by the
two subbands. For the spin up state of V1, the electronic states
mainly distribute on the left edge and defect site. As 585 LD
moves close to the left edge, this band exhibits serious
deformation, which indicates that a strong interaction exists
between the left edge and defect site. Similar to the spin up
state of C1, the electronic distribution for the spin down state of
C1 also lies mainly on the atoms connected to the C−C dimers.
For perfect ZGNRs, the electronic states near the EF are
contributed by the two edges.51,52 When 585 LD is introduced
in the ZGNR, the impurity states appear near the EF. The total
and partial density of states (PDOS) for 5-585-7 system are
plotted in Figure 3b, which also shows that the electronic states
near the EF are determined by both the 585 LD and the two
edges of ZGNR. It is well-known that the Eg of perfect ZGNR
is determined by the two peaks marked by the red dashed lines
near the EF. The PDOS shows that the 585 LD introduces
impurity states within the Eg of the perfect ZGNR, thus leading
Figure 4. (a−c) Isosurfaces of the spin density distribution (Δρ = ρ↑
− ρ↓) for 6-585-6, 5-585-7, and 1-585-11 systems. Blue and yellow
surfaces correspond to the isosurfaces of up (positive) and down
(negative) spin density (the spin-polarized color identification scheme
is also used in other figures below). The value of the isosurfaces is
0.005 e/Å3.
the two edges of ZGNR are still antiferromagnetically coupled,
which is similar to the case of perfect ZGNRs.51−53 The
magnetism on the atoms connected to the C−C dimers are
antiferromagnetically aligned which can be ignored compared
to those on the two edges. Since the ZGNR with 585 LD can
be considered as a combination of two ZGNR parts by an array
of C−C dimers, the atoms connected with the C−C dimers are
antiferromagnetically coupled with their corresponding left and
right edges, respectively. The calculated results demonstrate
that the four semiconducting systems and the half-metallic
system 2-585-10 possess a similar magnetic ordering and their
total magnetic moments are zero. However, for the metallic
system 1-585-11 displayed in Figure 4c, the magnetic alignment
on the two edges of the system become FM ordering, and the
magnetism on the left edge (0.08 μB per C atom) is weaker
than that on the right edge (0.33 μB per C atom), which makes
a total magnetic moment of 0.88 μB for this system.
Note that when 585 LD is shifted to the right edge of 12ZGNR, a similar effect of the defect location on the electronic
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Figure 5. (a) Energy difference (ΔE) between FM and AFM states versus tensile ε for the N-585-M systems, where the dashed line denotes the zero
energy difference. The solid circles, triangles, stars, squares, inverted triangles, and rhombus represent the ΔE of the systems 6-585-6, 5-585-7, 4-5858, 3-585-9, 2-585-10, and 1-585-11, respectively. (b) Spatial spin density distribution of the 5-585-7 system under the tensile ε of 1.0, 2.0, and 5.0%.
The value of the isosurfaces is 0.005 e/Å3. (c) Total magnetic moments for the N-585-M systems. The symbols represent the same systems as in (a).
Figure 5b, at the AFM state (ε = 1.0%), the spin ordering is
antiferromagnetically coupled between the two edges, but
ferromagnetically coupled along the C atoms connected to the
C−C dimers. And the total magnetic moment is little. When ε
≥ 1.9%, the magnetic configuration of this system becomes FM
state, in which the magnetic coupling between the two edges
changes from antiparallel to parallel. The atoms connected to
the C−C dimers are still ferromagnetically aligned, but are
antiferromagnetically aligned with their corresponding left and
right edges, respectively. Moreover, the spin densities on the
two edges and 585 LD increase with increasing ε, which is
consistent with the enhanced stability of the FM state as
discussed above. The spin ordering of the system 2-585-10 at
FM state is similar to that of the 5-585-7 system. For the
metallic system 1-585-11, the spin ordering on the defect site
transforms from antiferromagnetically to ferromagnetically
coupled when ε ≥ 5.0%, while on the two edges remain
ferromagnetically coupled.
The total magnetic moments of all the N-585-M systems
under ε are presented in Figure 5c. The calculated results
demonstrate that the magnetism is mainly contributed by the
two edges and 585 LD, and the magnetic moments on the two
sites increase slowly as ε increases, but the total magnetic
moments of these systems change little (0.9−1.1 μB).
For pristine ZGNRs, Eg increases monotonously with tensile
ε.42−44 However, when 585 LD is introduced, the electronic
properties of N-585-M systems under tensile ε display different
behaviors. For the two systems 2-585-10 and 1-585-11, there is
still no Eg opening within the range of the applied tensile ε. The
insensitivity of Eg with respect to ε suggests that the two
metallic systems can act as the conducting wires in graphenebased electronics. For the semiconducting systems, the tensile ε
and magnetic properties can be found. Thus, we will neglect
that case here.
In general, graphene materials corrugate under compressive
ε,53,54 which would affect their electronic properties. However,
the size of the unit cell that is tractable in DFT calculations is
too small to capture any long-range corrugations. Therefore, we
next only investigate the influences of tensile ε on the magnetic
and electronic properties of these N-585-M systems.
Under tensile, ε, pristine ZGNRs always keep the AFM state
as in the unstrained case.42−44 However, when 585 LD is
introduced, a different magnetic behavior is found. Figure 5a
gives the ΔE values of N-585-M systems as a function of ε. For
the four semiconducting systems, when ε = 0, ΔE > 0 and their
ground states are AFM configurations. As ε increases, ΔE
decreases gradually. Then, at the critical ε (εc) of 2.0, 1.9, 1.8,
and 1.2%, the AFM−FM transitions take place with ΔE < 0 for
the four systems, respectively. And it is clear that the εc for this
magnetic transition decreases gradually as 585 LD shifts away
from the center. Further increasing tensile ε will lead to the ΔE
more negative, which indicates that the FM states for these
systems become more stable. For the half-metallic 2-585-10
system in the unstrained case, the ground state favors AFM
configuration. When ε ≥ 0.7%, this system changes into the FM
state. And the absolute values of ΔE are slightly larger than
those of the system 3-585-9 at FM state (see Figure 5a). Note
that the metallic system 1-585-11 remains FM configuration
under ε = 1.0∼4.0% with ΔE values of −0.7∼−2.5 meV.
Further increasing ε does not change the FM ground state even
though the initial spin configuration is set as the AFM state.
For the four semiconducting systems, the magnetic alignments on the edges and the defect site under ε are similar.
Here, we use the system 5-585-7 as an example. As shown in
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Figure 6. Spin polarized band structures of the systems (a) 6-585-6 under ε = 1.0, 1.7, and 1.9%; (b) 5-585-7 under ε = 1.0, 1.7, and 1.8%; (c) 4-5858 under ε = 1.0, 1.5, and 1.7%; and (d) 3-585-9 with ε of 0.4 and 1.0%. The EF is set to zero.
always reduces Eg to zero rapidly, where a transition from
semiconductor to half-metal appears. The corresponding εc
values for the electronic phase transition are 1.7, 1.7, 1.5, and
0.4% for the 6-585-6, 5-585-7, 4-585-8, and 3-585-9 systems,
respectively. Further increasing tensile ε will make these AFM
half-metallic systems turn into FM metals quickly.
To better understand the effects of tensile ε on the electronic
properties of N-585-M systems, spin-polarized band structures
are calculated. We first discuss the cases of the four
semiconducting systems. At the AFM state, the locations of
VBM and CBM of 6-585-6 and 5-585-7 systems are the same as
their unstrained cases until the zero gap points, as shown in
Figure 6a,b. The band C1, which is completely contributed by
585 LD, is very flat and splits into a small band gap between the
spin up and down bands around the Γ point. This is similar to
the edge states of pristine ZGNRs51,52 and closely associated
with the ferromagnetic ordering along the defect site discussed
above.35,36 For the 4-585-8 system, the locations of VBM and
CBM under tensile ε of 1.0% remain invariant. The C1 band for
both spins is still degenerate around Γ point, which implies that
the spin ordering on the defect site is still antiferromagnetically
coupled. However, as ε further increases, the CBM moves to
the Γ point, the VBM keeps unchanged, and the band C1
exhibits a similar characteristic of the systems 6-585-6 and 5585-7 (Figure 6c). For the 3-585-9 system, the locations of
VBM and CBM as well as C1 do not change until the zero gap
with ε = 0.4%. As ε reaches 1.0%, the C1 band change is the
same as the systems 6-585-6 and 5-585-7, where the magnetic
alignment along the defect becomes ferromagnetically coupled.
When the four systems become AFM half-metals, the spin up
and down channels show semiconducting and metallic
behaviors, respectively, as shown in Figure 6.
For the four systems at FM state, the bands near the EF
experience stronger spin splitting, as shown in Figure 7a,b. The
electronic distributions of the bands near the EF show that the
α and β bands are completely contributed by the defect atoms
(Figure 7c,d). Around the Γ point, the two bands are very flat
and separated by a gap. These characteristics are similar to the
edge states of pristine ZGNRs and related with the
ferromagnetic ordering along the defect site.35,36 Moreover,
the gap between bands α and β around the Γ point broadens
with the increased tensile ε, which is associated with the
enhanced magnetism on the defect atoms.55 The distribution of
energy bands for the system 2-585-10 near the EF under ε is
similar to the 5-585-7 system at FM state, which is not further
discussed here. For the metallic system 1-585-11, the band
structures change little under the applied ε, which only involves
rising and falling of the bands near the EF.
As 585 LD moves from the center to the edge, the electronic
and magnetic transitions of 12-ZGNR versus tensile ε are
summarized in Figure 8b. Meanwhile, the cases of 8- and 16ZGNRs are also displayed in Figure 8a and c, respectively. In
the unstrained case, as 585 LD shifts from the center to the
edge, 8-ZGNR and 16-ZGNR also experience the transitions
from semiconducting to half-metallic and then to metallic
(Figure 8a,c). However, AFM configuration is always present
for 8-ZGNR even if 585 LD is located at the edge (Figure 8a).
Under tensile ε, the Eg values of all the semiconducting systems
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metals, where the semiconductor−half-metal transition is
absent. To understand this phenomenon, Figure 8d shows εc
for the semiconductor−half-metal and AFM−FM transitions as
functions of the W of ZGNRs when 585 LD locates at the
center. It can be seen that as W increases, εc values decrease
nonlinearly. When W lies between 10 and 14, the AFM halfmetal regions are present. However, when the W value is
smaller than 10 or larger than 14, εc values for the electronic
phase transition are higher than those of the magnetic
transition, which make the semiconductor−half-metal transition disappear. Further, increasing the tensile ε to 5.0%, these
systems remain the FM metallic, being similar to 12-ZGNR.
As discussed above, the position of the 585 LD in ZGNR
decides the intriguing electronic and magnetic properties and
should be well controlled. It is known that the graphene with
585 LD can be formed by translating two graphene sheets with
different arrangements relative to each other along the armchair
direction34,56 or be realized by reconstruction from an array of
divacancies,14,57 while a ZGNR can be cut from the graphene
sheet by scanning tunneling lithography.58,59 Thus, through
selecting the cutting location, the position of 585 LD in the
ZGNR can be controlled. On the other hand, it is noteworthy
that such 585 LD in BN nanoribbon is established by
implanting C2 (or N2 or B2) dimers into a double hexagonal
between the two ribbon domains.36,38 Because ZGNR has the
same structure of BN nanoribbon, this technique could be
introduced into ZGNR to design the position of 585 LD in
ZGNR.
Figure 7. Spin polarized band structures of the system 5-585-7 under
tensile ε (a) 2.0 and (b) 5.0%. The EF is set to zero. Charge density
isosurfaces of bands α (c) and β (d) that are labeled in (a). The value
of the isosurfaces is 0.02 e/Å3.
4. CONCLUSION
In summary, the effects of 585 LD locations on the electronic
and magnetic properties of 12-ZGNRs with or without tensile ε
for both 8- and 16-ZGNRs also decrease gradually. However, Eg
is always larger than zero before the two ZGNRs become FM
Figure 8. Magnetic and electronic phase transitions for the defective (a) 8-, (b) 12-, and (c) 16-ZGNR vs tensile ε as 585 LD moves from the center
to the left edge. (d) The variations of εc values for the semiconductor−half-metal (red circles) and AFM−FM (black squares) transitions with the W
of ZGNRs when 585 LD locates at the center.
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are systematically investigated using DFT calculations. The
results show that the position of 585 LD affects significantly the
electronic and magnetic properties of ZGNRs. Without ε, the
585 LD prefers to form near the edge. As 585 LD moves from
the center to the edge, the systems experience transitions from
AFM semiconductors to an AFM half-metal and then to a FM
metal. The AFM semiconductors have indirect band gaps,
which gradually decrease as 585 LD shifts close to the edge. By
increasing tensile ε, Eg values of all the AFM semiconducting
systems decrease and AFM semiconductors−AFM half-metal−
FM metal transitions occur. However, for defective 8- and 16ZGNRs, there do not exist AFM half-metal regions before
becoming FM metals because the εc values for the magnetic
and electronic phase transitions display nonlinear decreasing
trends with increased W of ZGNRs. Our work provides
fundamental guidance for finding potential applications of such
defective ZGNRs in the spintronic and electromechanical
devices.
■
AUTHOR INFORMATION
Corresponding Author
*Tel./Fax: 86-431-85095876. E-mail: [email protected];
[email protected].
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
We acknowledge support by National Key Basic Research,
Development Program (Grant No. 2010CB631001), and High
Performance Computing Center (Jilin University).
■
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