First-principles study on the electronic and transport properties of periodically nitrogen-doped graphene and carbon nanotube superlattices

0.53 MB·

by  Fuming Xu

First-principles study on the electronic and transport properties of periodically
nitrogen-doped graphene and carbon nanotube superlattices
Fuming Xu,1 Zhizhou Yu,2,3,∗ Zhirui Gong,1 and Hao Jin1
1College of Physics and Energy, Shenzhen University, Shenzhen 518060, China
2School of Physics and Technology, Nanjing Normal University, Nanjing 210023, China
3Department of Physics and the Center of Theoretical and Computational Physics,
The University of Hong Kong, Hong Kong, China
7
Promptedbyrecentreportson√3 √3graphenesuperlatticeswithintrinsicinter-valleyinterac-
1
×
0 tions,we perform first-principlescalculations toinvestigatetheelectronic propertiesof periodically
2 nitrogen-dopedgrapheneandcarbon nanotubenanostructures. Inthesestructures,nitrogen atoms
substituteone-sixthofthecarbonatomsinthepristinehexagonallatticeswithexactperiodicityto
n form perfect √3 √3 superlattices of graphene and carbon nanotubes. Multiple nanostructures of
a √3 √3graphen×eribbonsandcarbonnanotubesareexplored,andallconfigurationsshownonmag-
J ×
netic and metallic behaviors. The transport properties of √3 √3 graphene and carbon nanotube
7 ×
superlatticesarecalculatedutilizingthenon-equilibriumGreen’sfunctionformalismcombinedwith
1 density functional theory. The transmission spectrum through the pristine and √3 √3 armchair
×
carbon nanotubeheterostructureshows quantized behavior undercertain circumstances.
]
l
al PACSnumbers: 73.22.-f,73.63.-b,81.05.Zx,71.15.Mb
h
-
s I. INTRODUCTION discussed on tight-binding level31. A valley-field-effect-
e
transistorcontaining √3 √3 armchairCNTs with out-
m
×
As the firstartificiallyfabricatedtwo-dimensionalma- standing device functionality was presented in Ref. [31].
.
t terial, graphene exhibits extraordinary properties and is Nitrogen doping has been widely used in laboratory
a
m potentially suitable for a wide range of applications1–9. settings in an attempt to improve the carrier density
The honeycomb lattice provides the Bloch electrons andconductivity ofgraphenesystems32–34. Selective ad-
-
d in graphene a new degree of freedom, valley, which sorption of ammonia molecules at the edges of zigzag
n can be manipulated to store and process binary graphene nanoribbons has been achieved35, which offers
o information10–13. Therefore, graphene has been exten- opportunities for the precise control of dopant positions
c sively studied as a promisingvalleytronic material. Mul- in graphene systems. Hypothetically, if the dopant ni-
[
tiple setups have been proposed that utilize the intrinsic trogen atoms can be precisely controlled to periodically

1 characteristicsofgraphenenanostructures,suchaszigzag locate in the host graphene lattice, a favorablegraphene
v edges14, 5-7-5 line defects15–18, zero-line modes19–21, or superlatticewithintrinsicinter-valleyinteractionsiscon-
5 via extrinsic methods, such as strain engineering22–25 structed. Considering the substitution case, and taking
3 andtemperature-gradientdriving26,27,totunethevalley- the representative √3 √3 superlattice as an example,
5 ×
4 relatedcurrentsthroughgraphene-basednanostructures. nitrogen atoms will substitute one-sixth of the carbon
0 Recently,itwasfoundthatgraphenesuperlatticeswith atoms at the same positions in each honeycomb ring, as
. certain periodicities possess intrinsic inter-valley inter- illustrated in Fig.1. At present, it is difficult to realize
1
actions. For instance, theoretical work revealed that this structure; however, first-principles calculations can
0
7 in √3N √3N and 3N 3N graphene superlattices, elucidate the properties of the material in advance.
× ×
1 the band folding merges the valley degree of freedom Inthisarticle,wepresentfirst-principlesinvestigations
: inpristine graphene,anduniversalinter-valleycouplings onthe electronic propertiesof typical√3 √3graphene
v naturally arise28. Similar to the role of spin-orbit cou- and single wall CNT superlattices with ×periodic nitro-
i
X plinginspintronics,theinter-valleyinteractioncanserve gen dopants. The electronic band structures of multi-
r as valley-orbit couplings to effectively process the val- ple graphene ribbons and single wall CNT superlattices
a
ley information, which qualifies these graphene super- with typical zigzag and armchair chiralities are studied,
lattices as prospective valley-processing units in future including three types of zigzag ribbons, two types of
integrated valleytronic circuits. It was suggested that armchair ribbons, as well as zigzag and armchair tubes.
these graphene superlattices could be realized through All these superlattice nanostructures exhibit nonmag-
top-absorptionorperiodicaldopingonpristinegraphene. netic and metallic characteristics. The nitrogen-doped
Moreover, the latest investigations found that, owing to graphene ribbons have intrinsic band gaps of finite-size
the proximity effect, graphene on top of a topological- nature, and a flat band resides in the bulk gap in two
insulator substrate naturally shows these types of su- types of zigzag ribbons. The zigzag tube superlattice
perlattice patterns29,30. Based on the effective Hamilto- has a tiny energy gap at small system sizes, while no
nianproposedinRef.[28],theelectronicandvalleytronic band gap exists in armchair nanotubes. The transport
properties of multiple graphene and carbon nanotube properties of heterostructures consisting of pristine and
(CNT) nanostructures with √3 √3 superlattice were √3 √3grapheneribbonsandCNTsareexplored,adopt-
× ×
2
ingthenon-equilibriumGreen’sfunctionformalismcom-
bined with density functional theory. The transmission
spectra are spin dependent only near the transmission
gap in the case of zigzag graphene ribbons. Moreover,
a quantizedtransmissionplateauoccursin the transmis-
sion spectrum of a metallic armchair CNT heterostruc-
ture.
The rest of the paper is organized as follows. In Sec-
tion II, we introduce the computational details as well
as the geometricalstructures of multiple nitrogen-doped
graphene nanoribbons and CNTs with √3 √3 super-
×
lattice, which will be investigated in the electronic and
transport calculations. In Section III, we present the
electronic structures of these graphene nanoribbons and
CNTs superlattices, and their transport properties are FIG. 1. Top views of the geometric structures of (a) 2-
outlined. Finally, a brief summary of the main results is dimensional nitrogen-doped graphene superlattice, (b) 12-
providedinSectionIV.Forsimplicity,werefertothepe- zigzag ribbon (ZGR1), (c) 12-zigzag ribbon (ZGR2), (d) 12-
riodically nitrogen-dopedgraphene with √3 √3 super- zigzag ribbon (ZGR3), (e) 18-armchair ribbon (AGR1), and
× (f) 18-armchair ribbon (AGR2). The nanoribbons are ex-
lattice as nitrogen-doped graphene or √3 √3 graphene
× tendedperiodically along they direction,asindicated bythe
superlattice in the following text. Similar abbreviations
blue arrows. The white, gray, and blue balls represent the
also apply for the CNT case.
hydrogen,carbon, and nitrogen atoms, respectively.
II. COMPUTATIONAL METHODS AND ofzigzagand armchairnitrogen-dopedgraphene ribbons
GEOMETRIC MODELS
are denoted by the numbers of zigzag chains (N in
z
Fig. 1(b)) and dimmer lines (N in Fig. 1(e)) across the
a
To investigate the structural and electronic proper- ribbon width, respectively. For instance, N = 12 in
z
ties of √3 √3 graphene and CNT superlattices, first- Fig. 1(b) and N =18 in Fig. 1(e).
a
×
principles calculations are performed on a plane-wave Figure 1(b) presents the geometric structures of the
basis with the projector augmented wave (PAW)36 to 12-zigzag ribbon cut directly from the graphene super-
modeltheelectron-ioniccoreinteraction,asimplemented lattice,whichconsistsofsixdimmer linesalongthe peri-
intheViennaAbinitioSimulationPackage(VASP)37,38. odical direction in one supercell. Nitrogen atoms locate
The exchange and correlation interactions are approxi- on both zigzag edges in this configuration, which we re-
matedbythegeneralizedgradientapproximation(GGA) fer to as ZGR1. The calculation of total energy suggests
withthePerdew-Burke-Ernzerhof(PBE)functional39. A that the geometry of ZGR1 was less stable owing to the
plane-wavebasissetwithakineticenergycutoffof400eV presence of the nitrogen atoms on both edges. There-
is employed. In the calculations, 10 Monkhost-Pack k- fore, we constructe two different configurations of zigzag
pointsareusedalongthe1-dimensionalBrillouinzonefor graphene ribbons by substituting nitrogen atoms with
thezigzaggrapheneribbonsandarmchairCNTs,while8 carbon atoms along one edge of ZGR1 to form one pure
k-points are sampled for the armchair graphene ribbons carbon edge. We refer to these two structures as ZGR2
andzigzagCNTs. Allatomsinthe supercellarefullyre- andZGR3, as showninFigs. 1(c) and 1(d), respectively.
laxed with a residual force less than 0.02 eV/˚A, and the The molar Gibbs free energy of formation42,43 of ZGR3
total energies are converged to 10−5 eV. The transport from our first-principles calculationis 11 meV/atom less
properties of the two-probe systems are investigated us- than that of ZGR1, and 8 meV/atom lower than that
ing NanoDcal, which is a first-principles package within of ZGR2. This fact proves that ZGR3 is the most stable
the non-equilibrium Green’s function formalism40. The configurationofzigzagnitrogen-dopedgrapheneribbons.
double ζ plus polarization numerical orbital basis set is Similarly, two different configurations of armchair rib-
used. The mesh cutoff is set to be 3,000 eV and the bons of graphene superlattice, referred to as AGR1 and
convergence of the total energies is 10−5 eV. AGR2, are presented in Figs. 1(e) and 1(f), respectively.
Figure 1(a) shows the primitive cell of the bulk AGR2ismorestablesinceitstotalenergyis6meV/atom
√3 √3 graphene superlattice, which contains five car- lessthanthatofAGR1. WhenwrappingAGR1orAGR2
×
bon atoms and one nitrogen atom. The optimized in- withthesameribbonwidth,twoidenticalzigzagCNTsu-
plane lattice constant in our calculation is 4.22 ˚A. The perlatticesareobtained. Meanwhile,a√3 √3armchair
×
models of graphene ribbons are constructed by cutting CNT is realized by rolling up ZGR1. These CNT super-
the 2-dimensional bulk graphene superlattice with dif- lattices have the same chemical composition as the bulk
ferent edges and widths. All nanoribbons are hydrogen nitrogen-doped graphene except for the terminal hydro-
terminated in the calculations. According to the pre- genatoms,andwedenotethembyapairofindices(n,m)
vious studies of pristine graphene ribbons41, the widths as those used for pristine CNTs44,45. The spin degree of
3

(a) 1 (b) 1
V) 0 V) 0
e e
y ( y (
g -1 g -1
er er
n n
E E
-2 -2
-3 -3
X X X X

(c) 1 (d) 1
V) 0 V) 0
e e
y ( y (
erg -1 erg -1
n n
E E
-2 -2
FIG. 2. Two-probe configurations of (a) 12-zigzag nitrogen- -3 -3
X X X X
doped graphene ribbon, and (b) (6,6)-armchair nitrogen-
dopedCNTsandwichedbetweenpristinezigzaggraphenerib- FIG.3. Electronicbandstructuresof√3 √3nitrogen-doped
×
bons and armchair CNTs, respectively. The white, gray, and graphene ribbons: (a) 12-ZGR1, (b) 12-ZGR2, (c) 18-ZGR2,
blue balls denote the hydrogen, carbon, and nitrogen atoms, and (d) 12-ZGR3. The corresponding geometries are shown
respectively. The orange regions represent thelead regions. in Fig. 1.
A. Electronic Properties of √3 √3 nitrogen-doped
freedom is neglected in the electronic structure calcula- graphene nanoribbons×and CNTs
tions since these hydrogen-saturated √3 √3 graphene
×
ribbonsandCNTsarefoundtohavenonmagneticground
First, the band structures of nitrogen-doped zigzag
states in total energy computations.
graphene ribbons of different configurations are illus-
These√3 √3nitrogen-dopedgrapheneandCNTsu- trated in Fig. 3. Because of the band folding of the
×
perlattices may serve as valley-processing units in val- √3 √3 superlattice, all bands are centered at the Γ
leytronic applications. Therefore,to study the transport poin×t instead of K/K′ in pristine graphene. Compared
characteristicsofthe√3 √3graphenenanoribbonsand with the Dirac cone bands at the K/K′ points of pris-
×
CNTs, we construct two-probe structures by sandwich- tine graphene,electronsinthese √3 √3zigzagribbons
×
ingthese superlatticesbetweenelectrodesmadeofeither travelwith lower groupvelocities near the Fermi energy.
pristinegrapheneribbonsorCNTswiththesamesystem All three zigzag ribbons are metallic, with intrinsic en-
sizes. Panels (a) and (b) of Fig. 2 depict the two-probe ergygapsbelowtheFermienergylocateatE 1.5eV.
≈−
configurationsof12-√3 √3zigzaggrapheneribbonwith This behavior is straightforwardsince nitrogen is widely
×
pristine graphene ribbon leads, and (6,6)-√3 √3 arm- usedasann-typedopanttoshifttheFermilevelup. We
×
chair CNTs with pristine CNT leads, respectively. As label the magnitude of this intrinsic energy gap as ∆.
clearly demonstrated in this figure, the ribbon system is Forthe 12-ZGR1,anindirectenergygapof∆=0.61eV
hydrogen-saturatedwhile the CNT setup has cylindrical emergeswithitstopandbottompositionsresidingatthe
boundary conditions. The structures are also fully re- Γ point and approximately 1/5th of the Γ-X, as shown
laxed in VASP. Since pristine zigzag graphene ribbons in Fig. 3(a). A nearly flat band, highlighted by the red
exhibit antiferromagnetic ground states41, spin-resolved line, exists at the center of the energy gapand primarily
transport properties are evaluated in the transport cal- originates from the edge carbon atoms at the all-carbon
culations of graphene ribbon two-probe systems. side(right-handsideofFig.1(b)). Thisflatbandissimi-
lartotheedgestatesofpristinezigzaggrapheneribbons.
In Fig. 3(b), the indirect gap of 12-ZGR2 is 0.56 eV be-
tween Γ-X at the bottom and Γ point at the top. The
bulk energy gap is approximately half an electron volt
lower than that of 12-ZGR1. A flat band exists in the
III. NUMERICAL RESULTS AND bulk conduction bands, which is mostly caused by the
DISCUSSIONS edge state of the right-side zigzag carbon chain with ni-
trogen, as shown in Fig. 1(c). When the ribbon width
of ZGR2 increases, the bulk gap decreases. But the flat
We carry out extensive first-principles calculations on band is almost independent of the system size, as shown
the electronic and transport properties of carbon nanos- in Fig. 3(c). However, when N exceeds 16, as the case
z
tructures containing √3 √3 superlattices, and the nu- for 18-ZGR2, even though the energy gap of 0.39 eV is
×
merical results are presented in detail. still indirect, the top and bottom positions move to Γ
4

(a) 1 (b) 1 (a) 2 (b) 2
V) 0 V) 0 V) V)
Energy (e --21 Energy (e --21 Energy (e -20 Energy (e -20
-3 -3
-4 -4 -4 -4
X X X X X X X X
(c) 2 (d) 2
FIG.4. Electronicbandstructuresof√3 √3nitrogen-doped
×
armchair graphene ribbons, (a) 18-AGR1, and (b) 18-AGR2. V) V)
ThespatialconfigurationsofAGR1andAGR2arevisualized y (e 0 y (e 0
in Fig. 1(e) and Fig. 1(f), respectively. erg erg
En -2 En -2
(a) (b) -4 -4
1000 ZGR1 800 X X X X
meV) 680000 ZZGGRR23 eV) 600 AAGGRR12 sFiInGgl.e6w.aEllleCctNroTnsi:c(baa)n(d6,s0t)ruzicgtzuargesCoNfT√,3(×b)√(39,n0i)tzroiggzeang-dCoNpeTd,
( m 400 (c) (6,6) armchair CNT, and (d) (9,9) armchair CNT.
400 (
200 200
0 0
8 10 12 14 16 18 20 22 24 12 18 24 30 36 42 48
responding ∆ as a function of ribbon width in Fig. 5(a).
Nz Na
For a narrow ribbon (Nz < 14), ZGR1 has the largest
FIG. 5. (a) Evolution of band gap ∆ of the nitrogen-doped
gap, while ∆ of ZGR3 is the smallest. When increasing
zigzaggrapheneribbonsasafunctionofribbonwidthNz. (b) the ribbon width, the band gap∆ decreasesfor allthree
Bandgap∆of√3 √3armchairribbonsversusribbonwidth
× types of zigzag ribbons. The band gaps of both ZGR1
Na.
andZGR3exponentiallydecaywhenNz grows,but∆of
ZGR2 shows a linear decreasing relation with Nz. As a
pointandclosetoΓatΓ-X,respectively. Inotherwords, result, ZGR2 has the largestband gapfor Nz >14. The
decayingbehaviorofthebandgapsindicatestheirfinite-
ZGR2 gradually evolves from an indirect to a direct gap
size nature, which will eventually vanish at large system
material when the ribbon width grows. In contrast to
sizes. WenoticethatZGR3notonlyhasthesmallestgap,
ZGR1andZGR2,ZGR3hasasmallerdirectbandgapat
but also is the most stable structure among these zigzag
the samesize. Figure3(d)shows∆=0.25eVatΓpoint
ribbons. Wehavealsostudiedtheenergygapof√3 √3
in 12-ZGR3. The nearly flatbandis absentinZGR3 be-
×
armchair graphene ribbons at various ribbon widths, as
cause the corresponding edge state is broken. With the
presented in Fig. 5(b). The bulk gaps of both AGR1
exception of these differences, all nitrogen-doped zigzag
and AGR2 exponentially decay as the ribbon width N
graphene ribbons share common features owing to their a
increases. Analogous to the case of zigzag ribbons, ∆
close geometries. Most of these first-principles results
of the more stable configurationAGR2 is alwayssmaller
are qualitatively consistent with the tight-binding pre-
than that of AGR1. The finite-size gap of the armchair
dictions in Ref.[31].
ribbons is shown to be rather robust against the system
Second,numericalresultsonthedispersionrelationsof
√3 √3armchairgrapheneribbons areshowninFig.4, size. For instance, ∆ is around 100 meV at Na = 48 for
× both AGR1 and AGR2 systems.
which resemble the metallic features of nitrogen-doped
zigzag graphene ribbons. Both AGR1 and AGR2 have Finally, we explore the electronic band structures of
direct band gaps at Γ point where all of the electrical nitrogen-dopedsinglewallCNTswith√3 √3superlat-
×
bands focus. The intrinsic energy gaps of 18-AGR1 and tices. Typical chirality of zigzag and armchair is inves-
18-AGR2 are 0.55 eV and 0.29 eV, respectively. These tigated, and numerical results are shown in Fig. 6. It is
bulk gaps also reside around E 1.5 eV in the E k clearthatallofthenitrogen-dopedCNTsconsideredhere
≈ − −
maps. Similar to the pristine armchairgraphene ribbons exhibit metallic characteristics. Unlike nitrogen-doped
case,thereisnoedgemodeorflatbandinthedispersion graphene ribbon superlattices, these CNT superlattices
relations of these √3 √3 armchair graphene ribbons. do not have significant band gaps in their E k rela-
× −
The band gap of AGR2 is drastically smaller than that tions. As for zigzag CNT, no band gap can be observed
of AGR1 at the same ribbon width, and AGR2 is also in Figs. 6(a) and 6(b). For a smaller (6,0) zigzag CNT,
more structurally stable than AGR1. remarkable band crossings occur symmetrically around
Moreover,relationsbetweentheribbonwidthandbulk the Γ point at E 1.47 eV in Fig. 6(a). When the
≈ −
gap ∆ are studied, and the tendencies are visualized in tube size increases to (9,0), the band crossings gradu-
Fig. 5. We calculate the band structures of a series of ally evolve into band touches at the Γ point, as shown
zigzag ribbons with increasing widths, and plot the cor- in Fig. 6(b). Another distinct feature in the band struc-
5
tures of these zigzag CNTs is the linear bands, which
3
guaranteehighgroupvelocitiesofthe propagatingBloch spin.up
electrons. Linear bands can lead to the counterintuitive 2 (a) spin.down on (d) AAGGRR12
Kleintunnelingphenomenon,wherehigh-speedincoming 1 missi 2
electronscannormallypenetrateapotentialbarrierwith n ns
pbeerhfaevcitortrhaanssmbeisesniocno.nfiTrhmeedexiinstpenricsetinoef KCNleTins4t6u–n48n,elainndg missio 02 (b) ssppiinn..udpown Tra 1
teRinceeefr.s[g3oy1n]gtpairgpehdetix-cbitsientdsdiiitnnsgtelhxeeivsetclea.nsAceesoiffnosr√ma3ar×mll√cthu3abiCersNt.uTbFeosusr,peaexrtaliamnty-- Trans 201 (c) spin. up mission 20 (e) ((69,,60)) CCNNTT
ple, Fig. 6(c) demonstrates that a (6,6) armchair CNT spin.down s
hasanindirectgapof45meVnearthe Γpoint. Butthis 1 Tran 1
gap quickly closes as the tube size grew to (9,9), and
bandtouchingcanbeseeninFig.6(d). Wealsofindsev- 0 0
-2 -1 0 1 -2 -1 0 1
eral linear bands embedded in the bulk band structures.
Compared with those of zigzag CNT superlattices, the Energy (eV) Energy (eV)
bands ofarmchairtubes aremuchdenseratsimilar tube FIG. 7. Transmission versus energy through pristine and
diameters. nitrogen-doped two-probe systems, (a) 12-ZGR1, (b) 12-
ZGR2, (c) 12-ZGR3, (d) 18-AGR1, and 18-AGR2, and (e)
(6,6) and (9,0) CNT superlattices, respectively.
B. Transport Properties of Nitrogen-doped
Graphene and CNT Heterostructures
a lower energy, and the transmission at the HOMO is
spin-up polarized. Both of these transmission peaks are
We investigate the transport properties of nitrogen-
greater than one in magnitude.
doped graphene and CNT superlattices using the Nan-
oDcal package, which is currently the most popular Figure.7(d)showsthetransmissioncoefficientsoftwo-
first-principles quantum transport simulation software. probe armchair graphene ribbon systems with width
In particular, we calculated the transmission coeffi- Na = 18. Both of the pristine and nitrogen-doped arm-
cients through two-probe heterostructures consisting of chair grapheneribbons havenonmagnetic groundstates.
nitrogen-doped graphene ribbon (nitrogen-doped CNT) Therefore, spin is not involved in the calculation. Ow-
sandwiched between pristine graphene ribbon (pristine ing to the semiconducting nature of pristine armchair
CNT) leads, which are shown in Fig. 2. graphene ribbons, the 18-AGR1 and 18-AGR2 systems
The zigzag graphene ribbon systems are studied, and possess transmission gaps of 0.42 eV around E = 0. In
numerical results are provided in Fig. 7. We choose a the E > 0 region, almost quantized transmission peaks
12-zigzag ribbon and an 18-armchair ribbon as typical appears in both systems. In the case of E < 0, a step-
configurations, and then construct two-probe systems. increasing behavior of transmission is observed in the
The pristine zigzag graphene ribbon has a small band AGR1 two-probe system, while transmission peaks ap-
gap within its antiferromagnetic ground state41. When pearattheHOMOfortheAGR2system. BelowE = 1
−
pristine zigzag graphene ribbons are used as electrodes, eV, both systems have smooth transmission curves. It
a zero-transmission gap of 0.38 eV appears in the spin- is worth noting that the transmission function of the
resolved transmission coefficients of all two-probe con- 18-AGR2 system shows strong oscillations, and several
figurations with a system width of Nz = 12. The cor- transmission peaks approach one near E ≈0.4eV.
responding diagrams for nitrogen-doped ZGR1, ZGR2, The transmissions of CNT based two-probe systems
andZGR3two-probesystemsaredisplayedinpanels(a), are also evaluated. We consider the representative arm-
(b), and (c) of Fig. 7, respectively. Except for the same chairandzigzagchiralitiesandpresentthe numericalre-
zero-transmission gap, another common feature among sults in Fig. 7(e). Spin polarizations are absent in these
thesefiguresisthatthetransmissioncoefficientsareonly CNT systems. Typical (6,6) and (9,0) tubes are em-
spin-dependent in the energy range of E ( 1,1) eV, ployed to build two-probe systems, with pristine CNTs
∗ ∈ −
which corresponds to the π and π channels for all pris- as electrodes and nitrogen-doped CNT superlattices as
tine zigzag graphene based systems49. We also observe the scattering region. The (6,6) armchair CNT sys-
many spin-dependent resonant peaks in this range. As tem exhibits conductive behavior across the entire en-
for the 12-ZGR1 system, the transmission peak of spin- ergyrange. Remarkablequantizedtransmissionplateaus
down electrons from the highest occupied molecular or- ofT =1arefoundintheenergyrangesE [0,1]eVand
∈
bital (HOMO) is larger than that of spin-up electrons, E [ 1.75, 1.15] eV, which are the symbol of perfect
∈ − −
and exceeds 1. Both peaks are suppressed in the ZGR2 ballistic transport. Between the two plateaus, the trans-
system,inwhichthe transmissionofspin-downelectrons missionfunctionslowlyfluctuates fromoneto twointhe
is still larger. In contrast, for the 12-ZGR3 system, regionE [ 1,0]eV. In the case of a (9,0) zigzag CNT
∈ −
the transmission peak of spin-down electrons moves to system,thereisatransmissiongapof0.16eV,whichorig-
6
inates from the semiconducting electrodes. The trans- Several linear bands are identified in the dispersion re-
mission curve has a smooth shape below E = 1 eV, lations of nitrogen-doped carbon nanotubes, which im-
−
and wildly oscillates fromzero to more than three in the plies that these tubes have extraordinary ballistic trans-
region E [ 1,1] eV. The relatively large transmission portproperties. Thetransportpropertiesofpristineand
∈ −
ofthese tube systemsmaybe adirectresultofthe linear nitrogen-doped graphene ribbon/carbon nanotube het-
bands shown in Fig.6. erostructures are investigated using the first-principles
method. In particular, we have calculated the transmis-
sion coefficients as functions of the energy through two-
IV. SUMMARY probesystems. Two-probesystemsconstructedonzigzag
ribbons,armchairribbons,andzigzagtubesexhibitsemi-
In summary, we have performed first-principles inves- conducting characteristicswith transmissiongaps. Spin-
tigations on the electronic and transport properties of resolved resonant peaks are observed around the trans-
nitrogen-doped zigzag and armchair graphene ribbons mission gaps in the zigzag ribbon systems. The arm-
andcarbonnanotubeswith√3 √3superlattices,which chaircarbonnanotubeheterostructuresshowmetallicbe-
have been reported to possess×intrinsic inter-valley in- havior, and remarkable quantized transmission plateaus
teractions. The electronic band structures reveal that of T = 1 appear in wide energy ranges in the (6,6)
all nitrogen-doped graphene ribbons and carbon nan- CNT system. Given these extraordinary properties, the
otubes are nonmagnetic metals. Three types of zigzag √3 √3 zigzagandarmchairgraphene ribbons and car-
×
ribbons and two kinds of armchair ribbons are studied bon nanotubes could be promising materials for future
and they all have finite-size band gaps below the Fermi valleytronic applications.
energy, which gradually close as the ribbon width in-
creases. One nearly flat band originated from the edge
carbonatomsresidesinsidethebulkgapfortwoconfigu- ACKNOWLEDGMENTS
rationsofzigzagribbons. Numericalresultssuggestthat
stableribbonswithlowerGibbsfreeenergiesalsoexhibit This work was financially supported by the Na-
smaller band gaps in both zigzag and armchair cases. tional Natural Science Foundation of China (Grants No.
In contrast, nitrogen-doped carbon nanotube superlat- 11504240,11504241,and11604213),andNaturalScience
tices have no band gap in the case of zigzag chirality, Foundation of Shenzhen University (Grant No. 201550).
and a tiny gap of dozens meV exists in small armchair Z. Y. acknowledges the University Grant Council (Con-
tubes, which quickly vanishes as the tube size grows. tract No. AoE/P-04/08)of the Government of HKSAR.
∗ [email protected] 10 A. F. Morpurgo and F. Guinea, Intervalley Scattering,
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