Intertube effects on one-dimensional correlated state of metallic single-wall carbon nanotubes probed by 13C NMR

0.17 MB·

by  Noboru Serita

Intertube effects on one-dimensional correlated state of metallic single-wall carbon
nanotubes probed by 13C NMR
Noboru Serita,1 Yusuke Nakai,1,∗ Kazuyuki Matsuda,2 Kazuhiro
Yanagi,1 Yasumitsu Miyata,1,3 Takeshi Saito,4 and Yutaka Maniwa1,†
1Department of Physics, Graduate School of Science and Engineering,
Tokyo Metropolitan University, Tokyo 192-0397, Japan,
2Institute of Physics, Faculty of Engineering, Kanagawa University, Yokohama 221-8686, Japan,
3JST, PRESTO , 4-1-8 Hon-Chou, Kawaguchi, Saitama 332-0012, Japan,
4Nanomaterials Research Institute, AIST, 1-1-1 Higashi, Tsukuba 305-8565, Japan
7
(Dated: January 20, 2017)
1
0 The electronic states in isolated single-wall carbon nanotubes (SWCNTs) have been considered
2 asan idealrealization ofaTomonaga-Luttinger liquid (TLL).However,it remainsunclearwhether
n one-dimensionalcorrelatedstatesarerealizedunderlocalenvironmentaleffectssuchastheformation
a of a bundle structure. Intertube effects originating from other adjacent SWCNTs within a bundle
J may drastically alter the one-dimensional correlated state. In order to test the validity of the
9 TLL model in bundled SWCNTs, low-energy spin excitation is investigated by nuclear magnetic
1 resonance (NMR). The NMR relaxation rate in bundled mixtures of metallic and semiconducting
SWCNTsshowsapower-lawtemperaturedependencewithatheoreticallypredictedexponent. This

] demonstratesthataTLL statewiththesamestrengthasthat foreffectiveCoulomb interactions is
l realized in a bundled sample, as in isolated SWCNTs. In bundled metallic SWCNTs, we found a
e
- power-lawtemperaturedependenceoftherelaxation rate, butthemagnitudeoftherelaxation rate
r isoneorder of magnitudesmaller than that predictedbytheory. Furthermore,wefound an almost
t
s doubled magnitude of the Luttinger parameter. These results indicate suppressed spin excitations
.
t withreducedCoulombinteractionsinbundledmetallicSWCNTs,whichareattributabletointertube
a
interactions originating from adjacent metallic SWCNTs within a bundle. Our findings give direct
m
evidencethat bundlingreducestheeffectiveCoulomb interactions viaintertubeinteractions within
- bundledmetallic SWCNTs.
d
n
o I. INTRODUCTION i.e., Fermi liquids) for repulsiveinteractions.3–5 The the-
c oretical estimate of the Luttinger parameter for an iso-
[
lated SWCNT is approximately 0.2.

1 A single-wall carbon nanotube (SWCNT) can be
v thought of as a graphene sheet rolled into a seamless Although the formation of a TLL state in individual
3 hollow cylinder with a typical diameter in the nanome- SWCNTs has been proposed, the effects of intertube in-
5
ter range. A SWCNT can be either semiconducting or teractions in a TLL state remain elusive, particularly to
3
metallic, depending on the microscopic atomic arrange- what extent the proposedTLL state is realizedin an ac-
5
mentsandsymmetry(chirality),1 andas-preparedSWC- tualSWCNTsample. Infact,theelectronicpropertiesof
0
. NTs typically consist of mixtures of 2/3 semiconduct- SWCNTs are extremely sensitive to their environmental
1 ing and 1/3 metallic tubes. The small diameter and surroundings.8–10 It is well known that SWCNTs pack
0
high aspect ratio of a SWCNT lead to confinement of together closely and form a triangular lattice called a
7
electrons along its circumferential direction, and thus bundlestructure,11,12 whichcanalsogiverisetoenviron-
1
: a SWCNT is an ideal realization of a one-dimensional mental effects.13–17 For example, bundling of SWCNTs
v system.2 Due to the one-dimensional nature of SWC- produces a redshift of the optical transition energy, and
i
X NTs, electron-electron interactions are of great impor- has been understood as the consequence of the mutual
r tancebecausethelackofscreeningenhancestheeffective dielectric screening provided by adjacent SWCNTs in a
a Coulombinteractionsbetweenelectrons. Ithasbeenthe- bundle, which reduces the electron-electron repulsion in
oretically shown that a long-range Coulomb interaction each SWCNT.18,19 Thus, effective Coulomb interactions
converts isolated metallic SWCNTs into a Tomonaga- between adjacent metallic SWCNTs within a bundle of
Luttinger liquid (TLL),3–5 in which the low-energy elec- metallic SWCNTs may be largely screened out, leading
tron excitations are bosonic density waves of spin and to a significant deviation from the proposed TLL state.
charge.6,7InaTLLstate,physicalproperties,suchasthe In the case of bundled mixtures of semiconducting and
electronic density ofstates, andcorrelationfunctions ex- metallic SWCNTs, the first photoemission spectroscopy
hibit power-law behavior, and their exponents quantify (PES) experiment,20 which evidenced the TLL state, re-
the strength of the electron-electron interactions. The ported the same Luttinger parameter as the theoretical
strength of the effective electron-electron interactions is estimateforanisolatedSWCNT,whichwassubsequently
characterized by the charge Luttinger parameter (here- confirmed by other group.21 Contrary to the above ex-
inafterreferredtoasLuttingerparameter),whichranges pectationofthe strongdielectric screeningdue to metal-
from 0 (very strong interactions) to 1 (no interactions, lic SWCNTs within a bundle, previousPESexperiments
2
on bundled metallic SWCNTs22 identified a TLL state SWCNTsoot(MeijoNano-carbon)byadensitygradient
whichhasacomparableLuttingerparameter(=0.21)to ultracentrifugationtechnique.30 Theconcentrationofthe
thatofbundledmixturesofsemiconductingandmetallic metallic fraction was determined by optical absorption
SWCNTs (= 0.19).20,21 Ayala et al. concluded that the (ShimadzuUV-3600).31 Inordertoreduceferromagnetic
interactionbetween different metallic SWCNTs within a impurities, we performed an acid treatment and applied
bundle of only metallic SWCNTs is small enoughto sta- a density gradient ultracentrifuge method, as described
bilizeaTLLstate.22Theresultsoftransportexperiments inourpreviouspaper.32Afterthetreatment,thesamples
inisolatedandbundledSWCNTscanalsobeinterpreted were washed with ethanol and acetone. Vacuum filtra-
intermsofaTLLstate,23–25 althoughthereremaindiffi- tion was then performed to prepare buckypaper with a
culties ininterpreting the role ofthe contacts. Thus, the thickness of approximately 100 µm. The sample was fi-
effectofbundlingontheone-dimensionalelectronicstate nally annealed under a dynamic vacuum at 500 ◦C in
inSWCNTsremainselusive. Understandingthechanges order to avoid doping from adsorbed gas and molecules.
in the physical properties of SWCNTs due to bundling TheobtainedNMRsamplesweresealedinaquartztube
is very important not only from the perspective of fun- filled with 100 Torrof high purity helium gas. The aver-
damental physics but also for the device application of agediametersoftheSWCNTsampleswerecharacterized
SWCNTs, because SWCNTs naturally form bundles in by powder X-ray diffraction (XRD) at the BL8B sta-
typical synthesis processes. An understanding of inter- tion in the Photon Factory Facility, KEK, Japan. The
tube interactions due to bundling would allow the full DCmagneticsusceptibilitywasmeasuredusingaSQUID
potential of SWCNTs to be exploited for future nano- magnetometer (MPMS, Quantum Design). The SQUID
electronics. measurements indicated that the amount of ferromag-
Nuclear magnetic resonance (NMR) is a useful probe netic impurities in the purified sample was two orders of
for characterizing low-energy electronic states, such as magnitude smaller than in pristine material. 13C NMR
the density of states near the Fermi energy, without measurements were performed under a magnetic field of
electrical contacts, and may shed new light on the one- 9.4 Tesla. The nuclear spin-lattice relaxation rate T−1
1
dimensionalelectronicstatesofSWCNTs. Anadvantage was determined by a saturation recovery method. We
ofNMR is that it is a bulk-sensitive probe incontrastto foundthat the recoverycurve for the nuclearmagnetiza-
surface-sensitive PES experiments. Previous NMR mea- tion did not show a single exponential form, but could
surements of bundled mixtures of metallic and semicon- be fit to a stretched exponential form, as reported in a
ductingSWCNTsshowedaclearpower-lawtemperature previous paper,26 with a stretching exponent β = 0.82
dependence of the nuclear spin-lattice relaxation rate for the bundled mixed sample and β = 0.60 for the bun-
T−1,26 which is consistent with a TLL state. Previous dled metallic sample, both of which were temperature
1
NMR study on inner tubes of bundled double wall car- independent within experimental accuracy.
bonnanotubes27 wasalsoanalyzedintheframeworkofa
TLL state.28 However, it has not yet been resolved why
the obtained Luttinger parameter of the bundled mix- III. RESULTS AND DISCUSSION
tured SWCNTs (= 0.34)26 is approximately 70% larger
than the theoretical estimate and values from transport
Figure 1 shows a 13C NMR spectrum of the 13C-
and PES experiments.
enriched e-DIPS sample, which consists of bundled mix-
The purpose of this paper is to investigate the elec-
tures of metallic and semiconducting SWCNTs. In con-
tronic excitation microscopically by NMR to test the trast to the usual 13C NMR spectrum observed for our
validity of the TLL model in bundled SWCNTs. For unenriched metallic SWCNT sample,33 the spectrum in
this purpose, we used two different samples, one a mix-
Fig. 1 forms a doublet. Because the e-DIPS sample is
ture of metallic and semiconducting SWCNTs, and the almost entirely 13C enriched, we attributed the splitting
other consisting of highly concentrated metallic SWC- to the nearest neighbor 13C nuclear dipolar interaction.
NTs, where the adjacent environment of the metallic
We found from NMR measurements under a magnetic
SWCNTs may differ significantly by the formation of a
field of 4 Tesla that the splitting is magnetic field inde-
bundled structure.
pendent (not shown), which is one of the characteristics
of the well-known Pake doublets.34 From the splitting
we can estimate the carbon-carbon (C-C) bond length
II. EXPERIMENT
as follows. Here, we neglect the curvature of a graphene
sheet and assume that the local structure around a 13C
We used two different pristine SWCNTs produced by atom with three 13C nearest neighbors is a hexagonal-
e-DIPS (enhanced direct injection pyrolytic synthesis)29 honeycomb plane for simplicity. The central 13C nuclei
and an arc-discharge method. In the e-DIPS sample, at the origin (0, 0) experiences a dipolar field from the
13C isotopes were enriched to more than 90% in order threenearestneighbor13Cnuclearspinsat(r,0),( r/2,
−
to increase the NMR signal intensity, and no metallicity r√3/2), and ( r/2, r√3/2) on a graphene hexagonal
sortingwasperformed. Thehighlyconcentratedmetallic sheet, where r−is the C−-C bond length. These 13C atoms
SWCNTs (more than 95%) were prepared from Arc-SO can thus be thought of as three Pake pairs. Neighboring
3
295 K
0.01
nit) -1 K)
u s
y(arb. -1 T ) (1E-3
sit T1
n (
e
nt
I
1E-4
1 10 100
400 300 200 100 0 -100 -200 T(K)
Shift (ppm) FIG. 2. Temperature dependence of (T1T)−1 for bundled
FIG. 1. 13C NMR for bundles of mixed semiconducting and SWCNT samples with different metallicity measured under
metallic SWCNTs at 295 K under9.4 Tesla. 9.4 Tesla. The closed squares represent bundles of mixed
metallicandsemiconductingSWCNTs. Thecloseddiamonds
represent bundles of highly concentrated metallic SWCNTs.
Pake pairs on a hexagonal honeycomb lattice have been Theopencirclesrepresentbundlesofmixedmetallicandsemi-
conducting SWCNTs from Ref.26. The solid lines represent
previously reported for ThAl powder samples, and the
2 fitsto Tα.
AlinteratomicdistancewasdeterminedfromNMRspec-
tral doublets.35 The splitting corresponds to 3ν , where
D
νD = 32Irh3(2γπ)2, I = 1/2, γ = 10.705×2π MHz/T. The energy spin excitation significantly. Furthermore, we es-
obtained C-C bond length is 1.34 ˚A, which shows rea- timated the Luttinger parameter for the bundled metal-
sonable agreement with our recent XRD result.36 Thus, lic SWCNTs as 0.38 0.03, which is approximately two
13C enriched NMR can be applied for the determination times as largeas that±for the bundledmixtures of metal-
of the C-C bond length of SWCNTs. licandsemiconductingSWCNTs. BecausetheLuttinger
A noticeable characteristic of the TLL is a power-law parameterisameasureoftheelectron-electronrepulsion,
dependence of the physical properties with a critical ex- this larger parameter indicates that effective Coulomb
ponent describing the strength of the effective Coulomb interactions are weaker in bundled metallic SWCNTs
interactions. The NMR relaxation rate T−1 is known than in the bundled mixtured sample. To the best of
1
to be a useful probe for the electronic spin correlation our knowledge,this is the first evidence that bundling of
functions. Figure 2 shows the temperature dependence metallic SWCNTs weakens the electron-electroninterac-
of (T T)−1 of bundled SWCNT samples with different tion strength while bundling of mixtures of metallic and
1
metallicity (closed squares and diamonds), as well as semiconducting SWCNTs does not alter it.
the previous results for bundled mixtures of metallic Recently, Kiss et al. demonstrated that the magni-
and semiconducting SWCNTs (open circles).26 All the tude and temperature dependence of (T1T)−1 reported
SWCNT samples exhibit a power-law temperature de- by Ihara et al. can be explained quantitatively in the
pendence of (T T)−1 above 20 K. Note that (T T)−1 frameworkofTLLtheory.26,37TheyfoundthattheNMR
1 1
crosses over to a gap-like behavior at low temperatures, relaxationrate is enhanced by orders of magnitude com-
as reported previously.26 The origin of this behavior is pared to a Fermi liquid with the same density of states
beyond the scope of the present study. The power-law (DOS) due to a TLL state.37 They derived the equation
temperature dependence of (T T)−1 indicates the real-
izationofaTLLstate. Itisnot1eworthythattheabsolute (T T)−1 =A2 kBC(K) 2απ2 K[N(E )k T]K−2N(E )2,
values of (T1T)−1 and the temperature exponents differ 1 eff ¯h (cid:18)Ξ(n,m)(cid:19) F B F
among the samples. Following Ref.26, we estimated the (1)
Luttinger parameteras0.18 0.03forthe bundled mix- where A is the effective hyperfine coupling constant
eff
tures of metallic and semico±nducting SWCNTs (closed for 13C, (n, m) indicates the SWCNT chirality, N(E )
F
squares). The value of the obtained Luttinger parame- is the density of states at the Fermi energy, K is the
ter is almost the same as that derived theoretically,3–5 temperature exponent of (T T)−1 determined by exper-
1
and those obtained from transport23,24 and PES mea- iment, α is a constant depending slightly on the chiral-
surementsforbundledmixturesofmetallic andsemicon- ity (see in Ref.37), Ξ(n,m) = √3/2√n2+nm+m2 and
ducting SWCNTs.20,21 Incontrast,(T T)−1 forthe bun- C(K) = sin(πK)Γ(1 K)Γ2(K/2)/2. The dotted lines
1
dled metallic SWNCTs (closed diamonds) is one order in Fig. 3 represent th−e calculated (T T)−1 using the pa-
1
ofmagnitudesmallerthanthatforthe bundledmixtures rameters listed in the table. Note that in order to com-
ofmetallicandsemiconductingSWCNTs. Thisindicates pare the calculated values with the experimental result,
that bundling of metallic SWCNTs suppresses the low- we consider spin-diffusion effects. The observed T−1 for
1
4
bundled mixtures of metallic and semiconducting SWC- nm).43 Therefore, PES experiments can only probe the
NTsmaybeconsideredtobeanaveragevalueduetospin bundlesurfacewhereintertubeinteractionsareweakened
diffusion among the 1/3 metallic and 2/3 semiconduct- due to the smaller number of adjacent SWCNTs than in
ingSWCNTs. Therefore,theT−1 plottedinFig.3(a)is thebulkofthebundlesprobedby13CNMR,forwhichwe
1
takento be three times largerthanthe observedT−1 for estimateaskindepthof50µmconsideringtheelectronic
1
bundled mixtures of metallic and semiconducting SWC- conductivity of a single bundle.44
NTs plotted in Fig. 1, because undoped semiconducting Althoughthe originofthe weakenedLuttingerparam-
SWCNTs should exhibit a much longer T than metallic eterforbundledmixturesofmetallicandsemiconducting
1
SWCNTs. Note that our previous thermoelectric mea- SWCNTs observed in Ref.26 remains unknown, it might
surements suggest that the Fermi level for as-prepared be attributedto anenhanceddefectconcentrationinthe
SWCNT films lieswithin the bandgap.38,39 Asshownin sample, which was produced by laser ablation with non-
Fig.3(a),therelaxationratecalculatedintheframework magnetic Rh and Pt as catalysts.45 This method has a
oftheTLLtheoryreproducestheexperimentalresultsfor disadvantage of giving a low yield of SWCNTs, which
bundled mixtures of metallic and semiconducting SWC- leads to a large defect concentration. The GD ratio for
NTs quite well. In contrast, the experimental (T T)−1 the sample inferred from Raman scattering experiments
1
for the bundled metallic SWCNT sample is one order of was reported to be as high as 20, whereas it was more
magnitudesmallerthanthetheoreticallycalculatedvalue than 100 for the e-DIPS sample.29 For such defective
(see Fig. 3 (b)). The correlated electronic states for the SWCNTs, the average tube length effectively decreases,
bundled metallic SWCNTs are qualitatively consistent whichleadsto alargerLuttinger parameteraccordingto
with the TLL theory, as is obvious from the power-law Eq.(3.23) in Ref.5. Further studies are needed to clarify
behavior of (T T)−1, but the low-energy electronic spin theeffectsofdefectontheelectroniccorrelationinaTLL
1
excitations are quantitatively different from those pre- stateforSWCNTs,whichmayopenupanewmethodfor
dicted by the TLL theory (dashed line in Fig. 3 (b)) due manipulating nanotube properties.
to the reduced Coulomb interactions.
We ascribe the reduced Coulomb interaction observed IV. CONCLUSION
in the bundled metallic SWCNTs to intertube inter-
actions between neighboring SWCNTs. Two types of
In conclusion, the NMR measurements clarified con-
intertube interactions have been discussed,16–19 one of
trasting one-dimensional electronic states that depend
which is the direct coupling of the electronic states in
on the SWCNT metallicity within a SWCNT bundle.
adjacent SWCNTs (orbital hybridization effects), which
We found that a TLL model with the theoretically pre-
may impart a three-dimensional nature to the electronic
dicted strength for Coulomb interactions is realized in
states of SWCNTs. The second type of interactionis di-
bundled mixtures of metallic and semiconducting SWC-
electric screening induced by other adjacent nanotubes,
NTs. This demonstrates microscopically that individ-
leading to weakening of the Coulomb interactions. Di-
ual metallic SWCNTs within these bundled mixtures
electric screening has been proposed as a more robust
can be regarded as isolated metallic SWCNTs. In con-
and likely mechanism of intertube coupling than di-
trast, although the low-energy spin excitations for bun-
rect coupling.18,19 Considering the larger dielectric con-
dled metallic SWCNTs still display power-law behavior,
stant for a metallic SWCNT than for a semiconducting
which is the hallmark of a TLL state, electronic spin
SWCNT,41,42 we conjecturethat dielectric screeningis a
excitations are suppressed by one order of magnitude,
more naturalexplanationfor our NMR results,although
with weakened Coulomb interactions, than the bundled
the possibility of direct coupling cannot be fully disre-
mixturesofmetallicandsemiconductingSWCNTs. This
garded.
contrasting behavior indicates larger intertube interac-
We now discuss the different Luttinger parameters for tions in bundled metallic SWCNTs than in the bundled
bundled metallic SWCNTs observed in our NMR and mixtures. Our findings suggest a mechanism by which
previous PES measurements.22 The Luttinger parame- theone-dimensionalelectronicstatesinSWCNTscanbe
terobtainedbyPESexperiments(=0.21)iscomparable manipulated.
to that for the bundled mixtures of metallic and semi-
conducting SWCNTs,20–22 but is almost half that of our
ACKNOWLEDGMENTS
NMR estimate (= 0.38). This difference can be ascribed
to the fact thatPESmeasurementsaresurface sensitive;
the mean free path of a photoelectron in the experimen- This work was supported in part by JSPS/MEXT
talenergyrangeisseveral˚A,whichistwoordersofmag- KAKENHI Grant Numbers 15K04601, 16H00919, and
nitude smaller than a typical bundle size (order of 10 25246006.
∗ [email protected] † [email protected]
5
Aeff (eV) K (n,m) N(EF) (states/eV/spin/atom) α
Mixed (d=2.1 nm) 3.6×10−7 1.18 (15, 15) 0.00485 2.39×10−3
Metal (d=1.4 nm) 3.6×10−7 1.38 (10, 10) 0.0073 3.58×10−3
Mixed (d=1.6 nm, Ihara et al.) 3.6×10−7 1.34 (12, 12) 0.006 2.98×10−3
TABLE I. Parameters used for thecalculation of Eq.(1). N(EF) data were taken from Ref.40.
0.1 0.01
(a) Mixtures (b) Metal
-1 K) d = 2.08 nm -1 K)
s s
-1 T) (0.01 -1 T) (
T1 T11E-3
( (
d = 1.6 nm
1E-3 d = 1.4 nm
1E-4
1 10 100 1 10 100
T (K) T (K)
FIG.3. Comparisonbetweentheexperimental(T1T)−1andthatcalculatedbyTLLtheoryfor(a)bundledmixturesofmetallic
andsemiconductingSWCNTsand(b)bundledmetallicSWCNTs. Notethatthe(T1T)−1valuein(a)isthreetimeslargerthan
thoseinFig.1becauseofspin-diffusionaveraging(seetext). ThecalculatedresultsbasedonRef.37 reproducetheexperimental
(T1T)−1 quitewell in (a).
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