We have measured the thermoelectric power (S) of high purity single-walled
carbon nanotube mats as a function of temperature at various hydrostatic
pressures up to 2.0 GPa. The thermoelectric power is positive, and it increases
in a monotonic way with increasing temperature for all pressures. The low
temperature (T < 40 K) linear thermoelectric power is pressure independent and
is characteristic for metallic nanotubes. At higher temperatures it is enhanced
and though S(T) is linear again above about 100 K it has a nonzero intercept.
This enhancement is strongly pressure dependent and is related to the change of
the phonon population with hydrostatic pressure.Comment: 4 pages, 3 figure

A.B. Kaiser

C.L. Kane

D.S. Bethune

E.S. Choi

G. Mihály

I. Kézsmárki

I.V. Krive

J. Hone

K. Bradley

K. Sugihara

L. Forró

L. Grigorian

M. Bockrath

M. Tian

N. Barišić

N. Hamada

R. Gaal

R. Gaál

S. Iijima

Z.H. Wang

English

arXiv

We have measured the thermoelectric power (S) of high-purity single-walled carbon nanotube mats as a function of temperature at various hydrostatic pressures up to 2.0 GPa. The thermoelectric power is positive, and it increases in a monotonic way with increasing temperature for all pressures. The low-temperature (T<40K) linear thermoelectric power is pressure independent and is characteristic for metallic nanotubes. At higher temperatures it is enhanced and though S(T) is linear again above about 100 K it has a nonzero intercept. This enhancement is strongly pressure dependent and is related to the change of the phonon population with hydrostatic pressure

Barišić, N.

Gaál, R.

Kézsmárki, István

Mihály, G.

Forró, L.

OPUS Augsburg

RAPID COMMUNICATIONSPHYSICAL REVIEW B, VOLUME 65, 241403~R!Pressure dependence of the thermoelectric power of single-walled carbon nanotubesN. Barišić,1 R. Gaál,1 I. Kézsmárki,2 G. Mihály,2 and L. Forró11Institute of Physics of Complex Matter, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Switzerland2Department of Physics, Technical University of Budapest, H-1111 Budapest, Hungary~Received 12 March 2002; published 31 May 2002!We have measured the thermoelectric power ~S! of high-purity single-walled carbon nanotube mats as afunction of temperature at various hydrostatic pressures up to 2.0 GPa. The thermoelectric power is positive,and it increases in a monotonic way with increasing temperature for all pressures. The low-temperature (T,40 K) linear thermoelectric power is pressure independent and is characteristic for metallic nanotubes. Athigher temperatures it is enhanced and though S(T) is linear again above about 100 K it has a nonzerointercept. This enhancement is strongly pressure dependent and is related to the change of the phonon popu-lation with hydrostatic pressure.DOI: 10.1103/PhysRevB.65.241403 PACS number~s!: 73.63.Fg, 73.63.2b, 73.50.LwSoon after the discovery of multiwalled carbonnanotubes1 single-walled carbon nanotubes ~SWNT! weresynthesized with catalytic metal particles.2 SWNT span elec-tronic properties from metals to variable gap semiconduc-tors, depending on the chirality and the diameter of the rolledup graphene sheet.3 It was immediately realized that metallictubes represent the ultimate one-dimensional conductor, andthey generated considerable interest due to the possible real-ization of the Luttinger liquid ~LL! behavior in nature. In-deed, conductivity measurements performed on individualnanotubes have shown the canonical power-law behavior ofconductance as a function of temperature and voltage.4Early thermoelectric power ~TEP! experiments performedon nanotube bundles lead to qualitatively similar results:5–8 ametallic character due to hole carriers, a knee feature ~changeof slope! around 100 K, and preparation dependent magni-tude. The observed TEP was associated with intrinsic elec-tronic behavior, and the fact that the nanotube bundles con-tain both metallic and semiconducting ropes allowed adescription of the unusual shape of the S(T) curves in asimple two-band model, using a sufficient number of fittingparameters. It was also realized that in the high-temperaturerange the thermoelectric power is significantly larger thanexpected for bundles constituted predominantly of metallicropes.5Since SWNT’s may be contaminated by magnetic impu-rities coming from the catalysts ~Fe, Ni, Co! needed for theirgrowth, the high value of the TEP above 100 K questions itsintrinsic origin. The influence of the magnetic impurities hasclearly been experimentally demonstrated:9 in the presenceof transition-metal impurities the thermopower has a strongpeak, just around 100 K. This peak was associated with theKondo scattering of conduction electrons on the impurityspins. The enhancement of the TEP could be largely, albeitnot completely, removed by iodine neutralization.9 A nonin-trinsic, residual ‘‘Kondo term’’ may arise from magnetic im-purities trapped on the body of the nanotubes, even in thecase of nominally pure samples.The change of sign of the thermoelectric power upon de-gassing also raised the possibility of a nonintrinsic process.10The conductivity of doped semiconducting tubes can be ashigh as that of the metallic ones and the overall thermopower0163-1829/2002/65~24!/241403~3!/$20.00 65 2414may be determined by their contribution. Recently it wassuggested that hole doping due to oxygen adsorption ex-plains the sign and the shape of S(T), at least in the case ofbundles where semiconducting ropes dominate.10In this paper we report the results of thermoelectric powerexperiments on high-purity single-wall nanotubes under hy-drostatic pressures. We show that the low-temperature linearthermoelectric power arises from metallic ropes and it is con-sistent with the Luttinger liquid behavior. Our results onpressurized samples exclude the ‘‘residual Kondo’’ origin ofthe high-temperature TEP, and allow to separate the band andphonon contributions. We propose a model, in which theknee feature is coming from the change of the population ofphonons that are relevant for the electron scattering. Thispicture is further supported by comparison of the thermo-electric power in carbon-based metallic compounds, whichhave a similar local bond structure, but a quite different bandstructure.SWNT soot was purchased from Rice University, rich incatalytic particles. Most of these metallic blobs, covered witha graphitic shell, were eliminated using a purification methodelaborated in our laboratory.11 This purification method re-sults in open and less bundled, more dispersed nanotubes.The purified SWNT’s from the suspension were deposited ona filtration membrane and a thin film of buckypaper wasproduced. The buckypaper was heated in vacuum to 1200 °Cin order to eliminate absorbates. A thin slab of 3.031.030.01 mm3 was cut and mounted on a thermopower sampleholder, which fits into a clamped pressure cell. Small metal-lic heaters installed at both ends of the sample generated thetemperature gradient, which was measured with a Chromel-Constantan differential thermocouple. The pressure mediumused in this study is kerosene and the maximum pressure is2.0 GPa. The pressure was measured using a calibrated InSbpressure gauge. A similar sample arrangement and pressurecell was used in the study of the pressure dependence of theresistivity of SWNT’s by Gaal et al.12Figure 1 displays the resistance and the thermopower atambient pressure in the T54–300 K region. The resistancehas a negative slope in the whole temperature range, which ischaracteristic of an undoped sample. The low-temperatureincrease is consistent with the signature of the LL feature.4©2002 The American Physical Society03-1RAPID COMMUNICATIONSBARIŠIĆ, GAÁL, KÉZSMÁRKI, MIHÁLY, AND FORRÓ PHYSICAL REVIEW B 65 241403~R!At low temperatures, below about 40 K, the thermopower islinear ~see also the inset of Fig. 2!. The well-resolved linearTEP excludes the possibility of a gapped density of states, orhopping conduction through midgap impurity levels, whichmight be invoked to account for the low-temperature upturnin the resistance. At higher temperatures the thermoelectricpower is enhanced, then its slope changes around 100 K.These features are in good qualitative agreement with earlierstudies on pure nanotubes.5–8The temperature dependence of the TEP measured at vari-ous pressures is shown in Fig. 2. We found that the low-temperature linear part is not sensitive to the application ofpressure, within the experimental resolution. In contrast, athigh temperatures, the TEP is strongly pressure dependent.The distinct behavior at low and high temperatures suggeststhat the thermoelectric power has different contributions inthe two ranges. This observation excludes the possibility thatthe thermoelectric power is related to residual magnetic im-purities. Pressure does not influence the sample purity or theexchange coupling ~J! between the conduction electrons andthe magnetic impurity, thus it could modify a possible con-tribution of Kondo origin solely by shifting the Kondo tem-perature,FIG. 1. The thermoelectric power ~S! and resistance versus tem-perature of a SWNT mat at ambient pressure. The SWNT’s werepurified from catalytic particles and heat treated at 1200 °C invacuum prior to measurement.FIG. 2. The thermoelectric power of SWNT at 1 bar, 10 and 20kbars as a function of temperature. The low-temperature part isenlarged in the inset.24140TK'EFkBexpS 2 12uJuD~EF! D . ~1!Here D(«F) is the electronic density of states at the Fermilevel, which might have a pressure dependence. Such a pres-sure dependence should, however, also be reflected in themetallic low-temperature range, which is not observed.Moreover, TK should decrease with increasing pressure asD(«F) decreases. Instead, one rather observes a smearing ofthe shoulder due to the application of the pressure than astructure, which shifts with pressure.The pressure study also shows that characteristic S(T)shape shown in Fig. 2 and published by various groups5–8cannot arise from oxygen adsorption, either. In the dopedsemiconductor picture the TEP is interpreted in terms of theparticular shape of electronic density of states. Any pressureinduced modification of the density of states would rescalethe S(T) curve in the whole temperature range, in contrast tothe observed differences in the low- and high-temperatureranges.The linear temperature dependence at low temperatures ischaracteristic of a simple metal, obeying Fermi-liquid theory.Recent theoretical studies13,14 of the thermal transport in theLuttinger liquid phase showed that—though both the electri-cal and the thermal conduction are unconventional—the low-temperature thermopower still follows Mott’s formula of thelogarithmic derivative of the conductivity, s ,S52p23kB2e S ] lns~« !]« D«5«F. ~2!This leads to S5cT , with a nonuniversal coefficient c, whichis determined by the band shape and the scattering rate. Forthe Luttinger liquid of spatial extension L Eq. ~2! holds onlyfor low temperatures, while an enhancement is expected forkBT.\vF /gL (vF is the Fermi velocity, while g is the cor-relation parameter of the LL!.14 We do not believe this is thesource of the observed enhancement in our case, since, forrealistic values of defect-free nanotube segments (L,100 nm), the corresponding temperature is above therange covered by the experiments.The attenuation of the shoulder in S(T) with the pressureputs forward another explanation for the overall temperaturedependence.8,15 If inelastic scattering of electrons onphonons is of importance, then the thermoelectric power isexpressed asS5S0@11llS~T !# , ~3!where S0 is given by Eq. ~2!, l is the standard mass en-hancement due to renormalization by phonons, and lS(T) isthe temperature-dependent enhancement of the thermopower.The latter quantity contains the Eliashberg function, and ifthe phonon density of states has a peak then lS(T) will havea shoulder at the corresponding temperatures. This termgives a nonzero intercept of S(T) when extrapolated fromhigh temperatures. Furthermore, this term can fade away3-2RAPID COMMUNICATIONSPRESSURE DEPENDENCE OF THE THERMOELECTRIC . . . PHYSICAL REVIEW B 65 241403~R!thus changing the slope of S when the population ofphonons, which strongly scatter the charge carriers, dimin-ishes.The model can also account for the observed pressuredependence. High pressure increases the force constant act-FIG. 3. The thermoelectric power of several carbon-based com-pounds, such as intercalated graphite ~Ref. 16!, carbon nanohorns~Ref. 17!, alkali-metal doped C70 ~Ref. 18!, and SWNT’s. All thesamples show similar break in slope in the 100 K range.24140ing between the carbon atoms, shifting any feature in thephonon density of states to higher energies. Consequently,the population of the phonons, which strongly interact withthe charge carriers, decreases and the thermopower drops.This explanation is corroborated by the fact that the tempera-ture at which the shoulder in S develops somewhat increasestowards higher temperatures at high pressures.The phonon mode in the case of SWNT should be thevibration of the carbon atoms in the hexagons, since a similarfeature in S could be observed in other carbon-based materi-als, which are built up from the benzyl-ring units. Figure 3summarizes the Seebeck coefficient of intercalatedgraphite,16 carbon nanohorns,17 alkali-metal doped C70 ,18and SWNT’s. All the samples show similar break in slope inthe 100 K range.In conclusion, we have performed thermopower measure-ments on purified SWNT mat as a function of temperatureand hydrostatic pressure. While the low-temperature metallicthermopower was found to be pressure independent, thehigh-temperature unusual TEP contribution was stronglysuppressed by the application of pressure. We showed thatthe thermopower of our sample is due to metallic nanotubes,and we excluded nonintrinsic effects, such as Kondo scatter-ing of residual impurities or doping by adsorbed oxygen. Ourresults suggest that the temperature and pressure depen-dences are governed by the change of population of phonons,connected with the thermal excitation of the hexagons ~thebuilding units of the SWNT’s!.The sample purification by Klara Hernadi and useful dis-cussions with Walter Schirmacher are acknowledged. Thiswork was supported by the Swiss National Foundation forScientific Research and the NCCR Pool ‘‘MaNEP.’’1S. Iijima, Nature ~London! 354, 56 ~1991!.2S. Iijima and T. Ichihashi, Nature ~London! 363, 603 ~1993!; D.S.Bethune et al., ibid. 363, 605 ~1993!.3N. Hamada, S. Sawada, and A. Oshiyama, Phys. Rev. Lett. 68,1579 ~1992!.4M. Bockrath et al., Nature ~London! 397, 598 ~1999!.5J. Hone et al., Phys. Rev. Lett. 80, 1042 ~1998!.6L. Grigorian et al., Phys. Rev. Lett. 80, 5560 ~1998!.7M. Tian et al., Phys. Rev. B 58, 1166 ~1998!.8E.S. Choi et al., Synth. Met. 103, 2504 ~1999!.9L. Grigorian et al., Phys. Rev. B 60, 11 309 ~1999!.10K. Bradley et al., Phys. Rev. Lett. 85, 4361 ~2000!.11K. Hernadi, L. Thien Nga, and L. Forro ~unpublished!.12R. Gaal, J.P. Salvetat, and L. Forro, Phys. Rev. B 61, 7320 ~2000!.13C.L. Kane and M.P.A. Fisher, Phys. Rev. Lett. 76, 3192 ~1996!.14 I.V. Krive et al., Phys. Rev. B 63, 113101 ~2001!.15A.B. Kaiser et al., Synth. Met. 117, 67 ~2001!.16K. Sugihara, Phys. Rev. B 28, 2157 ~1983!.17R. Gaal et al. ~unpublished!.18Z.H. Wang et al., Phys. Rev. B 49, 15 890 ~1994!.3-3

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Pressure dependence of the thermoelectric power of single-walled carbon
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Pressure dependence of the thermoelectric power of single-walled carbon nanotubes

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