quantum transport through carbon nanotubes: proximity-induced

PHYSICAL REVIEW B 68, 214521 ~2003!

Quantum transport through carbon nanotubes: Proximity-induced and intrinsic superconductivity

A. Kasumov,1,2,* M. Kociak,1 M. Ferrier,1 R. Deblock,1 S. Gueron,1 B. Reulet,1 I. Khodos,2 O. Stephan,1 and H. Bouchiat11Laboratoire de Physique des Solides, Associe´ au CNRS, Baˆtiment 510, Universite´ Paris-Sud, 91405 Orsay, France2Institute of Microelectronics Technology and High Purity Materials, Russian Academy of Sciences, Chernogolovka,

142432 Moscow Region, Russia~Received 21 May 2003; published 31 December 2003!

We report low-temperature transport measurements on suspended single-walled carbon nanotubes~bothindividual tubes and ropes!. The technique we have developed, where tubes are soldered on low-resistivemetallic contacts across a slit, enables a good characterization of the samples by transmission electron micros-copy. It is possible to obtain individual tubes with a room-temperature resistance smaller than 40 kV, whichremain metallic down to very low temperatures. When the contact pads are superconducting, nanotubes exhibitproximity-induced superconductivity with surprisingly large values of supercurrent. We have also recentlyobserved intrinsic superconductivity in ropes of single-walled carbon nanotubes connected to normal contacts,when the distance between the normal electrodes is large enough, since otherwise superconductivity is de-stroyed by~inverse! proximity effect. These experiments indicate the presence of attractive interactions incarbon nanotubes which overcome Coulomb repulsive interactions at low temperature, and enable investiga-tion of superconductivity in a one-dimensional limit never explored before.

DOI: 10.1103/PhysRevB.68.214521 PACS number~s!: 74.10.1v, 74.70.2b, 74.50.1r

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I. INTRODUCTION

The hope to use molecules as the ultimate building bloof electronic circuits motivates the quest to understand etronic transport in thinner and thinner wires, ideally with oor two conduction modes. However a number of physiphenomena tend to drive such one-dimensional~1D! metallicwires to an insulating state at low temperature. The mbasic is the great sensitivity of 1D transport to disorder: awire has a localization length of the order of its elastic mefree path. It has also been shown that most molecularconductors undergo a structural Peierls transition to an inlating state at low temperature.1 Finally the repulsive Cou-lomb interactions between electrons, which are very weascreened in 1D, tend to destabilize the 1D Fermi liquidfavor of correlated states which are also insulating at ltemperature.

The purpose of this paper is to show that carbon natubes, because of their special band structure, escape sfate and remain conducting over lengths greater than 1mmdown to very low temperature. They do not present anytectable Peirls distortion and are weakly sensitive to disorMoreover, transport through the nanotubes is quantum coent, as demonstrated by the existence of strong supercurwhen connected to superconducting contacts. The obsetion of intrinsic superconductivity in ropes containing a fetens of tubes is even more surprising and indicates the pence of attractive pairing interactions which overcomestrong repulsive interactions.

Single-walled carbon nanotubes are constituted bysingle graphene plane wrapped into a cylinder. The Fesurface of graphene is very particular, it is reduced todiscrete points at the corners of the first Brillouin zone.2 As aresult, depending on their diameter and their helicity whdetermine the boundary conditions of the electronic wafunctions around the tube, single-walled nanotubes~SWNT!can be either semiconducting or metallic.3 When metallic

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they have just two conducting channels, only very weacoupled by electron-electron interactions. They are thus cacterized by a low electronic density together with a hiFermi velocity ~nearly as high as in copper! and relativelylarge mean free paths.4 These properties make them mucsought-after realizations of 1D conductors or more precisof 1D ladders with very small transverse coupling.5,6 At 1D,electron-electron interactions lead to an exotic correlaelectronic state, the Luttinger liquid,7 ~LL ! where collectivelow-energy plasmonlike excitations give rise to anomaliesthe single-particle density of states and where no long-raorder exists at finite temperature.

Proof of the validity of LL description with repulsive interactions in SWNT was given by the measurement of asistance diverging as a power law with temperature down10 K ~Ref. 8! with an exponent depending on whether cotacts are taken on the end or in the bulk of the tube. Frthese exponents the LL parameterg measuring the strengthof the interactions was deduced to beg50.2560.05. Thisvalue, which is much smaller than 1, corresponds to donant repulsive interactions. The extrapolation of this powlaw behavior down to very low temperature would indicaan insulating state. However, these measurements wereon nanotubes connected to the measuring leads throtunnel junctions. Because of Coulomb blockade,9 the low-temperature and voltage transport regime could notexplored.

We have developed a technique~described in Sec. II! inwhich measuring pads are connected through low-resistacontact to suspended nanotubes.10 It is then possible to ob-tain individual tubes with a resistance at room temperat~RT! no larger than 40 kV, which increases only slightly alow temperatures~typically a 20% resistance increase btween RT and 1 K! ~Sec. III!. The resistance vs voltagcurves also exhibit weak logarithmic nonlinearities at lotemperature. However, we find no simple scaling law btween the voltage and the temperature dependence of

©2003 The American Physical Society21-1

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A. KASUMOV et al. PHYSICAL REVIEW B 68, 214521 ~2003!

FIG. 1. Transmission electronic micrograp~TEM! of the nanotubes, suspended across abetween two metallic pads, and detailed viewthe contact region showing the metal meltedthe laser pulse.

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differential resistance. This suggests that several diffephysical mechanisms could contribute to the very lotemperature dependence of the resistance.

In Sec. IV we show that when the contact pads are suconducting, a supercurrent can flow through SWNT’s as was through ropes of SWNT’s.11 These experiments indicatein principle, that quantum coherent transport can take plthrough carbon nanotubes over micron-long scales. Howethe unexpectedly high measured values of the critical curin individual nanotubes, along with nonlinearities in theI -Vcharacteristics at voltages much higher than the superducting gap of the contacts raise the question of possintrinsic superconductivity.

Finally in Sec. V we present measurements on long roof SWNT’s connected to normal contacts which indeed shevidence of intrinsic superconductivity below 0.5 K, prvided that the distance between normal electrodes is laenough. We discuss the one-dimensional character oftransition and the physical parameters which governtransition, such as the presence of normal reservoirs, intube coupling, and disorder.

II. SAMPLE DESCRIPTION AND PREPARATION

The SWNT’s are prepared by an electrical arc methwith a mixture of nickel and yttrium as a catalyst.12,13

SWNT’s with diameters of the order of 1.4 nm are obtainThey are purified by the cross-flow filtration method.13 Thetubes usually come assembled in ropes of a few hundtubes in parallel, but individual tubes can also be obtainafter chemical treatment with a surfactant.14 Connection ofan individual tube or rope to measuring pads is performaccording to the following nanosoldering technique: A tarcovered with nanotubes is placed above a metal-coatedpended Si3N4 membrane, in which a 0.33100 mm2 slit hasbeen etched with a focused ion beam. As described in10, we use a 10-ns-long pulse of a focused UV laser be~power 10 kW! to detach a nanotube from the target, whi

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then falls and connects the edges of the slit below. Sincemetal electrodes on each side of the slit are locally moltthe tube gets soldered into good contacts and is suspe~see Fig. 1!.

The electrodes are usually bilayers~Re/Au, Ta/Au, Ta/Sn!or trilayers (Al2O3 /Pt/Au) of nonmiscible materials~in liq-uid or solid phases!, in which the lower layer~Re, Ta! has ahigh melting temperature in order to protect the nitride mebrane during the welding of the tube to the top gold lay~see Table I!. Gold was mostly chosen as the solder matebecause it neither reacts with carbon nor oxidizes. The ctact region is pictured in the transmission electron micscope~TEM! view of Fig. 1. Balls of metal molten by thelaser pulse can be seen on the edges of the slit.

Because the tubes are suspended, they can be structuand chemically characterized in a TEM working at moderacceleration voltages~100 kV! as shown in Fig. 1. We measure the lengthL and diameterD of a rope and estimate thnumber of tubesN in the rope throughN5@D/(d1e)#2,whered is the diameter of a single tube (d51.4 nm) ande isthe typical distance between tubes in a rope (e50.2 nm).

We can also check that no metal covers or penetratestubes. In addition we estimate, using electron energy-lspectroscopy~EELS!, that chemical dopants such as oxygare absent to within 2%~see Fig. 2!. The characterizationprocedures can of course deteriorate the samples, becauelectron irradiation damage15 which can cause local amorphization and induce an increase in the tubes resistance

The originality of our fabrication technique lies in thsuspended character of the tubes, the quality of the tuelectrode contact, and the ability to characterize the msured sample in a transmission electron microscope.

III. TRANSPORT IN THE NORMAL STATE

A. Measurement circuit and sample environment

The samples were measured in dilution refrigeratorstemperatures ranging from 300 K to 0.015 K, through filter

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QUANTUM TRANSPORT THROUGH CARBON . . . PHYSICAL REVIEW B68, 214521 ~2003!

FIG. 2. Typical electron energy-loss spectru~EELS! on a carbon nanotube rope~lower curve!,compared to the EELS spectrum of an amorphocarbon membrane~upper curve!. The peak at285.5 eV of carbon is visible in both spectra. Thoxygen peak~at 540 eV! is much larger in themembrane than on the tubes, and the O2 contentin the rope is estimated to be less than 1.5atomic content.

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lines. Good calibration of the thermometer and thermalition of the samples are only guaranteed below 1 K, sohigher-temperature data are only indicative. Magnetic fieof up to 5 T could be applied perpendicular to the contaand the tubes. The resistance was measured by runnismall ~0.01 nA–10 nA, 30 Hz! ac current though the sampand measuring the corresponding ac voltage using locdetection.

The two large~roughly 10 mm2) metallic contacts on ei-ther side of the suspended nanotube constitute, withground copper plate on the other side of the silicon watwo capacitances of the order of 3 pF which help filter oresidual high-frequency radiation.

When the tubes were contacted to superconducting etrodes or exhibited intrinsic superconductivity, the investigtion of the normal state was done by applying a magnfield large enough to destroy the superconductivity.

B. Individual single-wall nanotubes

Depending on their room-temperature resistance, wethat SWNT’s can be insulating or metallic at low tempeture. The SWNT samples with high-~larger than 40 kV) RTresistance become insulating, with an exponential increasresistance, asT is decreased. This insulating behavior coube due to the atomic structure of the tube, correspondingsemiconducting band structure, with a gap smaller thanexpected value at half filling because of doping by the ctacts. It could also be caused by the presence of disorder

TABLE I. Main features of the contacts of the investigatnanotubes.Tc denotes their transition temperature when theysuperconducting.

Contact Composition Tc

TaAu 5-nm Ta, 100-nm Au 0.4 KReAu 100-nm Re, 100-nm Au 1 KTaSn 5-nm Ta, 100-nm Sn 3 KCrAu 5-nm Cr, 100-nm Au <50 mKPtAu 5-nm Al2O3, 3-nm Pt, 200-nm Au <20 mK

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tube~the importance of which is discussed further along!. Inthe following, we focus exclusively on the SWNT samplwhich remain metallic down to low temperature. They apresented in Table I. Their resistance at room temperalies between 10 kV and 70 kV, and increases by less thanfactor of 2 between 300 K and 1 K.

The temperature dependence of the zero-bias resistanfour samples is shown in Fig. 3 in a log-log plot. The icrease of resistance asT is lowered can be described bypower law with a very small negative exponent which varbetween 0.01 for the less resistive tube and 0.1 for the mresistive one. Note that because of the very small valuethese exponents a logarithmic lawR}R02a ln T could fitthe data just as well. This behavior is observed down to

FIG. 3. Temperature dependence of the resistance of diffesingle tubes: ST1, ST2, and ST4 are mounted on Au/Ta contactsmeasured in a magnetic field of 4 T to suppress the supercontivity of the contacts. ST3 is mounted on CrIn contacts. Notelogarithmic scales. TEM micrograph of the corresponding sampThe dark spots are Ni/Y catalyst particles.

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mK without any sign of saturation. This weak temperatudependence has also recently been measured in samwhere good contact to electrodes was achieved by burthe tube ends over a large distance under metallic electrfabricated with electron-beam lithography.16,17 It is on theother hand in stark contrast with theT dependence of tubewith tunnel contacts,8,18which exhibit power laws with muchlarger exponents~of the order of 0.3! at high temperatureand exponentially increasing resistance at lower temperabecause of Coulomb blockade. It is not surprising thataddition to the intrinsic conducting properties of tubes~inter-actions, band structure, and disorder!, the way they are contacted should determine the temperature dependence oresistance. For instance, extrapolating the results obtaineLuttinger liquids between normal reservoirs,19 the resistanceof a ballistic tube on perfect contacts is expected to bein-sensitive to interactionsand to be given byRQ/25h/2e2

56.5 kV at all temperatures. In contrast, a tube on tuncontacts will turn insulating at low temperature becauseCoulomb blockade. Since our measurements are two wmeasurements, it is difficult to determine how much of tresistance is due to the contacts, and how much is due totube itself. However, the existence in these very sasamples of a large proximity effect along with a high supcurrent~see the following section! suggests that the transmision at the contacts is close to unity. We therefore attribthe excess resistance compared to the expected valueRQ/2 todisorder inside the tubes.

We can then try to quantify the amount of disorder withour SWNT samples and discuss the possibility of them sbeing metallic. To do this, we choose to consider the natube as a homogeneous diffusive conductor withM conduct-ing channels~in a SWNT M52) and apply the Drude formula which relates the conductance to the elastic meanpath l e throughG5M (e2/h) l e /L52GQl e /L. The values ofl e deduced in this way are given in Table I. We find rathshort mean free paths compared to the length of the tu~especially for sample ST4!, suggesting the presence of dfects in the tubes. The microscopic cause of these short mfree paths could be heptagon-pentagon pairs or defectsated by electron irradiation during observations in TEM.

One of the questions raised by these small values ofl e /L,or equivalently the small values ofG/GQ , is why thesesamples do not localize. Indeed, according to the Thoucriterion,20 a quantum coherent conductor is expected tocalize, i.e., becomes insulating at low temperature, if its cductanceG is smaller thanGQ . In contrast, we observe nsign of strong localization down to very low temperatuwhere quantum coherence throughout the whole sampexpected to be achieved. One possible explanation coulin the fact that the conductance of a SWNT could be setive to interactions even on good contacts as recesuggested.21 These authors, extending the calculations ofChannonet al.22 on chiral Luttinger liquids to the nonchiracase, predict that the two-contact conductance is renormized by a factor which depends on the boundary conditiimposed at the contacts, which can be of the order of theparameterg. In their calculation, there is no nearby gatescreen the interactions, and this is indeed our experime

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configuration. These theoretical results could then expwhy the high measured resistances do not lead to localizaat low temperature. However, the same LL theories23 predictthat for a well contacted sample the weak temperaturependenceG2G05aT2x should saturate at temperatursmaller than the energy scaleEc5hvr /L, wherevr is theplasmon velocityvr5vF /g. In our tubesEc is of the orderof 30 K or more, and we observe no saturation. Therefowe do not think that the low-temperature dependence ofresistance observed in these samples contains a clear sture of Luttinger liquid behavior .

We now examine the voltage dependence of the differtial resistancedV/dI, below 1 K, and with the contacts in thnormal state. Like the temperature dependence of the zbias differential resistance, thedV/dI has a weak power-lawdependence as a function ofV, which can also be fitted by alogarithmic law. This behavior at first glance is qualitativesimilar to what is observed in small metallic bridges preseing a small Coulomb-type anomaly in their differentiresistance.24 However in the present case the similarity btween temperature and bias voltage dependence isqualitative, as shown in Fig. 4: the decrease of differenresistance withV is slower than the corresponding temperture dependence. In addition,dV/dI saturates below bias values corresponding to an energy much larger than the tperature. In contrast to nanotubes connected with tuncontacts8 or small metallic constrictions,24 it is not possibleto scale the data using the reduced variableeV/kBT. Thisabsence of a voltage vs temperature scaling suggests thatemperature dependence of the resistance contains othertributions besides the expected increase due to electelectron interactions~for instance, weak localization contributions! and calls for further understanding.

C. Ropes of single-wall carbon nanotubes

Ropes of SWNT contacted using the same technicover a much wider range of resistances than individ

FIG. 4. Bias dependence at 50 mK of the differential resistaof individual tubes ST2 and ST3 in comparison with temperatdependence~temperature is expressed in eV units!.

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SWNT. The resistances vary between less than 100V and105 V at 300 K for ropes containing between 40 and sevehundred SWNT’s~see Table III!. There is no clear correlation between the number of tubes in a rope~deduced fromthe rope diameter! and the value of its resistance. This mindicate that in some cases only a small fraction of the tuare connected. In contrast to individual nanotubes, the roseem to verify the Thouless criterion: they strongly localwhen their resistance is above 10 kV at room temperatureand stay quasimetallic otherwise. This behavior is very silar to what is observed in quasi-1D metallic wires.25 Thetemperature dependence of the metallic ropes~see Fig. 5! isalso very weak. But for low-resistance ropes (R,10 kV) itis not monotonous, in contrast to individual tubes, andalready observed in Ref. 26: the resistance decreases linas temperature decreases between room temperature aK, indicating the freezing-out of phonon modes, and thincreases asT is further decreased, as in individual tubes.all samples a bias dependence of the differential resistanalso observed at low temperature~Fig. 6!. The relative am-plitude of these nonlinearities are much smaller than in invidual SWNT. This may be related to screening of electroelectron interactions in a rope, which does not exist insingle tube. The magnitude of the resistance variation witVincreases with rope resistance and is weaker than the csponding temperature dependence. The absence of sclaws in the reduced variableeV/kBT is more striking than forindividual tubes. In particular, the differential resistance sarates below voltages much larger than temperature.

FIG. 5. Temperature dependence of the resistance measuredifferent ropes mounted on various types of contacts. Forsamples the measurements were conducted in a magnetic fieldT. Note the logarithmic scales.

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D. Importance of intertube coupling in ropes

In order to determine whether a rope is closer to ansembly of ballistic tubes in parallel or to a single diffusivconductor, we need to evaluate the importance of intertcoupling and electron transfer between tubes within a roThe characteristic microscopic electron hopping energyt'between two carbon atoms on different tubes dependstheir relative distanced throught'}tGexp(2d/a). Herea isthe spatial extension of thepz orbital of carbon andtG is thehopping energy between two sheets of graphite.27 Given thedifferences in C-C distances and orbitals, the ratio betwperpendicular and parallel hopping energies in carbon natubes has been evaluated to be at mostt' /t i'0.01. In anordered rope containing identical individual tubes, authorsRef. 28 have shown that this low intertube coupling canduce a band gap of about 0.1 eV, turning a rope of metatubes into a semiconductor.

On the other hand, in a rope constituted of tubes wdifferent helicities, in the absence of disorder within ttubes, one finds that the intertube electronic transfer, defias the matrix element of the transverse coupling betweentubes, integrated over spatial coordinates, is negligiblecause of the longitudinal wave-function mismatch betweneighboring tubes of different helicities. The rope can thbe considered as a number of parallel independent ballnanotubes. The very small level of shot noise observedlow resistive ropes corroborate this statement.29 However, ithas been shown27 that the presence of disorder within thtubes favors intertube scattering by relaxing the strictthogonality between the longitudinal components of twave functions. Using a very simple model where disordetreated perturbatively30 we find that for weak disorder theintertube scattering time is shorter than the elastic scattetime within a single tube. In tubes longer than the elasmean free path, this intertube scattering can provide ational conducting paths to electrons which would otherwbe localized in isolated tubes. Consequently, disorderopes can be considered as anisotropic diffusive conduc

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FIG. 6. Differential resistance of four ropes in the normal stas a function of voltage bias and as a function of temperature~ex-pressed in units of voltage!. The difference between bias and temperature dependence tends to be weaker when the resistancerope increases.

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that, in contrast to individual tubes, exhibit a localizatilength that can be much larger than the elastic meanpath. This is why we have tentatively determined for earope an elastic mean free path from the value of its condtance using the multichannel Landauer expression for aordered conductor equivalent to the Drude formulaG52M (e2/h) l e /L, with the number of channelsM52Nt ,whereNt is the number of tubes inside the sample. Sincenumber of metallic tubes connected is statistically of theder or less thanNt/3, these values ofl e are certainly under-estimated. In addition, it may be possible that the metatubes in a rope are not all well connected to both electrodThen transport through the rope will proceed via intertutransfer. This is why ropes with many disordered metatubes might have high resistances~Table III!.

IV. PROXIMITY-INDUCED SUPERCONDUCTIVITY

A nonsuperconducting or normal metal~N! in good con-tact with a macroscopic superconductor~S! is in the so-called ‘‘proximity effect regime’’: superconducting correlations enter the normal metal over a characteristic lengthLNwhich is the smallest of either the phase-coherence lengtthe normal metalLf or the thermal lengthLT ~in a cleanmetal LT5\vF /kBT and in a dirty metalLT5A\D/kBT,whereD is the electron diffusion coefficient!. Both lengths,of the order of a few micrometers, can be much longer ththe superconducting coherence lengthj5hvF /D or A\D/D,whereD is the energy gap of the superconducting contac

If the normal metal’s length is less thanLN and if theresistance of the NS interface is sufficiently small, a gapthe density of states is induced in the normal metal, whicas large as the gap of the superconductor in the vicinitythe interface and decreases on a typical length scale ofLN .Consequently, a normal metal shorter thanLN between twosuperconducting electrodes~a SNS junction! can have a criti-cal temperature~equal to that of the superconductor alon!and exhibits a Josephson effect, i.e., a supercurrent atbias. This manifestation of the proximity effect has beentensively studied in multilayered planar SNS junctions31 andmore recently in lithographically fabricated micron scale mtallic wires made of normal noble metals between two mroscopic superconducting electrodes.32,33The maximum low-temperature value of the supercurrent~critical current! insuch SNS junctions of normal-state resistanceRN is pD/eRNin the short junction limitL!j or D!Ec ~Ref. 34!, andaEc /eRN in the limit of long junctionsL@j or Ec!D.33

Herea is a numerical factor of the order of 10 andEc is theThouless energyEc5\D/L2.

Probing the proximity effect in a normal wire connectto superconducting electrodes and, in particular, the etence of a Josephson current constitutes a powerful toothe investigation of phase-coherent transport throughnormal wire. In the following section we present experimetal results on carbon nanotubes mounted on superconduelectrodes showing evidence of large supercurrents windicate that coherent transport takes place on micron lenscales.

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A. Proximity effect in individual tubes

We have observed proximity-induced superconductivin the three different individual SWNT ST1, ST2, and STdescribed in the preceding section. These samplesmounted on Ta/Au electrodes, see Table II which are alayer ~5-nm Ta, 100-nm Au! with a transition temperature othe order of 0.4 K. This value is strongly reduced compato the transition temperature of bulk tantalum~4 K! due tothe large thickness of gold relative to tantalum.

1. Zero-bias resistance

For these three samples the zero-bias resistance exhibbroad transition around the superconducting transition teperature of the contacts and becomes zero at lower tempture except for the highest-resistance sample ST4 (RN570 kV) which has a residual resistance of 800V. Thetransition is shifted to lower temperature when a magnefield is applied in the plane of the contacts and perpendicto the tube axis. Above 2 T the resistance is field independand slightly increases when the temperature is loweredlow 0.2 K, as already mentioned in the preceding sect

TABLE III. Principal characteristics of ropes presented in thpaper. The numberN of SWNT in each rope is deduced from thdiameter of the rope. Mean free paths are estimated assumingall tubes participate to transport and that transmission at thetacts is of the order of unity.

SampleLength(mm) N ~approx.! R(T5290 K) R(4,2 K) l e ~nm!

R1PtAu 1.6 300 1.1 kV 1.2 kV 40R2PtAu 1 350 4.2 kV 9.2 kV 18R3PtAu 0,3 240 475V 500 V 9R4PtAu 1 30 620V 620 V 23R5PtAu 2 300 16 kV 21 kV 3R6PtAu 0.3 200 223V 240 V 30R3TaSn 0.3 300 2.2 kV 3 kV 3R5TaSn 0.3 300 700V 1.1 kV 9.2R1CrAu 0.4 200 400V 450 V 22R2CrAu 0.2 200 240V 280 V 26R1ReAu 0.5 200 1750V 2 kV 6R2ReAu 0.5 200 650V 700 V 18R3ReAu 1.7 200 65V 65 V 572

TABLE II. Summary of the characteristics of four SWNT in thnormal state. The mean free pathl e is estimated usingR5RQL/(2l e), and assuming a perfect transparency of the contThe actual mean free path could therefore be larger.

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ST4 TaAu 300 45 66 50ST2 TaAu 200 31 33 62ST1 TaAu 300 22.1 33 90ST3 CrIn 100 10.7 11.5 70

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~see Table III!. The critical field is of the order of 1 T and cabe also extracted as the inflection point of the magnetoretance depicted in Fig. 7. This value is surprisingly high sinit is ten times larger than the measured critical field ofcontact~0.1 T!. This high value of critical field could be duto local modifications of the bilayer Ta/Au film in the contaregion due to the laser pulse, in particular, the melted up

FIG. 7. Left panel: Temperature dependence of the resistancthree different single tubes ST1,2,4. mounted on TaAu, for differvalues of the magnetic field perpendicular to the tube axis inplane of the contacts.~The labels on the curves correspond to tvalue of magnetic field in tesla.! For some samples the resistancethe contacts exhibited several steps in temperature, probablycating inhomogeneities in the thickness of the gold layer. This mexplain the small-resistance drop observed on sample ST1 arouK at low field. Top right panel: field dependence of the transititemperature, defined as the inflection point ofR(T). Bottom rightpanel: Magnetoresistance of the single tubes measured at 50~the magnetic field is perpendicular to the tube axis in the planthe contacts!. This positive magnetoresistance only saturates at vhigh field ~2T!.

FIG. 8. I vs V curve of the single tube ST1, from which thcritical current is deduced. Right panel, data on a wider currscale showing the existence of voltage steps for currents aboveI c .The arrows indicate the current sweep direction.

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gold film is probably much thinner than the original one. Ithowever important to note that these critical fields are ofsame order of magnitude in all the samples measuredFig. 7 shows, the transition lineTc(H) is a linear function offield for all samples.

2. Bias dependence and critical current

The most striking signature of induced superconductivis the existence of Josephson supercurrents throughsamples.11 The existence of a supercurrent shows up involtage vs current curves and differential resistance, see8. For sample ST1, the transition between the superconding state~zero voltage drop through the sample! and the dis-sipative~resistive! state is quite abrupt and displays hysteesis at low temperature. It is characterized by a criticurrentI c50.14mA near zero temperature. Similar behaviwith smaller values of critical current is also observed in tother samples~see Table IV!. The productRNI c at T'0,varies between 1.6 and 3.5 mV. If we deduceD from Tc ofthe superconducting contacts, we find thatRNI c is more thanten times largerthan the maximum expected value (pD/e50.2 mV) for the short junction limit,34 Ec.D, to which allsamples correspond. It is then also interesting to note thaproduct eRNI c is closer to the gap of pure tantalumDTa50.7 meV. But it is difficult to understand why the inducegap could be the gap of pure tantalum whereas the resistdrop of the tube follows the transition of the Au/Ta bilaye

Somewhat unexpectedly and uncharacteristic of mSNS junctions, the normal-state resistance is not recoveabove the critical current, but theV(I ) curve shows furtherhysteretic jumps at higher currents.

These features also appear in the differential resistadV/dI ~see Fig. 9!. The superconducting state correspondsthe zero differential resistance at low dc current. At the crcal current the differential resistance displays a sharp pfollowed by smaller ones at higher current. Each peak cosponds to a hysteretic feature in the dcV-I curve. The peaksare linearly shifted to lower current when increasing manetic field and all disappear above 2 T. The temperaturefield dependencies of the critical current extracted from tdata are plotted in Fig. 9. The temperature dependencvery weak below 0.8Tc and decreases rapidly above. It do

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TABLE IV. Principal features of the superconducting junctioobtained with individual tubes.TC is the transition temperature othe contact-SWNT-contact junction,RN is the normal-state resistance, andI C is the critical current of the junction.Dcontact is the gapof the contacts estimated from their transition temperature.Thouless energyEC is computed using the mean free pathsl e esti-mated in the preceding section. These energies are expressmeV.

Length(mm) TC ~K!

RN

(kV) I C(mA) Dcontact

RNI C

~mV! EC

ST1 0.3 0.5 25 0.14 0.07 3.5 0.4ST2 0.3 0.45 33 0.075 0.07 2 0.3ST4 0.3 0.25 65 0.025 0.07 1.6 0.1

t

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FIG. 9. Differential resistance of the thresamples ST1, 2, and 4 for different magnefields. Right panels: Field and temperature depedence of the critical current, defined as the curent at which the first resistance jump occurs. Tcritical current disappears aroundHc51 T,which is also the value deduced from the lowtemperatureR(H) curves in Fig. 7.

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not follow the behavior expected for SNS junctions~neitherin the limit of short junctions nor long junctions where aexponential decay of the critical current is expected33!. Thefield dependence of the critical current is precisely linearall samples, with disappearance of critical current above

It is very difficult to understand these results in the framwork of conventional proximity-induced superconductivitIn particular, we have already mentioned that theI -V curvesexhibit nonlinearities, and signs of superconductivity at velarge bias, i.e., much larger than the gap of the Ta/Au ctacts~and even the gap of pure tantalum!. Such nonlinearitiesrecall manifestations of phase slips in 1D superconductor35

Above I c , small normal regions of size comparable to tinelastic lengthLN are nucleated around defects in tsample~phase slip centers!. They have not, to the best of ouknowledge, been observed before in SNS junctions. Thobservations by themselves suggest the possibility of intsic superconducting correlations in SWNT, which will bdiscussed further on.

It is therefore interesting to compare these results withsuperconductivity of other types of metallic nanowires. Rerence 36 reports superconducting nanowires fabricateddepositing thin films of amorphous MoGe on suspended

21452

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bon nanotubes. Disappearance of superconductivity inmost resistive wires is attributed to the formation of quantphase slips at very low temperature. The first data obtaiin these samples indicated disappearance of superconduity for normal-state resistance larger thanh/4e2. In a laterpaper,37 the authors show that what determines the suppsion of superconductivity is not the normal state resistabut rather the resistance per unit length. They find thattransition is suppressed for resistances per unit length lathan roughly 0.1 kV/nm. We have observed proximityinduced superconductivity in SWNT’s with a normal-staresistance up to 70 kV, with a resistance per unit length othe order of 0.25 kV/nm. Note however that the MoGnanowires contain typically 10 000 channels, whereasnanotubes only contain two conducting channels. This coparison tells us that proximity-induced superconductivityamazingly robust in our samples.

Finally signs of proximity-induced superconductivithave also been observed by other groups, on individSWNT ~Ref. 38! and on multiwall nanotubes,39 but withoutsupercurrents. In The Appendix of this paper we showresults on proximity-induced superconductivity in multiwananotubes.

TABLE V. Main features of the ropes suspended between superconducting contacts.TC is the transitiontemperature of the junction, whileD is the gap of the contacts.RN is the resistance at 4.2 K andI C is thecritical current of the junction. Thouless energyEC is computed using the mean free pathsl e computed in thepreceding section. Energies are in meV.

Length (mm) TC RN (V) I C D RNI C EC

R1ReAu 0.5 <50 mK 1750 0 0.12 0 0.01R2ReAu 0.5 <50 mK 650 0 0.12 0 0.03R3ReAu 1.7 1 K 65 2.7mA 0.12 0.175 mV 0.13R3TaSn 0.4 0.7 K 2200 0.54mA 0.6 1.5 mV 0.01R5TaSn 0.4 0.6 K 700 0.77mA 0.6 0.63 mV 0.03

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B. Proximity-induced superconductivity in ropes

We also found proximity-induced superconductivityropes of SWNT mounted on Re/Au or Ta/Sn, characterisof which are shown in Table V and Figs. 10–13.

It is interesting to note that in contrast to what was fouin SWNT’s, we only observe proximity-induced supercoductivity in ropes with a normal-state resistance less t10 kV. More resistive ropes, as previously mentioned,insulating at low temperature. The data of Fig. 10 for ropmounted on Re/Au show that although a resistance droobserved in the vicinity of the transition of the contacproximity-induced superconductivity is not always compleand is only slightly visible on the most resistive sample. Tmay result from the combined effects of the quality of tcontacts and disorder in the rope for which the conditLN.L may not be fulfilled in our available temperaturange. The critical current deduced at 50 mK from theI -Vcurves are given in Table V and compared to the theoretpredictions. The rope on Re/Au contacts is in the short jution regime (D,Ec) and the ropes on TaSn are in the lojunction limit. In all cases the measured supercurrentslarger than allowed by the theory of SNS junctions. Itnoteworthy that the two ropes mounted on tin have simcritical currents (I c'0.7 mA) in spite of the fact that theirnormal-state resistances differ by more than a factor of 3for the individual tubes, jumps in theI -V curves are alsoobserved at bias larger than the gap of tin. The temperadependence of the critical current inR3ReAu ~see Fig. 13! ismore pronounced than for individual tubes, and can beproximately fitted by an Ambegaokar-Baratoff law typicaltunnel junctions.40 In the case of ropes mounted on tin cotacts this temperature dependence is difficult to extractcause of the rounding of theI -V curves with increasing temperature. In contrast to individual tubes, the field dependais not monotonous. The critical current first increases up0.1 T where it goes through a maximum and decreasesearly at higher field up to 1 T. Such nonmonotonous behahas been predicted in a number of models describing nonmogenous superconductors and could be related to inteence between different electronic trajectories along the vous tubes of the rope and the existence of negative Josep

FIG. 10. Temperature dependence of the resistance of rR1ReAu, R2ReAu, R3ReAu mounted on Re/Au contacts in zero manetic field.Tc of Au/Re is 1 K. SampleR3ReAu becomes superconducting below 1 K, but the resistance steps above the transindicates that the superconductivity of the contacts may not bemogeneous.

21452

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couplings between these tubes. This recalls the nmonotonous magnetoresistance of amorphous superconing wires41 and in multiwall carbon nanotubes~see Appen-dix!, and may have a common origin.

Effect of magnetic-field orientation

For the ropes mounted on tin we investigated the magtotransport for different field orientations. We found that withe field parallel to the contacts~and perpendicular to thetubes! the critical fields were much larger than the criticfield of the contacts. This may be explained by a local thning of the metallic layer contacting the tube in the contregion after soldering. Figure 14 shows the magnetoretance for these two different field orientations. For thesamples the magnetoresistance was also measured betwand 20 T using the high-field facility in Grenoble at 1 K withthe magnetic field along the rope~see Fig. 15!. The magne-toresistance increases linearly with field and saturates oabove 10 T. This field is of the order of the ClogstoChandrasekhar42 criterion for destruction of superconductivity by pair breaking due to spin polarization:m0Hp5DSn/mB'7 T, whereDSn is the gap of tin. Unfortunatelythe high-field experiments were not conducted in the satemperature range as the low-field ones, and in the secmeasurement~low field!, because of thermal cycling, thsample exhibited less proximity effect. Nevertheless,seems as though the superconductivity depends on the otation of the magnetic field with respect to the tube andonly on its orientation with respect to the contacts, aspected for proximity-induced superconductivity.

C. Discussion

Observation of a strong proximity effect indicates thphase-coherent transport takes place in carbon nanotubethe micron scale. However in the case of single-wall tubthe surprisingly high values of critical currents cannot

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FIG. 11. Temperature dependence of the critical current of rR3ReAu. Main panel:I -V curves at different temperatures. InseTemperature dependence of the critical current~triangles! and fit tothe Ambegaokar Baratoff formula i AB(T)5 i 0D(T)/D(0)tanh@D(T)/2kBT# ~continuous line!.

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FIG. 12. Left panel: Temperature dependenof zero-bias resistance of ropesR3TaSn andR5TaSn. Right panels: differential resistanccurves taken at 0.1 T, with an example of thhysteresis with current sweep direction.

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described by the standard theory of SNS junctions. The plem of a SNS junction constituted of a Luttinger liquid btween two superconducting reservoirs has been considtheoretically for weakly transmitting contacts43 and for per-fectly transmitting contacts.44,45 In both limits the authorspredict that it is indeed possible to induce superconductiby a proximity effect. In the case of repulsive interactioand perfectly transmitting interfaces the zero-temperavalue of the critical current is not changed by the intertions. More recently it has been shown that the presencattractive interactions in a Luttinger liquid can result insignificant increase of the critical current46,47 and unusual

FIG. 13. V vs I curves of ropesR3TaSn and R5TaSn in fieldsranging from 0 to 1.5 T. Inset: field dependence of the critical crent deduced form theseI -V curves. The field is parallel to thecontacts and perpendicular to the tubes. Note the non monotobehavior.

21452

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temperature dependencies very similar to what we obsefor individual tubes. A more accurate fit of the temperatudependence of the critical current in the rope includingexistence of the inflection point can also be obtained usthe theoretical predictions of Gonzalez.47

Our data could thus be explained by the existence ofperconducting fluctuations intrinsic to SWNT. For an infininanotube, because of its 1D character, these fluctuationsnot expected to give rise to a superconducting state at fitemperature. However, the superconducting state couldstabilized by the macroscopic superconductivity of the ctacts. In such a situation, it is conceivable to expect the ccal current to be enhanced compared to its value in a cventional SNS junction and to be given by the critical curreof a superconducting 2-channel wire;I c5(4e2/h)D t ,48 de-termined by the value of the superconducting pairing amtudeD t inside the wire and independent of the normal-stresistance of the nanotube~in the limit where the mean freepath is larger than the superconducting coherence leng!.The existence of superconducting fluctuations intrinsicnanotubes may also help in explaining the positive magtoresistance observed in all our samples where the normstate resistance is recovered at fields much higher thancritical field of the contacts. In the following section wshow that these hypotheses are corroborated by the obstion of intrinsic superconductivity in ropes of SWNT.

-

usFIG. 14. Magnetoresistance of the ropeR3TaSn measured at 50

mK for the field parallel and perpendicular to the contacts, aalways perpendicular to the tube.

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V. INTRINSIC SUPERCONDUCTIVITY IN ROPESOF SWNT ON NORMAL CONTACTS

In the following we discuss the low-temperature transp~below 1 K! of suspendedropesof SWNT connected to normal electrodes. The electrodes are trilayers of sputteAl2O3 /Pt/Au of respective thickness 5, 3, and 200 nm. Thdo not show any sign of superconductivity down to 50 m

As shown in Fig. 16, different behaviors are observedthe temperature dependence of the zero-bias resistanceresistance of some samples (R3PtAu and R6PtAu) increasesweakly and monotonously asT is reduced, whereas the resistance of others (R1,2,4,5PtAu) drops over a relativelybroad temperature range, starting below a temperatureT*between 0.4 and 0.1 K (T1* 5140 mK, T2* 5550 mK, andT4* 5100 mK). The resistance ofR1PtAu is reduced by 30%at 70 mK and that ofR4PtAu by 75% at 20 mK. In both caseno inflection point in the temperature dependence isserved. On the other hand the resistance ofR2PtAu decreases

FIG. 15. Magnetoresistance of the ropeR3TaSnmeasured at 1 Kwith the field along the tube in the high-field facility at GrenobNote that the magnetoresistance increases in magnetic field uH510 T.

FIG. 16. Resistance as a function of temperature for thesamples described in Table VI, both in zero fields and large fie

21452

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by more than two orders of magnitude, and reaches a cstant value below 100 mK,Rr574 V. This drop of resis-tance disappears when increasing the magnetic field. Fothe samples we can define a critical field perpendicular toropes above which the normal-state resistance is recoveAs shown in Fig. 17 this critical field decreases linearly wtemperature, very similar to what is seen in SWNT and roconnected to superconducting contacts. We define a ztemperature critical fieldHc as the extrapolation ofHc(T) tozero-temperature~see Fig. 17!.

Above the critical field, the resistance increases withcreasing temperature, similar to ropes 3 and 6, and becoindependent of magnetic field. Figures 18 and 19 showin the temperature and field range where the zero-bias retance drops, the differential resistance is strongly currentpendent, with lower resistance at low current. These dsuggest that the ropes 1, 2, and 4 are superconductingthough the experimental curves forR2PtAu look similar tothose of SWNT’s connected to superconducting contact11

to

TABLE VI. Summary of the characteristics of six ropemounted on Pt/Au contacts.T* is the temperature below which thresistance starts to drop,I c is the current at which the first resistancincrease occurs, andI c* is the current at which the last resistanjump occurs.

L(mm) N R290 K R4.2 K

T*~mK! I c

I c*(mA)

R1PtAu 2 350 10.5 kV 1.2 kV 140 0.1mA 0.36R2PtAu 1 350 4.2 kV 9.2 kV 550 0.075mA 3R3PtAu 0.3 350 400V 450 V

R4PtAu 1 45 620V 620 V 120 0.1R5PtAu 2 300 16 kV 21 kV 130 20 nA 0.12R6PtAu 0.3 200 240V 240 V

ixs.

FIG. 17. Resistance as a function of temperature for samR1,2,5PtAu showing a transition. The resistance ofR1 is measuredin magnetic fields ofm0H5 0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.2, 0.0.6, 0.8, and 1 T from bottom to top. The resistance ofR2 is takenat m0H50, 0.05, 0.1, 0.2, 0.4, 0.6, 0.8, 1, 1.25, 1.5, 1.75, 2, andT from bottom to top. That ofR5 atm0H50, 0.1, 0.2, 0.3, 0.5, and1.4 T from bottom to top. Bottom right:Tc(H) for R2.

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there are major differences. In particular,V(I ) anddV/dI(I )do not show any supercurrent because of the existencefinite residual resistance due to the contacts being norm

Before analyzing the data further we wish to emphasthat this is the first observation of superconductivity in wirhaving less than 100 conduction channels. Earlier expments in nanowires37,41,49dealt with at least a few thousanchannels. We therefore expect a strong 1D behavior fortransition. In particular, the broadness of the resistance dwith temperature is due to large fluctuations of the supercducting order parameter in reduced dimension starting at3D transition temperatureT* . In the following we will try toexplain the variety of behaviors observed taking into accoseveral essential features: the large normal contacts, togwith the finite length of the samples compared to relevmesoscopic and superconducting scales, the number of twithin a rope, the amount of disorder, and intertube coupliWe first assume that all ropes are diffusive conductors butwill see that this hypothesis is probably not valid in the leresistive ropes.

A. Normal contacts and residual resistance

We first recall that the resistance of any superconducwire measured through normal contacts~a NSN junction!cannot be zero: a metallic SWNT, with two conducting chanels, has a contact resistance of half the resistance quanRQ/2 @where RQ5h/(2e2)512.9 kV], even if it is super-conducting. A rope ofNm parallel metallic SWNT will havea minimum resistance ofRQ /(2Nm). Therefore we use theresidual resistanceRr to deduce a lower bound for the number of metallic tubes in the ropeNm5RQ/2Rr . From theresidual resistances of 74V in sampleR2PtAu and less than170 V in R4PtAu we deduce that there are at least'90 me-tallic tubes inR2PtAu and'40 in R4PtAu. In both cases thismeans that a large fraction of tubes participate to transand justify a posteriori the hypothesis that ropes are diffusive conductors. In the other samples we cannot estimate

FIG. 18. Differential resistance ofR2PtAu andR4PtAu, at differ-ent temperatures. Right panel: temperature dependence ofI c* , thecurrent at which the last resistance jumps occur in thedV/dIcurves.

21452

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number of conducting tubes because we do not reachregime where the resistance saturates to its lowest value

B. Estimate of the superconducting coherence length

Assuming that the BCS relation holds we get for the sperconducting gapD51.76kBT* :D'85 meV for R2PtAu.We can then deduce the superconducting coherence lealong the rope in the diffusive limit :

j5A\vFl e /D. ~1!

This expression yieldsj2'0.3 mm, wherevF is the longitu-dinal Fermi velocity 83105 m/s. ~Consistent with 1D superconductivity,j2 is ten times larger than the diameter of thrope.! We now estimate the superconducting coherelength of the other samples, to explain the extent or abseof observed transition. Indeed, investigation of the proximeffect at high-transparency NS interfaces has shown thatperconductivity resists the presence of normal contacts oif the length of the superconductor is much greater thanj.50

This condition is nearly fulfilled inR2PtAu (j2'L2/3). Us-ing the high-temperature resistance values and assumigap equal to that ofR2PtAu we find j1'L1/2, j4'L4/2, j3'2L3, andj6'2L6. These values explain qualitatively threduced transition temperature ofR1PtAu andR4PtAu and theabsence of a transition forR3PtAu andR6PtAu. Moreover, wecan argue that the superconducting transitions we see ardue to a hidden proximity effect: if the Al2O3 /Pt/Au contactswere made superconducting by the laser pulse, the shoropes~3 and 6! would become superconducting at tempetures higher than the longer ones~1, 2, and 4!. It is howevernot possible to explain the behavior of sample 5 with tsame kind of argument, since the same expression yiel

FIG. 19. Differential resistance as a function of current fsamplesR1,2,4,5PtAu in different applied fields. SampleR1: Fieldsare 0, 0.02, 0.04, 0.06, 0.08, 0.1, 0.2, and 1 T. SampleR2: Fieldsare 0, 0.2, 0.4, 0.6, 0.8, 1, 1.25, 1.5, 1.75, 2, and 2.5 T. SampleR5:Fields are 0.02, 0.04, 0.06, and 0.08 T. SampleR4: Fields are 0,0.02, 0.06, 0.1, 0.15, 0.2, and 0.4 T. Bottom: Field dependence oI c

for samplesR2PtAu andR4PtAu. Note the linear behavior.

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coherence lengthj5 much shorter than the length of thsample, and nonetheless no complete transition is seenbelieve that this is due to the strong disorder in this samwhich is very close to the localization limit. Figure 17 showthat the transition even disappeared after thermal cycwhen an increase of room-temperature resistance led to cplete localization at low temperature.

C. Role of the number of tubes

Another a priori important parameter is the numbertubes in a rope: the lesser are the tubes in a rope, the cthe system is to the strictly 1D limit, and the weaker is ttransition. If we compare the two ropes in Fig. 20, it is clethat the transition both in temperature and magnetic fieldmuch broader in the ropeR4PtAu with only 40 tubes than inthe ropeR2PtAu with 350 tubes. Moreover, there is no infleion point in the temperature dependence of the resistancthe thinner rope, typical of a strictly 1D behavior. We alexpect a stronger screening ofe-e interactions in a thick ropecompared to a thin one, which could also favor supercondtivity as we will discuss below.

D. Role of disorder and intertube coupling

As is clear from expression~1! for the superconductingcoherence length, disorder is at the origin of a reductionthe superconducting coherence length in a diffusive samcompared to a ballistic one and can in this way also decrethe destructive influence of the normal contacts. More suand specific to the physics of ropes, we have seen thatorder also enhances intertube coupling, so it can increase

FIG. 20. Resistance as a function of temperature~continuousline! and magnetic field~scatter points! for samplesR2PtAu andR4PtAu. Insets: TEM micrographs of the samples.

21452

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dimensionality of the superconducting transition: weakly dordered ropes such asR1 andR4 will be more 1D-like thanthe more disordered ropeR2. Of course, disorder must aways be sufficiently small so as not to induce localizatioThese considerations may explain the variety of behavobserved and depicted in Fig. 21.

Finally, disorder is also the essential ingredient whichveals the difference between the normal state and the suconducting state. In a ballistic rope we would not expectobserve a variation of the resistance over the superconding transition because in both cases the resistance of theis just the contact resistance.

To gain insight in the transport regime, we have pformed shot noise measurements of the ropesR1,3,4,6PtAu,in the normal state~higher level of 1/f noise in the moreresistive ropesR2,5PtAu made the analysis of shot noise impossible in those samples!, between 1 and 15 K. We foundsurprisingly strong reduction of the shot noise, by more tha factor of 100, which is still not well understood, but wouindicate that all the tubes in these ropes are either compleballistic or completely localized,29 in strong apparent contradiction with the observation of the superconducting trantion of R4PtAu, with a 60% resistance drop.

It would however be possible to explain a resistancecrease in ballistic ropes turning superconducting, if the nuber of conducting channels is larger for Cooper pairs thanindividual electrons. In his recent theoretical investigationsuperconductivity in ropes of SWNT, Gonzalez51 has shownthe existence of a finite intertube transfer for Cooper paeven between two tubes of different helicities which havepossibility of single-electron intertube transfer. This Cooppair delocalization could lead to the opening of new channwhen a rope containing a mixture of insulating and ballistubes becomes superconducting.

E. Signatures of 1D superconductivity

Reminiscent of measurements of narrow superconducmetal wires,49 we find jumps in the differential resistance athe current is increased~Fig. 22!. For sample 2 the differential resistance at low currents remains equal toRr up to 50

FIG. 21. Resistance as a function of temperature for all samwhich undergo a transition, plotted in reduced unitsR/Rmax andT/T* .

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nA, where it strongly rises but does not recover its normstate value until 2.5mA. The jump in resistance at the firsstep corresponds approximately to the normal-state retance of lengthj2 of sample 2. Each peak corresponds tohysteretic feature in theV-I curve@Fig. 22~b!#. These jumpsare identified as phase slips,35,49,52which are the occurrencof normal regions located around defects in the sample. Sphase slips can be thermally activated~TAPS!, leading to aroughly exponential decrease of the resistance insteadsharp transition, in qualitative agreement with our expemental observation@Fig. 22~a!#. At sufficiently low tempera-ture, TAPS are expected to be replaced by quantum phslips, which, when tunneling through the sample, contriban additional resistance to the zero-temperature resistan

Also, in sample 2 the current at which the first resistanjump occurs~60 nA, see Fig. 19! is close to the theoreticacritical current of a diffusive superconducting wire48 withgap D2585 meV (I C5D2 /Rje'20 nA), whereas the current at which the last resistance jump occurs (2.4mA, seeFig. 18! is close to the theoretical critical current of a ballitic superconducting wire with the same number of conduing channelsI C* 5D2 /Rre'1 mA.52

We also expect this currentI C* 5D2 /Rre to be the criticalcurrent of a structure with this same wire placed betwesuperconducting contacts with gapDS even if DS,D2 andcan thus be much larger than the Ambegaokar-Baratoffdiction RNI C'DS /e.40 Intrinsic superconductivity mighthus explain the anomalously large supercurrent measurethe experiments described in the preceding section, whnanotubes are connected to superconducting contacts.also interesting to compare the low-temperature quadrdependence of the critical currents which is very similarall samples both on normal and superconducting contac

FIG. 22. ~a! Resistance ofR2PtAu plotted on a log scale asfunction of the inverse temperature atH50. We have subtractedthe low-temperature residual resistance~contact resistance!. Theslope yields an approximate activation energy of 0.8 K which habe compared to the condensation energyEj of Cooper pairs in asample of lengthj Ej5Mn(Ef)D

2j.1 K. Note that this charac-teristic energy is much smaller in our samples containing onlychannels than in whiskers where phase slips can only be obsevery close toTc . ~b! V(I ) anddV/dI(I ) curves showing the hysteretic behavior inV(I ) at each peak in thedV/dI(I ) curve forsampleR2PtAu.

21452

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F. Effect of magnetic field

It is difficult to saya priori what causes the disappearanof superconductivity in carbon nanotubes. The valueHc(0) perpendicular to the tubes, should be compared todepairing field in a confined geometry,53 and corresponds toa flux quantumF0 through a lengthj of an individualSWNT of diameterd, m0HC5F0 /(2Apdj)51.35 T. ButHC(0) is also close to the fieldm0Hp5D/mB51.43 T atwhich a paramagnetic state becomes more favorable thansuperconducting state.42,54Note that this value is of the samorder as the critical field that was measured on SWNT cnected between superconducting contacts, i.e., much hithan the critical field of the contacts.

The linear dependence of the critical current with manetic field observed in all samples is very similar to the dpresented in the preceding section on SWNT on supercducting contacts and appears strongly related to the lindependence inTc(H). This linear scaling with magnetic fieldis surprising since it is not expected to take place in asystem and is more typical of 2D superconductivity.55 A de-pairing mechanism based on spin splitting of the quasipacle energy states could however provide a possible explation. Experiments performed with various field directiocompared to the tube are thus necessary for a better unstanding of the influence of magnetic field on supercondtivity in carbon nanotubes.

VI. CONCLUSION

Data depicted in the preceding section show the existeof intrinsic superconductivity in ropes of carbon nanotubin which the number of tubes varies between 30 and 4The question of the existence of superconducting corrtions in the limit of the individual tube cannot be answeryet. It is of course tempting to consider the high supercurrmeasured on superconducting contacts as a strong indicthat superconducting fluctuations are present also in invidual carbon nanotubes. However since unscreened Clomb repulsive interactions in these samples are expectesuppress superconductivity, precise investigations of invidual carbon nanotubes on normal contacts are necessais essential to conduct experiments on sufficiently losamples~such as the ropes presently studied! so that intrinsicsuperconductivity is not destroyed by the normal contaNote that recent magnetization experiments56 also stronglysupport the existence of superconducting fluctuations be10 K in very small diameter~0.4 nm! individual tubes grownin zeolites.

We now discuss what could be the relevant mechanfor superconductivity in carbon nanotubes. Observationsuperconductivity in carbon based compounds was repoa long time ago. First in graphite intercalated with alkametal atoms~Cs,K!, superconducting transitions were oserved between 0.2 and 0.5 K.57 Much higher temperaturewere observed in alkali-metal-doped fullerenes58 because ofthe coupling to higher-energy phonons. In all these expments it was essential to chemically dope the system toserve superconductivity. There are no such chemical dopin the ropes of carbon nanotubes studied here. As show

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previous works there is some possibility of hole dopingthe tubes by the gold metallic contacts in which electrowork function is larger than in the tubes.59,60 However, al-though this doping could slightly depopulate the highestcupied energy band in a semiconducting tube, it is verylikely that it is strong enough to depopulate other lowenergy subbands for a metallic tube with a diameter innanometer range. More interesting would be a mechanrelated to the 1D electronic structure of carbon nanotubepurely electronic coupling mechanism has been indshown to induce superconducting fluctuations in coupdouble chain systems such as ladders.61 The relevance of thismechanism has been considered also in carbon nanotaway from half filling but the very small order of magnitudfor the energy scale of these superconducting fluctuationnot compatible with our findings.5

Recent estimations of the electron-phonon couplconstants51,62,63in carbon nanotubes seem to be more proising. It is shown that the breathing modes specific to carnanotubes can be at the origin of a strong electron-phocoupling giving rise to attractive interactions which can posibly overcome repulsive interactions in very small diametubes. The possible coupling of these rather high-enemodes to low-energy compression modes in the nanohave been also considered, following the Wenzel Bardsingularity scheme initially proposed by Loss and Marwhere low-energy phonons are shown to turn repulsive inactions in a Luttinger liquid into attractive ones and drive tsystem towards a superconducting phase.64 The suspendedcharacter of the samples may be essential in this mechan

ACKNOWLEDGMENTS

A.K. acknowledges the Russian foundation for basicsearch and solid-state nanostructures for financial supand CNRS for a visitor’s position. We thank M. Devoret,Dupuis, T. Giamarchi, J. Gonzalez, T. Martin, D. Masloand C. Pasquier for stimulating discussions, and P. Lafaand L. Levy for the high-field measurements at LCMI.

APPENDIX: PROXIMITY-INDUCEDSUPERCONDUCTIVITY IN MULTIWALL CARBON

NANOTUBES

We have also investigated multiwall carbon nanotubestin contacts. We show in Fig. 23 theI -V curves recorded aseveral temperatures on a multiwall carbon nanotube wi

*Present address: RIKEN, Hirosawa 2-1, Wako, Saitama 351-0Japan.

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