7
In dian Jou rnal o f C he mi slry Vo l. 44A. May 2005. pp. 968-974 Proximity-induced superconductivity, spin entanglement and Luttinger liquid in carbon nanotubes prepared in alumina templates I *. J Haru ya l11a U & N Koba yas hi I 'Aoyama C;akuin Univers il Y. 5- 1 0-1 Fuchinobe. Sagalllihara. Kanagawa 229-8558. Japan .1 ST. CREST. 4- 1- 8 !-i on-machi. Kawaguchi. Sailama JJ2-()O 12 . Japan Email: [email protected] ma .ac.jp Receil'ed <'\ Decelllber 2004 Prox imil y- induced s up erconduclivilY has been observed in mulli - wa ll ed carb() n na nol ubes (M WNTs ), prepared in nanoporous alumina le mpl ales. wilhin J diffusive charge lranspo rt reg ime. As th e I J) ,lIl iso lropy of of sp in cnlangleme nl in cohercnl eleclron pairs of th e MWNT is observed. O n red uc in g th e lenglh of lh e MWNT be low a mca n fr ee palh. il exhibilS Tomonaga-Lullingcr liquid behaviour. The slu dy indicales a possi bililY lhal Cooper pairs. injecled from a s up e rc onduelor eleclrode arc separaled il1l o indi vidual spin by the TLL behaviour of MWNTs. II'C Code: Inl. Cl 7 138213: C2SI3: CO-iI3 J S/ OO Introduction Ca rbon nCln otube (CN), an i dea l one-d imensional ( I D) molecular conductor, ex hibit s a variety of exciting quantum and mesoscopic ph enomena . Tomo na ga-Luttin ge r liquid (TLL ), which is a non- Fermi liquid shows I D rep ul si ve Coulomb interaction among electrons which ma y be rel ev ant for investigating CNs l . Rece ntly. its correlation with Cooper pairs is attracting considerable attention. Since efficient injection of Cooper pairs from metal superconductors into CNs, which can ca use proximity-induced superconductivity (P IS ), arc d ifficult to produce due to its poor interfa ce, only one gro up has succeeded in producing single-walled CNs (SW Ts) suspe nded between metal superco nductors 2 . In addil i on . I D phenomena. such a TLL , cou ld have a strong influ ence on th e injected Cooper pairs (or co herent electron pairs). Rech er and LOSS1 have predicted that strong Cou lomb repulsion in TLL of two CNs co uld effici en tl y split Cooper pairs. which wue inj ec ted from one superconducto r, into two oppos it e- moment spins and eac h spin being pl aced on each CN. Bena el al 4 have al so predicted thi s by show ing tunneling probabiliti es from a superco nductor to two CNs within TLL state. Furthermore. if Cooper pairs in C s actua ll y have strong entanglement a report ed by Buit elaal .5, eve n two spins separated and placed on two different C s ca n be in the entangled sta te. Thi s molecular spin- en tan gler w ill operate as spin quantum bit and spin teleportation archit ec tur e, since it can re so l ve th e problem of decoherence and de -e ntanglement. Herein, we report the successful inj ec ti on of Cooper pairs from Nb electrode ane! eme rge nce of prox imity-indu ced superconductivity in multi-wall ed CNs ( MWNTs). which were sy nthesized in nan opo re s of alumina templat es, within a diffu si ve charge transport re gime. In thi s PIS , we show th e en hancement of spi n entanglemen t incoherent el ec tron pairs of thi s MWNT as th e I D an i so tropy of MWNTs becomes stron ge r. By short en ing the leng th of this MWNT bel ow a mean free path , MWNT can be in a I D ballistic charge transport re gim e, and ex hibit TLL. We al so demonstrate that Cooper pa irs. injected from a superconductor, are se parat ed into individual spin by this TLL of M NNTs 4 Materials and Methods Highly tran s parent b/MWNTs interface Figure I a shows a sc hematic cross-sec ti on of our Au/Nb/MWNTs/A I alTay sa mple, wh ich was prepared using a nanoporous alumina templ ate. We have ea rli er reported th e sy nthesi s of MWNTs in t he nan opores of alumina template s, wit h chem i ca l vapou r deposition (C YD ) in a catal ytic meth od 6 . In thi s structu re, th e open top ends of th e MWNTs, which were standing in th e nan opores, cou ld be end-bonded by normal- conductor metal electrodes evaporated on th e top ends of the MWNT arr ay , as we ll as th e bottom ends connected to th e Al substrate (Fi g. I a&b). Thi s is a junction ve ry different from those in t he CN field-

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Page 1: Proximity-induced superconductivity, spin entanglement …nopr.niscair.res.in/bitstream/123456789/20118/1/IJCA 44A(5) 968-974... · Proximity-induced superconductivity, spin entanglement

Indian Jou rnal of Chemi slry Vol. 44A. May 2005. pp. 968-974

Proximity-induced superconductivity , spin entanglement and Luttinger liquid in carbon nanotubes prepared in alumina templates

I Takesuel. ~· *. J Haruya l11a U & N Kobayas hi I

'Aoyama C;akuin Univers ilY. 5- 10-1 Fuchinobe. Sagalllihara. Kanagawa 229-8558. Japan ~ .1 ST. CREST. 4- 1-8 !-ion-machi. Kawaguchi. Sailama JJ2-()O 12. Japan

Email: lakesue @ee.aoyama .ac.jp

Receil'ed <'\ Decelllber 2004

Prox imily- induced superconduclivilY has been observed in mulli -wa lled carb()n nanol ubes (M WNTs), prepared in nanoporous alumina lempl ales. wilhin J diffusive charge lransport reg ime. As the I J) ,lIl isolropy of MWNT~ becom~s

~ l ro n ger. ~nhancemc nl of spin cnlangleme nl in cohercnl e leclron pairs of the MWNT is observed. On red ucing the lenglh of lhe MWNT be low a mca n free palh. il exhibilS Tomonaga-Lullingcr liquid behaviour. The sludy indicales a possi bililY lhal Cooper pairs. injecled from a superconduelor e leclrode arc separaled il1lo indi vidual spin by the TLL behaviour of MWNTs.

II'C Code: Inl. Cl 7 138213: C2SI3: CO-iI3 J S/OO

Introduction Carbon nClnotube (CN), an idea l one-d imensional

( I D) molecular conductor, ex hibits a variety of exc iting quantum and mesoscopic phenomena. Tomonaga-Luttinger liquid (TLL), which is a non­Fermi liquid shows I D repulsive Coulomb interaction among electrons which may be rel evant for investigating CNs l . Recently. its correlation with Cooper pairs is attracting considerable attenti on. Since effici ent injection of Cooper pairs from metal superconductors into CNs, which can cause proxi mity-induced superconductivity (PIS), arc difficult to produce due to its poor interface, only one group has succeeded in producing single-walled CNs (SW Ts) suspended between metal superconductors2

.

In addil ion . I D phenomena. such a TLL, cou ld have a strong influence on the injected Cooper pairs (or coherent electron pairs). Recher and LOSS1 have predicted that strong Cou lomb repulsion in TLL of two CNs could efficien tl y split Cooper pairs. which wue injec ted from one superconductor, into two oppos ite- moment spins and each spin being placed on each CN. Bena el al 4 have also predicted thi s by showing tunneling probabiliti es from a superconductor to two CNs within TLL state. Furthermore. if Cooper pairs in C s actua ll y have strong entanglement a reported by Buitelaal.5, even two spins separated and placed on two different C s can be in the entangled sta te. Thi s molecular spin­en tangler will operate as spin quantum bit and spin

teleportation architec ture, since it can reso lve the problem of decoherence and de-entanglement.

Herein , we report the successful injec ti on of Cooper pairs from Nb electrode ane! emergence of prox imity-induced superconductivity in multi -wa lled CNs (MWNTs). which were synthesized in nanopores of alumina templates, within a diffusive charge transport regime. In thi s PIS, we show the enhancement of spi n entanglemen t incoherent electron pairs of thi s MWNT as the I D an iso tropy o f MWNTs becomes stronger. By shorten ing the length of thi s MWNT below a mean free path , MWNT can be in a I D balli stic charge transport regime, and ex hibit TLL. We also demonstrate that Cooper pairs. injected from a superconductor, are separated into individual spin by this TLL of M NNTs4

Materials and Methods Highly transparent b/MWNTs interface

Figure I a shows a schematic cross-sec ti on of our Au/Nb/MWNTs/A I alTay sample, wh ich was prepared using a nanoporous alumina temp late. We have earli er reported the synthesis of MWNTs in the nanopores of alumina templates, with chem ical vapou r deposition (CYD) in a cata lytic method6

. In thi s structu re, the open top ends of the MWNTs, which were standing in the nanopores, cou ld be end-bonded by normal­conductor metal electrodes evaporated on the top ends of the MWNT array , as well as the bottom ends connected to the A l substrate (Fig. I a&b). Thi s is a junction very different from those in the CN fi eld-

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TAKESUE el (II. : PROX IMITY- INDUCED SUPERCONDUCTIVITY IN CA RBON ANOTUBES 969

(a) I (b) Nb r-----------------~ ,

Au 1pm

SIN

l~m I Junction

• I Porous Alumina •

Membrane (c) Electrode

A I Substrate

Magnetic field , H

Substrate

200 nrn

5nm

Fig. I - (a) 5chcIllati c cross-sections of an array or end-bonded Aul b/MW T s/A I junclions. sy lllh.:sized inlo the nanopor.:s ()r alumina templates by chem ical vapour c\t:pos iti on(,·7 The 7~ of our Nb was 3bout 8. 1 K - 9K and lie W3S about 1500 Gauss. The mc:ln out.: r dia lllctcr of the MW Ts was about 80 nln. and the shell thickness was 20nm . T he average characteristi cs or the Nb/MWNTs/A I.iunclions (- 1(

1) in one ~IITay were measured by the quasi-rour terminal method. One should. however, note Ihal the number of MWNTs

conlribu ting to Ihe prox imily dTt:ct does not correspond to Ih is number because it is not possib le thai all o r Ihe Nb/MWNT, .iuncliolb ha ve exact ly the same struclures and cause prox imity dTect simu l13neously. (b) Schemalic overview or th e end -bonckd MWf\:T. (c) Schemal icv ieworanelectrodelCNjunctioninageneralrield-ellcct tran sistor. (d) SEM top-v iew image or MWNT~ growing rrom Ihe nanoporcs and accumulated on Ihe surrace of the alum ina template. (e) SEM lop-v iew image or the alumina tt:mplate ri ght after Ihe CU lling orr or Ihe accumulated MWNTs. One can conrinl1 the open " heads" or the MWNTs in the pores. although some or the pore, arc emply. (I) SEM overview image of a MWNT array observed arler etching out the alumina template. Thi s implies a high n.:gularily . equal lengths. and open top port ions in the MW Ts. (g) Cross-secti onal (CS) TEM image or the disordered gl'aphite I ~t ye rs in Ihe MWNTs.

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970 INDIAN J C HEM, SEC A, MA Y 2005

effect transistors (Fig. I c) in the following ways: (i) the contact is fo rmed to top ends of all the shell s in the MWNTs, (ii ) the electrode materials s li ghtly diffuse into the top ends of the MWNTs, and, (iii ) the interface is not affected by the annea ling atmosphere. We have successfully observed a variety of quantum and mesoscopic phenomena in these MWNTs, e.g., a Coul omb blockade in a single tunnel juncti on, Altshu ler-Aronov-Spivak (AAS) oscillations, weak loca li zati on, and anti-localizat ion. These observations are evidence that a highl y-transparent interface could be fo rmed in thi s structure.

However, we could not exactl y contro l the length of the' MWNT in the earli er reported method , because thi s was done by only optimizing the volume of the cobalt catalyst and the time for CV D so that the tunnel length meets the thickness of the alumina template. It was difficult to grow the length to the different thicknesses of alumina templates. Since the MWNTs grow instantaneously when the chemical vapour reacts with the cobalt catal ys t, the MWNTs grow above the alumi na template surface and, in most cases. accumulate (Fig. I d) . Thi s made end-bond ing difficult.

In contrast, In the present method we used ultrasoni c clean ing in order to cut off these accumul ated MWNTs from the templ ate surface. We simply immersed the sample in water at room temperature for I hour with ultrasound. After ultrason ic cleaning, all the MWNTs that accumulated on the template surface were successfully cut off (Fig. Ie), leading to a highl y regu larly aligned MWNT array wi th open top ends and of the same lengths, independent of the template thickness (Fig. I f). In general, it is hard to cut off graphite (or CNs) with perfect crystal structures by any method without causing damage (even by ultrasou nd sonication). Our MWNTs also have graphite structures but it is slightly disordered (Fig. I g). This is one reason why the accumul ated MWNTs were eas il y cut off.

Then, we sli ght ly etched out the temp late surface and sputtered Au/Nb on these open top ends of the MWNTs in order to end-bond , and in vest igated the opt imal annealing conditi ons for obtaining hi ghly transparent interfaces without damage. As a result, we found th at annea ling at 6S0°C fo r 30 min . in a vacuum was the best conditi on for achieving the larges t. stahl e, and reproducible conductance without any breaks due to the diffusion of Nb to the Al substrate through the MWNTs.

Figure 2a shows a cross-sectiona l HAA DF TEM image around the Nb/MWNTs in terface of such a sample. A slight diffusion of Nb parti cles into all the shells at the top ends of the MWNTs is observed . These particles easily form NbC at the in terface (Fig. 2b). As explai ned in the int roduction. the presence of NbC res ul ts in a hi gh ly-transp<tn.:nt Nb/MWNT interface. In contrast, the junction which annealed at ISO°C did not show any NbC (Fig. 2c) or current fl ow.

Moreover, a hi ghly transparent MWNTs/AI ­substrate interface (- 100 Q) was obtai ned simultaneously by the automatically- formed end­bonded structure (i t shou ld be noted th at the resistance of MW Ts/AI is higher Ihan that of the Nb/MWNT interface, because of [he absence of NbC). Thi s is because the annea li ng temperature is near both the melting point of AI (- 650°C) and the sy nthes is temperature of MWNT.

Nb diffll'>ion

MWNT

10 nm 10 nm

Fig. 2 - (a) Hi gh-a ng le annul ar da rk-fie ld (HAADF) image o r J

cross-sect iona l TEM (CSTEM ) around the Nb/MWNT inte rrace array anneal ed at 650 °C for 30 min . High-resolution CSTEM images a ro llnd the Nb/MWNT inte rface array anne;i1 ed at 650°C for 30 min (b), and at t50 °C (c).

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TAKESUE el at.: PROXIMITY-INDUCED SUPERCONDUCTIVITY I CARBON NA OTUBES 97 1

Results and Discussion Proximity-induced superconductivity in Nb/multi-walled nanotubel AI junctions

• The main panel of Fig. 3 shows the ze ro-b ias resistance versus temperature relati onship fo r different magneti c fi e lds (H ). The res istance begi ns to decrease at T= 3.8 K (defined as TpJ at H=O T, due to th e prox imity effect of the Nb electrode. As the tem perature decreases below T= 1.2 K, which is the Tc of th e AI substrate, the Cooper pair wave fun cti on (C PWF) starts to diffu se due to the proximity effect of AI. Conseq uentl y, one could successfull y find a PIS at Tr=O.6K at H=O T and also a di stinct proximity-induced superc urrent (inset). This presents strong ev idence for the presence of highly-transparent Nb/MWNT. interfaces witho ut any damage and also hi ghl y transparent MWNTs/AI interfaces.

The resistance drop is gradual as the temperature decreases, with two steps between th e onset temperature and Tc at H=O T (F ig. 3). Secondly , the transiti on between the superconducting state and th e di ssi pati ve state is very abrupt , show i ng hyste res is loops and sta ircases at cu rrents above Ie (inset). Thi s behav iour is simil ar to that in ballistic SWNT sys tems2

.

The former can be understood by pinning of the CPWF in th e MWNTs. In PIS , the CPWF diffuses from S (Nb) to N (MWNT) following the small er of ei ther the phase coherence length (L,,=(DLd» 112) or the thermal diffusion length (L$=(flDI21T.kn I /2

). Since in the present case Ln. is shorter than Lc)J in thi s temperature region, the res istance drop shou ld follow L$=(hDI21T.kn ln Indeed, we found that the low­temperature part of the measurement data at H=O T agrees with the Ro cc 14.3x TI I2 relationship as shown by the dotted line in Fig. 3. This means that the CPWF quickl y diffuses at the temperatures (F=2.8 -3.8 K) around Tpx and hence, resistance drops abruptly. Then, it shows a plateau at 7"=2. 1 - 2.8 K, due to the presence of thi s pinning of CPWF. Finally , after depinning, the CPWF fo llows temperature dependence of Lq, at T < 2. 1 K. The res istance step remains even under an increasing magnetic field, whereas according to Buitelaar el 0 1.

5, it di sappears.

Thi s might be due to the presence of stronger pinning centers in ou r disordered M WNTs. The second term correlated to the inset might be interpreted as a result of a (quantum) phase slip center, in which the CPWF is pinned by a normal conducting state formed in

30.--------------------------,

4

Temperature, K

H = OT T = 0 36 K

-10 -5 0 5 10 15 Current, pA

Fig. :1 - Zero-b ias resistance (No) versus temperature relalionship for different vJlues of magneti c field perpendicular 10 Ihe MWNT axi s. The labe ls on the curves correspond 10 Tesla (T ). Inset: Proximity-induced Josephson supercurrent.

some parts of the superconductor wi re and the phase slips throughout these parts.

However, there are so me di fferences in the case of SWNTs. One of these is that the Ro vs temperature relati onshi p (Fig. 3) remai ns relati vel y unchanged even when a field of H= I T was app li ed . Since the cri ti ca l magnetic field (HJ of Nb is about O. IST. the PIS should disappear under H= IT This is di sc ussed in the next section.

Spin entanglement enhanced by one-dimensional anisotropy

Figure 4a shows that the relati onship of the normalized Ro versus the magnetic filed (H ) strongly depends on the MWNT structures . The ratio of the length of th e Cooper-pa ir leakage (Lpx) due to the PIS state in the MWNT to the tube length. (LlUbJ was set to the same va lue in all the samples by normali zing with Tpx . We found that the upper He (Hd has almost the same values (Hc2=2 .8 - 3.2 T) in all of the samples. but the slope in the relationship drasticall y decreases as LlUbc increases (three red lines) and <p decreases (LlUhc and <p dependence of the slopes are shown more di st inctly in Fig. 4b&c). In particular, it is surpri si ng that Ru majntain? the same val ue up to H- I AT and abruptly increases at around Hc2 only in the samples with LlUbe=1.6 11m and <p-IO nm, while the Ro increase is gradual in the other samples. This is the reason for the enhanced He. as menti oned in the previous section . Fields appli ed along the tube longitud inal axis also led to more or less similar behaviour with increased Hc2 .

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972 IN DIAN J CHEM. SEC A. Mil Y 2005

(a) 1 ,', . 0 LtUb~_=. 0. 6p rn l

~-- ' -~-9

Ltube = O.Spm t.

• Ltube= 0.6pm • (Low T Anneal) •

1.0 TIT px = 0.45

o 5 2 ')

-' 4

Iviagn etic Fleld[T esla) (d)

--:' =!

(e) ~ !II <J c:

'" • +" <J ::J

1 . I .'" • a

"0 c: 0

U a:: .", •

"0 !II N

• 0

a 20 40 60 SO

'" ~ {

,) (nrn) 0.0001 0 .0 1 0.1 In [HI (Tesla)

Fig . .f - (a) Relati onship between the normali zed zero-bias resistance (No) and Ihe magneti c field (H ) perpendicu lar tl) th e tubc a x i ~ . on

different MWNT k ngth s (L,,,,,,, : the sa me <Il- XOllm) and diameters (<1» w ithin PI S at the normali zed temperailire C/!! ;,,=0 . .f5 j .

(b) /:;1 No(f!=2 TjlNo(l-!=OT) I//:; H vs lube length (L"'bc ) under (j)=XO nm. (c) Tube ouler diametcr (<Il) under L,,,t>.: =().Xp m. (d) Conductance vs logarithmic magneti c- fi eld relalionships follow ing wea k loca li zation. on the MWNTs w ilh I D ani sotropy .

Herein . we have confi rmed that only the magnetoresistance behaviour and He:. of the Nb elec trodes were independent of the tube structures in all the samples. Thi s implies that the leakages in the CPWF into the MWNTs govern the magneto­resistance behaviour and /-/e2 for the Nb/MWNTs junctions. The suppression of the magnetores istance increases at high fi elds indicating that the suppress ion of coherent elec tron-pai rs ( i .e .. Cooper pai rs in Nb) breaks under high fi elds and, hence, the induced spin coherence and entanglcmcnt in the elec tron pai rs of the MWNTs. In addition , the change in L lllbc from 0.8 flm to 1.6 flm and that in <p from 80 nm to 10 nm induce the I D ani so tropy along the tube's longitudinal direction. Hence, the enhancement of the I D ani sotropy induces the spin entanglement and coherence in the elec tron pairs under high fie lds.

The tube-s tructure dependence of magneto­resistance excludes some non-intrinsic ori gins for thi s induction, such as (i ) the influence 0[" Nb nanoparticles and NbC present in the top portion of the MWNTs, and (ii ) the pinning of magnetic fluxes (Abrikosov latti ce) partially penetrating the MWNTs

by defects and impurities. The relaxation of Pauli ­paramagnetic- limi ting Cooper-pair break ing (PPLC B) by I D electron-phonon coupling 7-') . may be a poss ibilit y for the essen tial origin, assu ming the weak coupl ing case.

[t is well known th at PPLCB is C:JlI sed by with a

Pauli limiting fi eld (HI'=4Tj nflll , whcre flll is the Bohr magneton ), ariscn from opposite energy shift s of two spins in a Cooper pair on applied f ieJds in metal s. Thi s becomes mor~ signifi cant than orbital pai r breaking under large ric in dirty superconductors. aile! deprcsses magnetoresistance and Hc~ be low the va lue expected on the bas is of orbita l Cooper-pai r breaki ng7

-1) . The presence of thi s PPLCB can be assumed in our MWNTs as well as in fu llercnes and graphite. Since the spin orbit interaction alld electron­phonon coupling can relax thi PPLCB . the magnetoresistance and Hc~ depress ions are released . atta ining larger values 7 [t is we ll known that SWNTs have no spin-orbit interacti ons bu t have electron ­phonon in teraction s (EP[ ) 10. 11, part icularl y wi th

acoustic phonons at high temperatures and high vo ltages .

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TAKESUE ela/.: PROXIMITY-INDUCED SUPERCONDUCTIVITY IN CARBON NANOTUBES 973

[n the present case, at low fields , EPl can be estimated for weak loca li zat ion as G ex: G O+(e"lh)ln(H) relationship at T=7K, which has the absent proximity effect, in the three samples (Fig. 4d)1 2. From this relationsh ip, Lin"" LB=( 11 leH) "2 is obtained by the fie ld where magnetic length, LB, becomes small er than in elast ic scattering length , Lin , wi th increasin g fields (i.e., the trans ition field (Hin) from the field independent magnetoconductance (MC) to the field dependent MC due to the Landau orbital effect). We can estimate Lin""LB = lS I nm from Hin "" 300 Gauss (shown by the arrow) for the sample with

LlUhe =0.8 IJ.m (<I> "" 10nm), Lin""LB =262 nm from Hin "" I 00 Gauss for the sample With Ltubc = 1.6 IJ.m( <I> ""

80nm), Lin""LB =415 nm from Hin "" 40 Gauss for the sample wi th Ltu he =0.8IJ.m( <I> "" 80nm). Because Lin ex: T p/2 and p is about 2 in our MWNTs 12, these Li1l result In Lin=704 nm, Lin= 1222nm, and Lin=1936nm, respectively, at T= 1.5K. around wh ich the proximity effect is observed. This EP[ still has the potential to survive in the MWNTs via the leaked Cooper pairs at T<Tc. This resul t for the sample with LlU bc =0.8IJ.m (<I>

"" 10nm) implies th·at the EP[ in our MWNTs is 100 times weaker than that reported by Langer el a/. 1-', reflecting the highl y transparent Nb/MWNTs interface. The Lin=704 nm gives Tin =1. 32 X 10-1" s. by using Lin=(DTin)"2 and D=0.37 m/s2 as the maximum case6

. This Tin = 1.32 X 10-12 s in MWNTs is a reasonable va lue. because it is three ti mes small er than the elec tron-acoustic phonon relaxation time of Tic "" 3 X 10-12 s reported in a ballistic SWNT with a weak interaction ", reflecti ng well our disordered MWNTs. Furthermore, the coupling strength should. in general, be proportional to Ltu hc and 1/<1> (i.e., to the confinement into 10 anisotropy). The Lin est imated above agrees we ll qualitatively with these relat ionshi ps.

Since the relaxation of PPLCB by this EP[ becomes significant in th e 10 anisotropic sa mpl es because of the stronger EPI, the suppress ion of the M R increase also becomes signi ficant in the sampl es with the induced 10 anisotropic shell s in ou r MWNTs.

Possi ble spin splitting of Cooper pairs by TOlllonaga­Luttinger liquid

When the length of the MWNT was reduced below mean fee path - 700 nm (ref. 6), the MWNTs became balli stic charge transport regime and showed power law hehavior at temperatures> Tc- l OK (Fig. 5). Thi s

o ()

c;: u ::;

v r

is u

L , 2 o

:--.:

I O- I.--..,...""I"""""""""~_""I"""""''''''''I''I'''I''!'-~~~''''' __ I::::\p. : ----- C II. (T It.:a - 1.2fi) __ •. _. Cal. (Tu.:cy. ~ (77)

-- Cal. (Tc'-. :a. - o.s." )

C( = I 28 " . ,

\ '

, ,

10

ex = 0.77

100 TClllp·c ralli rc (K )

1000

Fig. 5 - Temperature dependence o f the ze ro- bias cond u~ \,Ulce Go o n a doubly logarithmic sca le in NbN/MWNTs/A I jllncti~) !l ~ .'fifil Ihe 600 nm·l ength MWNTs w ithin a ba ll.is ti c charge transpo rt reg ime and TLL state

power exponent a- 0.8 is in .good agreement with a es timated for Au-end junction I, whi ch corresponds to our junction structure, indicating the presence of TLL. Correlation exponent, g, which is an indicator of the strength of electron-electron interact ion is esti mated to be g - 0.25 from the formu la for the a =[ I Ig- I ]/4 (ref. I). [n contrast, this behaviour disappears and conductance suddenly increases around Tc and, then starts to decrease again at T < 7K, fo llow ing power law with the a - 1.28 larger than a - 0.8 mentioned above (Fig. 5). This result stresses separation of Cooper pairs, injected fro m NbN , into individual spin by TLL of the MWNTs4. Bena el al. predicted that a tunneling probability, f AB, of Cooper pairs from one superconductor to the end of two CNs within TLL is given by f AB-(eV/h)(kTIE)llIg - 1112 , when Cooper pairs are separated into two spins, which tunnel into two different CNs. We can obtain a - l.5 by in serting g -0.25 into this fo rmul a. The val ue of a - 1.5 is almost the same as the observed a - 1.28 in Fig. 5. suggest ing possible sp litting of Cooper pairs by TLLI 4. Recller and Loss have suggested that using low di mens ional superconductors as the orig i n of Cooper pair inj ection and increasing the separation length between two CNs increased the spl itting efficiency. There is, however, still no other experimental ev idence, which shows spi n separation and those entanglement states.

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974 INDIA N 1 CHEM. SEC A. MA Y 2005

Conclusions We report the proximity induced superconductivity

in MWNTs synthesized in nanoporous alumina templates, within a diffusive charge transport regime. Sp in entanglement is observed in coherent electron pairs of thi s MWNT en hanced by the I D ani sotropy. By reducing the length of the MWNT below the mean free path , there is a possibility that TLL in the MWNTs can separate Cooper pairs, which were injected from NbN electrode, into indiv idual spin.

Acknowledgement We thank T Akazaki, H Takayanagi , H Shinohara,

R Saito, Y Miyamoto, W Tsukada, M Thorwart, and M Dresselhaus for fruitful help, discussion , and encouragement. This work was partially supported by the project "Carbon Nanotube Electronics" in the Special Coord inat ion Funds of the Japanese Government.

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