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Nernst effect and disorder in the normal state of high-T cuprates c F. Rullier-Albenque1, R. Tourbot1, H. Alloul2, P. Lejay3, D. Colson1, A. Forget1 1 SPEC, Orme des Merisiers, CEA, 91191 Gif sur Yvette cedex, France 2 Laboratoire de Physique des Solides, UMR 8502, Université Paris-Sud, 91405 Orsay, France and 3 CRTBT, CNRS, BP166X, 38042 Grenoble cedex, France 6 0 (Dated: February 2, 2008) 0 We have studied the influence of disorder induced by electron irradiation on the Nernst effect in 2 optimally and underdopedYBa2Cu3O7−δ single crystals. Thefluctuation regime above Tc expands n significantlywithdisorder,indicatingthattheTc decreaseispartlyduetotheinducedlossofphase a coherence. In pure crystals the temperature extension of the Nernst signal is found to be narrow J whatever the hole doping, contrary to data reported in the low-Tc cuprate families. Our results 6 showthatthepresenceof”intrinsic”disordercanexplaintheenhancedrangeofNernstsignalfound in the pseudogap phase of thelatter compounds. ] n PACSnumbers: 74.40.+k72.15.Jf74.25.Fy74.62.Dh o c - r The nature of the pseudogap phase remains a key is- for the first time that the presence of defects induces p suetounderstandsuperconductivityinhigh-T cuprates. the apparition of a Nernst signal in a large temperature u c Amongthevarietyofscenarioswhichhavebeenproposed rangeaboveT inbothcompounds. Thisisastrongcon- s c . [1], an important one is to consider the pseudogap as firmation that phase fluctuations do play a role in the t a a precursor to superconductivity, its opening being at- decrease of T induced by disorder. Moreover we find c m tributed to a phase-incoherent pairing, the long range that the onset temperature of the Nernst effect is not - coherence occuring only at T [2]. An experimental sup- muchdependent onthe defectcontentand remainsclose d c n portforthisdescriptionofthepseudogapregimehasbeen to thatofthe pure system. We shalldiscuss the implica- o set outrecently by the occurence ofa substantial Nernst tions of these results on the analysis of the existing data c signal in the normal state of some underdoped cuprates on systems with lower intrinsic T such as LaSrCuO or c [ well above the transistion temperature Tc [3, 4, 5]. As La-doped Bi2201 [4]. 2 this signal is known to be associated with vortex mo- Thesinglecrystalsusedinthisstudyweregrownusing v tion in the mixed state of superconductors, it has been 8 the standard flux method. Very small contacts with low suggested that these Nernst effet experiments reveal the 0 resistance (< 0.1Ω) were achieved by evaporating gold existence of vortex-like excitations surviving in the nor- 3 pads on the crystals on which gold wires were attached 7 mal state. In any case this Nenst signal can hardly be laterwithsilverepoxy. Subsequentannealingshavebeen 0 explainedwithoutinvokingsuperconductingfluctuations performed in order to obtain crystals with oxygen con- 5 [4, 6, 7, 8, 9]. This has been recently reinforced by new tent ˜7 and ˜6.6. The T values are defined here as the 0 c measurementsof a diamagneticresponse whichhas been / zero resistance temperatures. The irradiation were car- t found to track the Nernst signal [10] a ried out with 2.5MeV electrons in the low temperature m facilityoftheVanderGraaffacceleratorattheLSI(Ecole It has been considered somewhat independently by - Polytechnique, Palaiseau). During irradiation, the sam- d Emery and Kivelson[11] that in a sufficiently bad metal ples were immersed in liquid H2 and the electron flux n classical and quantum phase fluctuations of the super- waslimitedto1014e/cm2/s toavoidheatingofthesam- o conducting order parameter can depress T well below c c ples during irradiation. The thicknesses of the samples its mean-field value. We have previously shown that the : (20 to 40 µm) are very small compared to the penetra- v defect induced decrease of T could be partly explained c i tion depth of the electrons, which warrants an homoge- X withinthisscenario[16]. Onemightwonderwhetherthis neous damage throughout the samples. We report here results as well in a large range of incoherent phase fluc- ar tuations above T . In order to test this possibility, we data taken on three YBCO7 samples : a pure one with c T =92.6K and two irradiated ones at different electron have undertaken a systematic study on the influence of c fluences with respective T =79.5K and 48.6K,and four defects on the Nernst effect. We have chosen to perform c experimentsinoptimallydopedYBCO7 andunderdoped YBCO6.6 samples : pure with Tc = 57K and irradiated with T =45.1K, 24.2K and 3K. YBCO6.6 compounds whichareknownto be veryhomo- c geneous systems with little intrinsic disorder [13]. The The Nernst signal E is the the transverse electrical y controlled introduction of defects has been achieved by response to a thermal gradient ∇ T//x in a presence of x using electron irradiation at low temperature which re- a perpendicular magnetic field B//z. For the measure- sults in the creation of point defects such as Cu and O ments the sample was attached on one end to a copper vacancies in the CuO2 planes [14]. We demonstrate here block with the other end free. The temperature gradi- 2 ent was created with a small RuO2 resistance attached to the free end. The measurements were performed un- der vacuum (10−2 to 10−1 mbar) and a heater power rangingfrom0.01to 0.2mWwasusedto createtemper- ature gradients from 0.5 to 0.8K/mm depending on the temperature of measurement. The thermal gradient was measuredwithadifferentialchromel-constantanthermo- couple. The data were taken at fixed T with magnetic field sweeps from 0 to 8T. At some given value of the magnetic field, the thermal gradient is removed, which allows us to subtract offset voltages due to contact mis- alignement or an eventual contribution of the wires. As described by Wang et al. [4], the Nernst coefficient ν =E /(−∇ T)B is the contribution of two terms : y x E α 1 ν = y = xy −Stanθ (1) (−∇ T)B h σ iB x where α is the off-diagonalPeltier conductivity (J = xy y α (−∇ T)), θ = σ /σ is the Hall angle and S the xy x xy thermopower. Thequantityofinterestistheoff-diagonal term α which involves the normal-state term αn and xy xy the vortex contribution αs . In order to probe the in- xy fluence of disorder on the latter, it is very important to determine as well the influence of disorder on Stanθ. We have therefore measured Ey, S and tanθ separately FIG. 2: (color online) Temperature evolution for the pure in each sample by using the same electrodes for mea- andtwoirradiatedunderdopedYBCO6.6 samplesof: (a)the suring resistivity and Hall effect in one setup and the Nernstcoefficient determinedbytheinitialslopeofey versus B ( the T dependence of Stanθ is also plotted for the pure thermopower and Nernst coefficients in another one. Letuspresentfirsttheresultsobtainedonunderdoped and the most irradiated samples), (b) αxy/σB determined from Eq.1 and (c) the resistivity. The arrows in (b) indicate crystals. Figure 1 shows several curves of the Nernst theonset temperature of the vortex Nernst contribution. signal e = E /(−∇ T) as a function of magnetic field y y x for the pure crystal. does not exceed the ”melting” field B (T) necessary to m depinvortices(around2T and1Trespectively at35and 45K).Thentherapidincreaseofe aboveB reflectsthe y m motion of vortices induced by the thermal gradient. As T is increased across T the Nernst signal initially drops c rapidly(curvesat55and58K)andthendecreasesgradu- allyapproachingastraightlinewithnegativeslope. This behaviouris clearlydisplayedinFig.2ainwhichwehave plotted the T variation of the Nernst coefficient ν determined as the initial slope of e versus B. This negative y contributionwhichhasbeen previouslyobservednearT c [15]is foundto displayaminimum at85K andtovanish around 200K. This behaviour which is quite different from that observed in the other underdoped cuprates, willbeseenbelowtoresultnaturallyfromthehighvalue of Stanθ/B in this clean system. The effect of electron irradiation is recalled in Fig. 2c FIG. 1: (color online) Nernst signals ey = Ey/|∇T| versus wherethe resistivitycurvesρ(T)areplottedforthepure magneticfieldinthepureunderdopedYBCO6.6 crystalforT ranging from 35 to 200K and two irradiated samples. As reported previously [16], Matthiessen’s rule is well obeyed at high T, which indicates that the hole doping of the CuO2 planes and the ∗ For T < 55K, e is zero as long as the magnetic field pseudogap temperature T are not significantly modi- y 3 fied [17]. The initial parts of the low T upturn of ρ(T) have been associatedwith a Kondo-likespin flip scatter- ing [12]. As for the Nernst coefficient one observes in Fig.2a that the pronounced minimum which is present for the pure sample is smoothed out by the introduction of disorder. We have reported on the same graph the temperature dependence of Stanθ/B for the pure and the most irradiated sample. In the pure sample both S and tanθ being quite large [18], −Stanθ/B dominates in Eq.1. Such a negative value of ν has been predicted theoretically in the framework of the Boltzmann theory bytakingintoaccounttheroleoftheFermisurfaceshape at two dimensions [20]. When increasing the defect content x, we find that S varies slightly while tanθ/B decreases roughly as 1/x [22], resulting in a decrease of Stanθ/B when T decreases. The T variation of the c totaloff-diagonalPeltiertermα /σB obtainedbycom- xy FIG. 3: (color online) The Nernst coefficient ν is plotted biningthedataforStanθ andν isplottedinFig.2-b. In versus temperature for pure and irradiated single crystals of all samples the normal state contribution αnxy presents a YBCO7. The values of Tc and Tν are respectively indicated broad peak around 110K and then decreases with tem- bydashedandfullarrows. TheT dependencesofν (circles), perature. Such a behavior has been quite generally ob- Stanθ/B ( diamonds) and αxy/σB (squares) are shown in served in underdoped cuprates [4] and might therefore theinset for the purecrystal. be characteristic of the normal state quasiparticles. As αn /σB correspondsto a carrier-entropycurrentone ex- xy pectsthatitshoulddecreasetozeroatT →0.Therefore it seems legitimate to interpret any deviation from this deduced from the paraconductivity in the ρ(T) curves. tendencyasamanifestationofavortexcontribution. We In order to compare results obtained on YBCO7 and havethusindicatedbythearrowsinFig.2bthebestesti- YBCO6.6 wehavereportedinFig.4thevalues ofTν asa mateoftheonsettemperatureTν ofthesuperconducting functionTc forthedifferentsamples. Inbothcompounds contribution. This determination leads in fact to values we observe that the Nernst signal extends in a larger which nearly coincide with those of the minimum of the temperature rangewhen decreasingTc. Let us point out Nernstcoefficient. Twoimportantresultscanbededuced that this effect corresponds to very small values of the fromthis plot.Firstit isclearlyseenthat the onsettem- vortexNernstsignalasonecanseethatthe temperature peraturedoesnotexceed85KinpureYBCO6.6,showing corresponding to a value of the vortex Nernst signal of that the fluctuation regime is quite narrow (∼ 25K) in 30nV/KT nearly follows the Tc decrease. this compound despite the fact that the pseudogaptem- These results clearly show that superconducting fluc- perature T∗ is & 300Kwhatever the experimental probe tuations survive in the normal state of both optimally [21]. Second we find that Tν is nearly the same for all doped and underdoped YBCO when T is decreased by c the samples while T has been decreased down to 5K by the introductionof disorder. As Tν canbe consideredas c irradiation. This is a strong indication that the presence the characteristictemperature below which local pairing of defects plays a prominent role in the observation of a remains significant, the T decrease induced by disorder c Nernst signal in the normal state of these samples. canonlybe explainedbytaking into accountboth phase As for YBCO7, the Nernst coefficients are reported in fluctuations and pair-breaking effects. This gives strong Fig.3 for the three samples studied. In the pure crystal support to our previous interpretation of the quasi lin- the magnitude ofthe negativevalue ofν is muchsmaller ear decrease of Tc with defect content which is observed than in the underdoped case. This results from the fact downtoTc =0[16]. Itisworthmentioningherethatthe thatStanθ/Bisalsosmaller[22]asshownbythedecom- roleofquantumphasefluctuationshasalsobeeninvoked position displayed in the inset of Fig.3. This Stanθ/B to explainthe Nernst effectobservedin the normalstate term varies very little with defect content and the esti- of low Tc cuprates when superconductivity is suppressed mate of Tν is about the same whether we use the raw by magnetic fields [26, 27]. data for ν or the corrected values α /σB. For all the One striking point which can be seenhere is the small xy samples the drop of the Nernst signal is very rapid at range of superconducting fluctuations observed in the Tc but while it vanishes at ˜10K above Tc in the pure pure YBCO6.6 and YBCO7 compounds. This is much sample,itpersists upto ˜85K,thatis to say35Kabove smaller than the corresponding observations done in T , in the most irradiated one. The fairly narrow fluctu- other ”pure” cuprates such as LaSrCuO or La-doped c ationrangefoundinthepuresampleissimilartotheone Bi2201 [3, 4]. Let us recall here that the presence of ex- 4 should display if they were grownwithout local inhomo- geneities. Such a conclusion might as well apply to the variouscupratefamilies [32]andis reinforcedbythe fact that the maximum of Tν is in most cases of the order of 100K[4]. Moreoverourresultsrevealthatdefectsinduce more phase fluctuations in the underdoped phase than for optimal doping, which might be due to lower phase stiffness and less efficient screening. It is therefore our opinion that the link between the large range of Nernst signalandthe pseudogapphasehastobe foundinprior- ityintheoccurenceofdefectsandinthelargesensitivity to disorder of the superconducting-pseudogapphase. [1] T. Timusk and B.Statt, Rep.Prog. Phys. 62, 61 (1999) [2] V.J. Emery and S.A.Kivelson, Nature 374, 434 (1995) [3] Z.A. Xu et al, Nature 406, 486 (2000) [4] Y. Wang et al., Phys. Rev. 64, 224519 (2001) [5] I. Wang et al., Phys. Rev.Lett. 88, 257003 (2002) FIG. 4: (color online) The values of Tν are plotted versus [6] H. Kontani, Phys.Rev.Lett. 89, 237003 (2002) Tc togetherwiththeT valuescorrespondingtovortexNernst [7] I. Ussishkin et al., Phys. Rev.Lett. 89, 287001 (2002) contributions of 10 and 30nV/KT for YBCO7 (empty sym- [8] S. Tan and K. Levin,Phys. Rev.B69, 064510 (2004) bols) and YBCO6.6 (closed symbols). These data are com- [9] C.HonerkampandP.A.Lee,Phys.Rev.Lett92,177002 pared to the temperature ranges of the Nernst signal mea- (2004) sured in ”pure” single crystals of Bi2Sr2−yLayCuO6 with [10] Y. Wang et al., cond-mat/0503190. y=0.4 and y=0.5 [4]. [11] V.J.EmeryandS.A.Kivelson,Phys.Rev.Lett.74,3253 (1995) [12] F.Rullier-Albenque, H. Alloul, R. Tourbot, Phys. Rev. Lett. 91,047001 (2003) tended vortex fluctuations in these underdoped cuprates [13] J. Bobroff et al., Phys.Rev.Lett 89, 157002 (2002) has been invoked as a strong indication that d-wave su- [14] F.Rullier-Albenqueetal.,Europhys.Lett.50,81(2000) [15] N.P. Ong et al, Annalen derPhysik, 13, 9 (2004) perconductivity is closely connected to the pseudogap [16] F.Rullier-Albenque, H. Alloul, R. Tourbot, Phys. Rev. state [4, 10]. Our results show that this argument fails Lett. 87,157001 (2001) in pure underdoped YBCO6.6, suggesting that the en- [17] H. Alloul et al, Phys. Rev.Lett. 67, 3140 (1991) ergyscalesofTν andT∗ arenotconnected. Wecaneven [18] ThevaluesofS andoftanθ measuredinthissampleare see that in these clean systems Tν and Tc increase with quite comparable to those reported in the literature for increasing hole doping while T∗ definitely decreases. underdoped YBCO6.6 [19] It has been previously suggested that the low T in [19] J.R. Cooper and J.W. Loram, J. Phys. I France 6, 2237 c (1996) somecupratefamilies couldbe due to the presenceofin- trinsic defects asdeduced fromthe analysisof 17O NMR [20] V. Oganesyan and I. Ussishkin, cond-mat/0312588 (2004) data [28]. One can wonder whether this might also ex- [21] J.L. Tallon and J.W. Loram, Physica C 349, 53, (2001) plainthemagnitudeoftheNernsteffects.Wehavethere- [22] HalleffectmeasurementsonZn-subsitutedorelectronir- forecomparedinFig.4thetemperatureextensionsofthe radiatedYBCO7crystalshaveshownthatcotθincreases Nernst signal of our irradiated samples with those ob- linearly with thedefect content x [23, 24]. t(Taine∼d 3in6Kth)ewBhii2cShr2c−oyrLreasypCounOds6tfoamopiltyim[4a]lfdoorpying=a0n.d4 [[2234]] TA..RL.eCgrhisieenteatl.a,lJ.,.PPhhyyss..R(Ferva.nLceet)t.I36,71,6200588(1(919939)1) c for y = 0.5 (T ∼ 29K ) with T∗ ∼ 300K comparable [25] The thermoelectric power S is very small (≤2µV/K) in c this optimally doped crystal. to that of YBCO6.6 [29]. The quite good agreement be- [26] C. Capan et al., Phys.Rev B 67 100507(R) (2003) tween the ranges of vortex Nernst signal found in these [27] R. Ikeda,Phys. Rev.B 66, 100511(R) (2002) different samples indicates that the ”intrinsic” disorder [28] J. Bobroff et al., Phys.Rev.Lett. 78, 3757 (1997) in Bi2Sr2−yLayCuO6 could also be responsible for the [29] Y. Hanakiet al, Phys.Rev.B 64, 172514 (2001) enhanced Nernst signal. Indeed cation disorder on the [30] H. Eisaki et al., Phys. Rev.B 69, 064512 (2004) [31] K. Fujita et al, cond-may/0508594, to be published in Sr site has been recently identified [30, 31]. It is then Phys. Rev.Lett natural to conclude that the ”anomalously” high val- [32] K. McElroy et al, Science 309, 1048 (2005) ues of Tνwith respect to T found in La-doped Bi2201 c are indicative of the values of T that these materials c 5 35K 4 45K 3 ) 55K K / V µ 2 T ~ 57K ( c y e 58K 1 62K 64K 68K 0 70K 110K 150K 200K 85K -1 0 2 4 6 8 B (T) (c) 800 ) m 600 c . Ω 400 µ ( ρ 200 0 ) (b) T K 100 / V n ( 50 B σ / y x 0 α ) (a) T K / 100 V Stanθ/B n ( θ n 0 a t S , ν -100 0 50 100 150 200 T (K) 75 ) T 50 120 K a s / B / V 25 xy n Stanq /B ( 0 80 n ) T n K 80 120 160 / V T (K) n 40 ( n 0 -40 40 80 120 160 T (K) 120 YBCO 7 100 YBCO 6.6 80 ν T ) K 60 10 nV/KT ( T 40 30 y=0.4 La-Bi2201 20 T y=0.5 c 0 0 40 80 T (K) c