PHYSICAL REVIEW B 86, 014520 (2012)

Superconducting gap and pseudogap in near-optimally doped Bi2Sr2−xLaxCuO6+δ

J. K. Ren, Y. F. Wei, H. F. Yu, Ye Tian, Y. F. Ren, D. N. Zheng, and S. P. ZhaoBeijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

C. T. LinMax-Planck-Institut fur Festkorperforschung, Heisenbergstraβe 1, D-70569 Stuttgart, Germany

(Received 2 May 2012; revised manuscript received 6 July 2012; published 26 July 2012)

We present a tunneling study of the superconducting gap and pseudogap from near optimally doped submicronBi2Sr2−xLaxCuO6+δ intrinsic Josephson junctions whose self-heating is significantly suppressed. We find thatas temperature decreases a pseudogap develops around T � = 165 K while the superconducting gap starts toopen at Tc0 = 40 K, which is well above the superconducting transition temperature Tc of 30 K. We discuss thetemperature-dependent properties of the superconducting phase and pseudogap phase. Our results demonstrate aclear two-gap feature of the system with precursor pairing up to Tc0.

DOI: 10.1103/PhysRevB.86.014520 PACS number(s): 74.55.+v, 74.25.Dw, 74.72.Gh, 74.72.Kf

I. INTRODUCTION

So far, in the simple single-layered Bi2Sr2−xLaxCuO6+δ

(Bi2201) cuprate superconductors, the nature of the pseudogap(PG) and its relation to the superconducting (SC) gap remainunclear. Some spectroscopic studies like scanning tunnelingmicroscopy (STM) and angle-resolved photoemission spec-troscopy (ARPES) were in favor of a pseudogap that arisesfully from precursor superconductivity (single-gap picture).1–3

On the other hand, a pseudogap phase from distinct originsunrelated to superconductivity (two-gap picture) was alsodemonstrated.4–10 In an ARPES study combined with Kerreffect and time-resolved reflectivity techniques, a pseudogapthat opens at a characteristic temperature T � with particle-holeasymmetry was observed, which may result from variousforms of density-wave or nematic order.8 By employing differ-ent incident photon energies, Nakayama and coworkers foundtwo distinct pseudogaps above the superconducting transitiontemperature Tc, and the smaller one had the similar energyscale with the superconducting gap.9 Also, in ARPES,10

Nernst,11,12 and specific heat13 experiments on the Bi2201materials pairing fluctuation above Tc has been observed butwith remarkably different temperature ranges up to about 110,70, and 40 K, respectively, for the samples with similar Tc.

Giaever’s planar-type tunnel junctions proved to be a usefultool for the study of BCS superconductors, from whichthe superconducting gap, the density of states (DOS), thequasiparticle scattering rate, and the effective phonon spectrumcan be found.14,15 For the tunneling study of Bi-based cupratesuperconductors, in addition to the STM technique mentionedabove,1,4 intrinsic Josephson junctions (IJJs)16–25 and breakjunctions25–27 have been used. As a distinct technique, the IJJsutilize electron tunneling between the CuO2 planes within thecrystal,16 which avoid various surface problems and providethe cuprate version of the planar-type junctions with highstability during temperature-dependent measurements. Earlierstudies using IJJs suffered from samples self-heating24,25 andmany efforts were made to solve the problem.17–21 Oneeffort involved optimizing the surface-layer contact20 andreducing the junction size well below 1 μm.21 These provedsuccessful in suppressing heating and the tunneling spectra ofdouble-layered Bi2Sr2CaCu2O8+δ (Bi2212) superconductors

with negligible distortion were obtained. Recently, the super-conducting gap and pseudogap properties were extensivelyexplored considering the gap profiles in momentum spacesuch as the d-wave form and separate locations of thesuperconducting gap and pseudogap.22,23

In this paper, we focus on the near optimally doped Bi2201system and present the first study of the intrinsic tunnelingspectra with negligible heating since the earlier work inRef. 24. We will show that for the Bi2201 crystals with Tc =30 K, a pseudogap will open at T � = 165 ± 15 K while thesuperconducting gap starts to form at a temperature Tc0 =40 K > Tc. The two energy gaps then coexist below Tc0. Wewill determine the temperature-dependent superconductinggap and pseudogap, and the lifetime parameters of the twophases from the spectral fits. Our results demonstrate a cleartwo-gap feature of the Bi2201 system with precursor pairing upto Tc0, which naturally explain many of the previous separateexperimental observations.4,5,7–10,13,28

II. EXPERIMENT

Square-shaped mesa-structured IJJs were fabricated on nearoptimally doped Bi2Sr2−xLaxCuO6+δ crystals with x = 0.4,which were grown by the traveling solvent floating zonemethod and had a Tc of 30 K and transition width less than 2 K.The mesa fabrication process was similar to that used for theBi2212 cuprate superconductors.20–23 In this work, 28 mesaswith sizes ranging from 0.4 to 4 μm were defined on eachcrystal. Low-temperature crystal cleavage with immediate Aufilm counterelectrode evaporation was performed in vacuumto ensure low contact resistance20 and a CaF2 insulating layeras thin as possible (usually slightly above the mesa height)was used for the easier liftoff process.23 Systematic changes inthe temperature dependence of the resistance across mesa andthe tunneling I -V characteristics of different-sized mesas onthe same crystal were found. When mesa sizes decreased below1 μm, self-heating induced spectra distortion became negligi-ble, as in the case for the Bi2212 IJJs described in Ref. 21.

In Fig. 1(a) we show the measured intrinsic tunnelingconductance σ (V,T ) = dI/dV at 4.2 K for five mesas withdifferent sizes on a crystal. Each mesa contains eight IJJs and

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REN, WEI, YU, TIAN, REN, ZHENG, ZHAO, AND LIN PHYSICAL REVIEW B 86, 014520 (2012)

FIG. 1. (Color online) (a) Experimental intrinsic tunnelingspectra at 4.2 K for five mesas with different sizes on aBi2Sr1.6La0.4CuO6+δ crystal near optimal doping. V corresponds tothe voltage per IJJ. The inset shows the spectrum of the 4-μm mesa inexpanded and linear scales. (b) I -V curves of the 4-μm and 0.4-μmmesas where I/S is the current per μm2.

V corresponds to the voltage per IJJ. The curves are plottedsemilogarithmically where the spectra change, as mesa sizereductions can be seen. For the 4-μm mesa, self-heating issignificant, as can be seen from the much faster decrease of σ

when voltage increases above 30 mV. A notable change of thespectra is that the 4-μm mesa displays a clear double-peakstructure located below the voltage of the main broaderpeak (see also inset plotted in linear scales) and, as mesasize decreases, it gradually disappears. This structure locatesbetween 15 and 18 mV, a range approximately equal to thesuperconducting gap voltage (see below), and could be madepresent by heating since heating is known to result in muchsharper superconducting peaks in the tunneling spectra.21,25

According to the ballistic phonon transport model19 thetemperature rise for an IJJ mesa is proportional to P/(κablph),where P = IV is the power generated in the mesa and κab andlph are the in-plane thermal conductivity and phonon mean freepath, respectively. For the Bi2212 crystals near optimal dopingthe experimentally measured κab

29 can be well described byκab(W/Km) ≈ 2.4 + 0.06T (K) in the temperature range of4.2 ∼ 70 K.21 Similar data for Bi2201, however, are notavailable in the literature but could be close in value tothose of Bi2212 for the similar doping strength.30 It is, thus,illustrative to use the result to estimate the temperature rise�T in the present experiment. In this case, neglecting thetemperature dependence of lph and for a mesa at 4.2 K, wehave �T (K) = T − 4.2 = αP/(2.4 + 0.06T ) or �T (K) ≈

√488.4 + 16.7αP − 22.1, where α is a parameter to be

determined experimentally.21

In Fig. 1(b), we plot the I -V curves of the 4-μm and 0.4-μmsamples at 4.2 K. For the IJJ biased at 18 mV as indicatedby a short arrow, the power generated in the 4-μm mesa isP = 0.25 mW. At this bias, since the superconducting peakis present, we expect the mesa temperature should be lowerthan Tc. Taking T = 20 K, we find α = 229 mm−1. For the0.4-μm mesa at the bias of 90 mV (indicated by a long arrow),we see that the I -V curve starts to deviate from the dashedohmic line. At this bias point P is 0.18 mW and we find thetemperature rise �T to be 12.2 K. Below this bias point, �T

will soon reduce to a few K. Since κab increases as T increases,the tunneling data obtained at higher temperatures would beless affected by heating as compared to that at 4.2 K discussedabove. To be on the safe side, we will use the tunneling spectraat V < 90 mV, whose self-heating should be negligible, forthe spectral model fits below.

III. RESULTS AND DISCUSSION

Figure 2 shows the temperature variation of the tunnelingspectra measured from the IJJ in the 0.4-μm mesa. The dataare normalized to that at T = 190 K, above which the curvesbecome definitely gapless. The spectra are seen to display asmooth and continuous evolution in the entire temperaturerange of the experiment. A clear feature, especially whencompared to the Bi2212 samples near optimal doping,22,23

is that the conductance peaks are much less sharp and arebroadened. In the inset of Fig. 2 we plot half the conductancepeak position, which shows a weak temperature dependenceand has a value above 20 meV, corresponding to the pseudogapmagnitude seen in ARPES experiments.5,8–10 These resultssuggest that the pseudogap exists and plays an important role inthe tunneling spectra down to the lowest temperature of 4.2 K.

In Fig. 3(a), we show the temperature dependence of thezero-bias conductance σ (0,T ) (squares), which is largelyrelated to the density of states near the Fermi level and is,thus, sensitive to the formation of an energy gap. Startingfrom 150 K, the data show a clear decrease as temperaturedecreases, indicating the opening of a pseudogap. In the inset

FIG. 2. (Color online) Temperature dependence of the tunnelingspectra of the IJJ in the 0.4-μm mesa. The spectra are normalized tothe one at T = 190 K slightly above T �. (Inset) Half the conductancepeak position obtained from the raw tunneling spectra σ (V,T ).

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FIG. 3. (Color online) (a) Temperature dependence of normalizedtunneling conductance at zero bias (squares, left scale) and at V =108 mV (circles, right scale). (b) Derivative of the temperaturedependence of the zero-bias conductance in (a). (Inset) Raw tunnelingspectra σ (V,T ) at two temperatures near T �.

of Fig. 3, two tunneling spectra at T = 150 and 180 K areplotted. The former shows a clear gapped structure while forthe latter it starts to appear but is still submerged in the noisybackground. From these results we estimate the pseudogapopening temperature to be T � = 165 ± 15 K, which is in goodagreement with the NMR measurements.28 In Fig. 3(b), weplot the derivative of σ (0,T )/σ (0,190 K) shown in Fig. 3(a),in which the T � range appears as a less steep part. BelowT � the curve increases faster as temperature decreases, whichcorresponds to a faster decrease of the σ (0,T ) data in Fig. 3(a).One important observation in Fig. 3(b) is that at a temperatureTc0 ∼ 40 K > Tc, the curve suddenly becomes much steeper,suggesting a further accelerated decrease of σ (0,T ) or theopening of a new energy gap. In Fig. 3(a), the conductancedata σ (108 mV,T ) at large bias, which reflect R−1

N , where RN

is the IJJs normal-state resistance, are also plotted (circles).These experimental results suggest that a pseudogap first

opens at T � and, as temperature is lowered down, thesuperconducting pairs start to form, possibly at Tc0, thusopening up the superconducting gap. Such a two-gap pictureis consistent with the ARPES observations.8,10 However, thepresent pair formation temperature Tc0 = 40 K is considerablylower and agrees with the value inferred from the specific-heatmeasurement.13

In order to obtain the further information of the su-perconducting gap and pseudogap, we note that for theBCS superconductors McMillan and Rowell15 successfullyremoved the nonsuperconducting contribution in the tunnelingspectra by normalizing them to that in the normal state. Sucha technique was also applied in the tunneling experimentsof cuprate superconductors.4,23,27 In Fig. 4(a) we show the

FIG. 4. (Color online) (a) Normalized experimental (symbols)and calculated (lines) tunneling spectra σ (V,T )/σ (V,40 K) at fourtypical temperatures (curves for T < 35 K shifted vertically forclarity). (b) �s from fits to the normalized σ (V,T )/σ (V,50 K)and σ (V,T )/σ (V,30 K) spectra are shown as squares and circles,respectively. Both deviate clearly from the BCS d-wave gap closingat respective temperatures (dashed and dotted lines) as compared withthe fit to σ (V,T )/σ (V,40 K) (triangles) that shows a good agreementwith the BCS prediction (solid line). (Inset) Relative weights of thePG (red line) and SC (blue line) phases seen in momentum space.The yellow line represents the Fermi surface. The θp angle indicatesa point below and above which the PG and SC phases prevail.

tunneling spectra normalized to that at Tc0 = 40 K at fourtypical temperatures (symbols). We see that the conductancepeak positions now appear slightly below 20 meV, suggestinga superconducting gap around 10 meV.2,3,5 To fit these datawe consider a DOS in Dynes’ form31 that is often used in thetunneling experiments,14,22,23,26,31

Ns,p(θ,ω) = Re

[ω + iγs,p√

(ω + iγs,p)2 − �2s,p cos2(2θ )

], (1)

where a d-wave gap � cos(2θ ) is considered and the subscriptsdenote both the SC and PG parts for later consideration. θ and γ

are the angle of in-plane momentum measured from (π,0) andthe parameter characterizing the lifetime effects, respectively.The I -V curves of IJJs can be calculated from14

I (V ) = 1

eRN

∫ ∞

−∞n(ω)n(ω + eV )[f (ω) − f (ω + eV )]dω,

(2)

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in which n(ω) is the DOS of two identical electrodes and f (ω)is the Fermi function. To fit the spectra in Fig. 4(a) with puresuperconducting contribution, we use the following effectiveDOS for n(ω):

n(ω) = 8

π

∫ π/4

0Ns(θ,ω) cos2(2θ )dθ, (3)

where cos2(2θ ) comes from the directional tunneling matrixelement20,25,27 and integration is performed from 0 to π/4 dueto symmetry which covers the whole Fermi surface.

In the Bi2212 materials, superconducting pairs are found toreside dominantly in the nodal region above an angle denotedas θp in momentum space, particularly in the temperature rangefrom Tc to Tc0.23 However, in the case of Bi2201 there isevidence of the presence of the superconducting gap at theantinode.5,7–9 In the inset of Fig. 4 we schematically show therelative weights of the SC and PG phases, as suggested inRef. 6 for samples on slightly overdoped side, which justifythe integration over the whole Fermi surface in Eq. (3). InFig. 4(a), the solid lines are the fitting results using Eqs. (1)–(3).We see that the fits appear satisfactory and the gap parameter�s follows nicely the predicted BCS curve from 4.2 K upto Tc0 = 40 K, as can be seen in Fig. 4(b) (triangles, γs notshown but later in Fig. 5 for clarity). We note that in the case ofBi2212 similar fits would lead to �s much below the BCS linesfor temperatures near and above Tc so a superconducting gaplimited in the nodal region must be considered.23 In Fig. 4(b)the squares and circles are the results from fits to the spectrathat are normalized to Tc0 = 50 K and 30 K, respectively.Both results display considerable deviation from the BCS lines,which confirms a pair formation temperature of Tc0 = 40 Kas found from the direct experimental zero-bias conductancedata.

The above results indicate that the SC phase develops at Tc0

and it coexists with the PG phase at all temperatures below. ThePG phase may result from various forms of the density-waveor nematic order.8 In the Nernst experiments the SC phaseand PG phase are attributed to the spatially distinct regionsthat have coherent and incoherent properties in nature.12 In

these cases the two phases are expected to reside in the sameCuO2 plane. On the other hand, two different energy gaps havebeen separately observed when photons with different energiesare used, which indicates that they may reside in layers ofdifferent depth and surface properties may play a role.9 Inthe present IJJ experiment, there is no surface present so itis reasonable to assume that the SC and PG phases coexistin the same CuO2 plane. Since Bi2201 is a single-layeredsystem and there would be a single electronic energy bandnear the Fermi level, the pseudogap that first develops shouldbe a soft gap and there remain finite densities of states for thesuperconducting pairing.5,9 This is understandable in stronglycorrelated systems since the Green’s function has the generalform G(k,ω) = Gch(k,ω) + Ginch(k,ω).32 If we consider thatthe coherent and incoherent parts correspond to the SC andPG phases, respectively, the DOS that enters in Eq. (2) can bewritten as n(ω) = ns(ω) + np(ω) that reads

n(ω) = 4

π

∫ π/4

0[Ns(θ,ω) + Np(θ,ω)] cos2(2θ )dθ, (4)

where we have used Eq. (1) for both phases.In Fig. 5(a), the �s and γs parameters obtained above

are plotted as up-triangles. Using these data for Ns(θ,ω) inEq. (4) for T < Tc0 and unity for T � Tc0, one can obtainthe �p and γp parameters by fitting to the normalized spectraσ (V,T )/σ (V,190 K), which are displayed as down-trianglesin Fig. 5(a). Two fitting results at 70 K and 4.2 K are shownin Fig. 5(b) and the densities of states used at these twotemperatures are shown in Figs. 5(c) and 5(d), respectively.

The data in Fig. 5 give a visualized picture of the two-gapscenario seen from the present tunneling experiment. First,the pseudogap magnitude is a constant and its temperature-dependent property is solely reflected in the lifetime parameterγp that decreases monotonically with decreasing temperature.As temperature decreases, the superconducting gap starts toopen at Tc0 > Tc, which follows the BCS gap prediction,while the γs parameter experiences a fast decrease near Tc

and quickly saturates at lower temperatures. These resultsnaturally explain the observation of the two pseudogaps above

FIG. 5. (Color online) (a) Parameters of thePG and SC phases as indicated. Squares are halfthe conductance peak position shown in the insetof Fig. 2. (b) Experimental (symbols) and fitted(lines) spectra σ (V,T )/σ (V,190 K) at 70 K and4.2 K (curves at 4.2 K shifted vertically forclarity). [(c) and (d)] Densities of states usedin the fits in (b).

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SUPERCONDUCTING GAP AND PSEUDOGAP IN NEAR- . . . PHYSICAL REVIEW B 86, 014520 (2012)

Tc9 and conform with the precursor pairing idea suggested in a

number of experiments.8,10–13,23 Furthermore, we see that thelifetime parameter γs , which is an average of the quasiparticlescattering rate and pair decay rate in the superconducting state,remains large at low temperatures. This can be caused bythe coexisting pseudogap phase with a γp size comparable tothe superconducting gap �s . The densities of states plottedin Figs. 5(c) and 5(d) provide examples that the pseudogapis a soft gap and the superconducting gap develops on theFermi surface with the remaining densities of states. Finally,we point out that the present two-gap picture with precursorpairing up to Tc0 is remarkably similar to the situation inBi2212 materials,23 although the tunneling spectra of the twomaterials differ substantially in their appearance. However, aclear difference exists whereby, in Eqs. (3) and (4), integrationsare performed on the whole Fermi surface, whereas, in thecase of Bi2212, a boundary θp should be considered, belowand above which the pseudogap and superconducting phaseslocate predominantly. Although there is evidence that thesuperconducting gap expands to the antinode in Bi22015,7–9

that supports the present consideration, the precise cause forsuch a difference remains to be identified.

IV. SUMMARY

We presented a tunneling study of the superconducting gapand pseudogap in near optimally doped Bi2Sr2−xLaxCuO6+δ

cuprate superconductors using the intrinsic Josephson junctiontechnique. The self-heating effect, a notorious obstacle inIJJ experiments, was carefully considered and analyzed byfabricating mesas with different sizes on the same crystal.When the mesa size was decreased down to the submicronlevel, heating became largely negligible in the bias rangesufficient for the spectroscopic study. Based on the detailedanalysis of the measured spectra via approaches often usedin tunneling experiments, we found that, as temperaturewas decreased, a pseudogap first developed around T � =165 K while the superconducting gap started to open atTc0 = 40 K, which was well above the superconductingtransition temperature Tc of 30 K. The temperature-dependentsuperconducting gap, the pseudogap, and the lifetime pa-rameters were discussed and compared to results fromother spectroscopic studies. Our results demonstrated a cleartwo-gap feature of the materials with precursor pairing upto Tc0.

ACKNOWLEDGMENTS

We thank J. R. Shi for fruitful discussions and H. F.Yang and C. Z. Gu for kind helps during sample prepa-rations. This work was supported by the National NaturalScience Foundation of China (Grant No. 10974242) and theMinistry of Science and Technology of China (Grant No.2011CBA00106).

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