Two pseudogaps with different energy scales at the antinode of the high-temperature Bi 2 Sr 2 CuO 6 superconductor using angle-resolved photoemission spectroscopy
K. Nakayama, T. Sato, Y.-M. Xu, Z.-H. Pan, P. Richard, H. Ding, H.-H. Wen, K. Kudo, T. Sasaki, N. Kobayashi, T. Takahashi
aa r X i v : . [ c ond - m a t . s up r- c on ] J un Two pseudogaps with different energy scales at the antinode of the high-temperatureBi Sr CuO superconductor using angle-resolved photoemission spectroscopy K. Nakayama, T. Sato, Y.-M. Xu, , ∗ Z.-H. Pan, , † P. Richard, , H. Ding, , H.-H. Wen, , ‡ K. Kudo, , § T. Sasaki, N. Kobayashi and T. Takahashi , Department of Physics, Tohoku University, Sendai 980-8578, Japan Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA World Premier International Research Center, Advanced Institutefor Materials Research, Tohoku University, Sendai 980-8577, Japan Beijing National Laboratory for Condensed Matter Physics,and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China and Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan (Dated: November 8, 2018)We have performed high-resolution angle-resolved photoemission spectroscopy on single-layeredcuprate Bi Sr CuO to clarify the origin of the pseudogap. By using various photon energies,we have succeeded in directly observing two different pseudogaps with two different energy scaleswhich coexist in the antinodal region: one reflects the d x − y -wave pairing strength while the otherhas a larger energy scale suggesting an origin distinct from superconductivity. The observed two-pseudogap behavior provides a key to fully understand the pseudogap phenomena in cuprates. PACS numbers: 74.72.-h, 74.25.Jb, 79.60.-i
I. INTRODUCTION
The pseudogap observed in the excitation spectrumas a suppression of spectral weight in the normal stateof cuprate superconductors [1] has attracted much atten-tion since it is closely related to the mechanism of high- T c (transition temperature) superconductivity. The openingof the pseudogap has been interpreted as either a precur-sor of Cooper pairing above T c without phase coherence[2] or as the development of some sort of ordered statewhich competes with superconductivity [3–5]. However,in spite of intensive studies, the origin of the pseudogapis still highly controversial. This is largely due to thelack of consensus on the energy scale of the pseudogap.Some experiments pointed out that the pseudogap has adifferent energy scale from that of the superconducting(SC) gap, indicative of the presence of two energy scales(possibly two distinct energy gaps) in the SC state [6–11]. This two-gap behavior suggests that the pseudogaphas a competing nature and is not directly related to su-perconductivity. It has been reported that the two-gapbehavior is pronounced in low- T c systems such as heav-ily underdoped Bi Sr CaCu O (Bi2212), single-layeredBi Sr CuO (Bi2201), and La − x Sr x CuO (LSCO) [6–11]. On the other hand, even in the low- T c systems,there are some recent experimental studies reporting thepresence of single energy scale where the SC gap below T c and the pseudogap above T c show an identical energyscale with no evidence for the two-gap behavior [12–16],strongly supporting a pairing origin of the pseudogap.The apparent contradiction requires further experimen-tal investigation on the energy scale of the pseudogap inlow- T c cuprates to elucidate the origin of the pseudogap.In this paper, we report high-resolution angle-resolved photoemission spectroscopy (ARPES) results on single-layered cuprate Bi2201. By comparing ARPES dataobtained with two different photon energies (8.437 and21.218 eV), we clearly found two energy scales at theantinode below T c . We demonstrate that these energyscales persist even above T c , suggesting the presence oftwo different types of pseudogaps coexisting in the samemomentum ( k ) region. We discuss the implications ofthe present experimental results in relation to the exist-ing models as well as the origin of the pseudogap. II. EXPERIMENTS
High-quality single crystals of slightly overdoped(Bi,Pb) Sr CuO δ (Pb-Bi2201; T c ∼
21 K) and nearly-optimally doped Bi Sr . La . CuO δ (La-Bi2201; T c ∼
32 K) were grown by the floating-zone [17, 18] and thetraveling-solvent floating-zone methods [19], respectively.High-resolution ARPES measurements were performedusing VG-SCIENTA SES2002 and MBS A1 photoemis-sion spectrometers with xenon (Xe) and helium (He)plasma discharge lamps [20]. We used one of the Xe-Ilines ( hν = 8.437 eV) and the He-I α line (21.218 eV) toexcite photoelectrons. The energy resolution was set at2-4 meV and 6-12 meV for the measurements with the Xeand He lamps, respectively. The angular resolution wasset at 0.2 ◦ . We cleaved samples under ultrahigh vacuumbetter than 4 × − Torr to obtain a clean and freshsample surface for ARPES measurements. The Fermilevel ( E F ) of samples was referenced to that of a goldfilm evaporated onto the sample holder. FIG. 1: (Color online): (a) and (b) Plot of ARPES inten-sity at E F for Pb-Bi2201 ( T c ∼
21 K) as a function of two-dimensional wave vector measured at 10 K with the Xe-I ( hν = 8.437 eV) and the He-I α (21.218 eV) lines, respectively.The intensity at E F was obtained by integrating the spectrawithin ±
15 meV with respect to E F . Red curve representsthe Fermi surface determined by smoothly tracing the exper-imentally determined k F points. (c) and (d) ARPES spectrameasured at 10 K along the orange arrow shown in (a) and(b), respectively. (e) and (f) Same as (c) and (d), but mea-sured along the pink arrow. III. RESULTS AND DISCUSSION
First we present ARPES data in the SC state. Fig-ures 1(a) and 1(b) show the ARPES intensity plot at E F of Pb-Bi2201 as a function of the two-dimensional wavevector measured with the Xe-I and He-I α lines, respec-tively. While the ARPES intensity distribution in the k space is different between these plots likely due to matrix-element effects, we find a nearly identical Fermi-surfaceshape (red curve) centered at the ( π , π ) point as deter-mined by tracing the Fermi wave vector ( k F ) points. Inthe SC state, both the Xe-I and He-I α spectra commonlyshow a holelike band crossing E F in the nodal region[Figs. 1(c) and 1(d)] and a clear leading-edge shift towardhigher binding energy in the antinodal region [Figs. 1(e)and 1(f)]. Although these experimental results suggestthe similarity of the basic electronic structure betweenthe He-I α and Xe-I spectra, a closer look further revealsmarked differences in the gap behavior.Figures 2(a) and 2(b) display symmetrized ARPESspectra of Pb-Bi2201 measured at k F points with variousFermi-surface angles φ at 10 K (below T c ) with the Xe-Iand He-I α lines, respectively. The gap size, defined bythe energy separation between the peak position and E F ,monotonically increases on going from the nodal (bottom FIG. 2: (Color online): (a) and (b) k dependence of thePb-Bi2201 ( T c ∼
21 K) ARPES spectra at 10 K, measuredat various k F points shown by circles in (c), using the Xe-Iand He-I α lines, respectively. The coloring of the spectra isthe same as that of the circles in (c). Each spectrum hasbeen symmetrized with respect to E F to remove the effect ofthe Fermi-Dirac distribution function. (c) Schematic Fermisurface and definition of the Fermi-surface angle φ . (d) Com-parison of symmetrized spectra at the antinodal k F point mea-sured with the Xe-I and He-I α lines. The black arrow and thedashed line denote the peak position for the Xe-I and He-I α spectrum, respectively. (e) k dependence of the gap size at10 K obtained with the Xe-I and He-I α lines (∆ Xe and ∆ He ).The gap size was determined by fitting the symmetrized spec-tra with the phenomenological gap function convoluted withthe energy resolution [21]. (f) and (g) Same as (d) and (e)but measured in La-Bi2201 ( T c ∼
32 K). in the panel) to the antinodal (top) regions, which is con-sistent with the anisotropic gap opening in the SC state.As also visible in Fig. 2(d), there is a striking differencebetween the He- and Xe-spectra on the peak positionaround the antinode, i.e. the peak in the He spectrum islocated at much higher binding energy than that of theXe spectrum (18.5 and 11.5 meV, respectively). We use∆ Xe and ∆ He to note the gap size obtained from the Xe-and He-spectra, respectively. In Fig. 2(e), we plot esti-mated ∆ Xe and ∆ He at 10 K at various k F points. The k dependence of ∆ Xe is well fitted by the d x − y -wave gapfunction with a small admixture of higher order compo-nent, representing the energy scale of the SC gap [16].Although ∆ He shows a quantitative agreement with ∆ Xe near the node, it gradually deviates from ∆ Xe with ap-proaching the antinode. Similar trend is also observed inLa-Bi2201, whose T c value (32 K) is much higher thanPb-Bi2201 (21 K). As shown in Fig. 2(f), the differencebetween ∆ Xe and ∆ He (arrow vs dashed line) exceeds 20meV at the antinode, whereas ∆ Xe and ∆ He appear iden-tical near the node. As visible in Fig. 2(g), the observedsignificant deviation of ∆ He from the ideal d x − y -wavegap function appears similar to previous ARPES resultswhich have been interpreted with two types of energygaps in different k regions, i.e. (i) the SC gap which domi-nates the gap symmetry near the node , and (ii) the largegap which develops near the antinode [6–8]. The goodagreement between ∆ He and ∆ Xe near the node in thepresent ARPES result is consistent with the pairing na-ture of the gap around the node in the He-spectra. Inaddition, the marked difference between ∆ He and ∆ Xe near the antinode provides a direct evidence for the pres-ence of two energy gaps below T c (a small gap and a largegap) even in the same k region, although we cannot com-pletely rule out a possible k z dependence of the gap sizeto account for the difference between ∆ He and ∆ Xe . Thisobservation should be strictly distinguished from previ-ous works reporting the “two gaps” [6–8], in the sensethat two gaps appear simultaneously at the antinodal re-gion.To clarify how these gaps evolve into the pseudogapabove T c , we have performed ARPES measurements at24 K (just above T c ) on Pb-Bi2201 with the Xe-I andHe-I α lines. As seen in both sets of data in Fig. 3(a),the symmetrized spectrum near the node shows a sin-gle peak at E F , while the spectrum at the antinode ex-hibits spectral weight suppression in the vicinity of E F - a signature of the pseudogap opening [Fig. 3(b)]. Inthe antinodal region, the characteristic energy scales ofthe pseudogap are ∼
12 meV and ∼
20 meV for the Xe-and He-spectrum, respectively, which are similar to thevalues of ∆ Xe and ∆ He below T c in the antinodal region,as shown in Fig. 3(c). It is thus inferred that there ex-ist two pseudogaps above T c with precursor-pairing andunknown origin which smoothly evolve from the d x − y -wave SC gap and the larger gap below T c , respectively.It is emphasized that, although a few previous ARPESresults suggested a two-pseudogap-like behavior [22, 23],the present ARPES result directly demonstrates for the FIG. 3: (Color online): (a) and (b) Photon-energy depen-dence of symmetrized k F spectra in Pb-Bi2201 ( T c ∼
21 K)at 24 K measured at φ ∼ ◦ and ∼ ◦ , respectively. (c) k de-pendence of the gap size in the SC ( T = 10 K) and pseudogap(24 K) states of Pb-Bi2201 measured with the Xe-I and He-I α lines. first time the presence of two energy scales at the antin-ode.The present observation solves the contradictionamong recent ARPES experiments. While some studiessupported the pairing origin of the pseudogap [12–16],others pointed out that the pseudogap is not directly re-lated to the pairing [6–9]. Such difference is naturallyunderstood by taking into account the presence of twopseudogaps. Namely, the former studies detected onlythe small gap and the latter observed mostly the largegap, essentially because of the difference in the exper-imental conditions such as the photon energy. In fact,the previously reported pseudogap values of ∼
15 meV[13, 15] and ∼
35 meV [7, 9] for La-Bi2201 (which diverseamong different groups) agree well with the maximumvalues of ∆ Xe and ∆ He , respectively. In addition, the dif-ference of the gap anisotropy in the pseudogap phase ofLa . Ba . CuO [22, 24] can also be explained withinthe two-pseudogap picture.Finally, we discuss the implication of the observedphoton-energy dependence. We revealed that the mea-surements using the Xe-I ( hν = 8.437 eV) and the He-I α (21.218 eV) lines are sensitive to the small gap and thelarge gap, respectively. One explanation of such behav-ior is that the two different gaps suffer different matrix-element effects during the photo-excitation process andthey can be selectively observed by specific conditionsof the photon energy. This explanation may be valid ifthere are two different bands producing the small andthe large gaps, respectively, as the bilayer-split bands inBi2212 obey different matrix elements [25]. On the otherhand, Bi2201 is a single-layered system and there wouldbe a single band near E F . In this case, the appearanceof two energy scales on the single coherent quasiparticleband may be explained by the idea that the large gap isnot a complete gap but rather a soft gap [9], and the re-maining density of states within the large gap contributesto the formation of the small gap. It is also possible toattribute the large and the small gaps to the incoherentand the coherent parts of the spectral function. In ei-ther case, the two gaps basically arise from a single-bandspectral function and their intensity ratio would not de-pend on the photon energy. Hence we think that thepresent observation may not be simply explained by thematrix-element effect. Another explanation is that thedifference between the He- and Xe-spectrum originatesfrom the surface / bulk sensitivity. In this case, it is in-ferred that the large gap, which seems not directly relatedto the superconductivity, is either (i) an extrinsic featurestabilized at the surface or (ii) an intrinsic feature in bulkwith much pronounced influence at the surface. On theother hand, the small gap, which is closely related to thepairing, would reflect bulk properties because electronsexcited with the Xe-I line have a relatively long escapedepth (20-40 ˚A) as compared to that excited with theHe-I α line (5-10 ˚A) [20]. The bulk nature of the smallgap is also supported by a basic agreement between ∆ Xe in La-Bi2201 ( ∼
14 meV) and an energy scale observedin the B g Raman spectrum ( ∼
17 meV) [26]. Whilemost of previous results on Bi2201 [7, 9, 15, 16, 23] agreewith the expectation that the spectral weight related tothe small gap feature is enhanced as the photon energyis lowered ( i.e. the photoelectron escape depth becomeslonger), there is one exceptional result which shows thesmall gap feature at the antinode even with hν = 22.5eV in optimally doped La-Bi2201 with a zero residual re-sistivity [13]. Since the authors reported that the smallgap disappears in another optimally doped sample witha finite residual resistivity [13], the disorder effect maybe an essential ingredient in suppressing the small gapcomponent and also in causing the difference in the elec-tronic states between surface and bulk. In any cases,the pairing interaction is essential in realizing the originof the pseudogap, and we conclude that the scenario as-suming the opening of a single competing pseudogap isinsufficient for the correct understanding of the pseudo-gap phenomena in cuprates. IV. CONCLUSION
In conclusion, we have performed high-resolutionARPES study of Bi2201 by using the Xe and He dis-charge lamps. The result clearly shows the presenceof two energy scales in the antinodal region below andabove T c , indicating the existence of two different pseu-dogaps. We have concluded that the smaller pseudogaporiginates from the precursor pairing above T c , while thelarger pseudogap is not directly related to the supercon- ductivity. The present findings put a strong constraintin modeling the pseudogap phenomena of cuprates. ACKNOWLEDGMENTS
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