Electronic crossover suggested by Raman scattering in overdoped (Y,Ca)Ba2Cu3Oy
aa r X i v : . [ c ond - m a t . s up r- c on ] J a n Electronic crossover suggested by Raman scattering in overdoped(Y,Ca)Ba Cu O y T. Masui, ∗ T. Hiramachi, K. Nagasao, and S. Tajima
Dept. of Physics, Graduate School of Science,Osaka University Machikaneyama 1-1, Toyonaka, Osaka 560-0043, Japan
Abstract
The electronic Raman scattering in overdoped (Y,Ca)Ba Cu O y was investigated with changinghole concentration in the superconducting state. It was found that the superconducting responsessuch as the pair-breaking peaks in the A g and B g spectra and the anisotropy of the pair-breakingpeak in XX and Y Y polarizations radically change at around the carrier doping p =0.19. Sinceboth a - and c -axis resistivities strongly suggest the closing of pseudogap at p ∼ p =0.19 in superconducting Raman response is attributed to the electronic crossover dueto the collapse of the pseudogap. ∗ Electronic address: [email protected] . INTRODUCTION A rough sketch of the electronic phase diagram for high- T c superconducting cuprates(HTSC) was established at the early stage of these twenty years-studies [1]. However, inspite of a tremendous amount of studies, we are still far from the complete understanding ofthe phase diagram. Compared to the underdoped electronic state governed by a mysteriouspseudogap [2], the overdoped state has been less studied so far. It is partly because theelectronic state is supposed to merely approach a conventional Fermi liquid metal.Recently the overdoped state is reexamined in detail, in relation to a quantum criticalpoint (QCP). Tallon and coworkers have been insisting a QCP at the carrier doping level p =0.19 where the pseudogap energy estimated from specific heat falls to zero [3]. A recentneutron experiment also suggested that the resonant magnetic modes show a qualitativechange at the same doping level [4]. On the other hand, there are reports that physi-cal properties are clearly distinguished between the under- and over-doped regimes at theboundary of optimal doping p =0.15-0.16 [5, 6, 7]. The former results suggest that the pseu-dogap line and the ” T c dome” are independent in the phase diagram, which indicates thatthe pseudogap is irrelevant to the superconductivity pairing and not a precursor of super-conductivity. By contrast, the latter facts support the picture in which the pseudogap is aprecursor of superconductivity and thus its line merges to the T c dome near the optimumdoping, as is predicted by the t-J model [8, 9] and/or phase fluctuation model[10].One of the approaches to the phase diagram problem is to see the electronic changethrough the superconducting properties such as a superconducting gap. Among variousexperimental methods, Raman scattering measurement has an advantage in determining k -dependence of gap energy as a bulk property [11] in contrast to surface sensitive probes suchas angle-resolved photoemission spectroscopy (ARPES). Thanks to this advantage, we havebeen studying superconducting gaps of YBa Cu O y (Y123) by Raman scattering technique.In the heavily overdoped sample Y . Ca . Ba Cu O y , we found some anomalies in the pair-breaking peaks, and interpreted them as the evidence of s -wave component admixture andan increase of chain-plane coupling[12, 13]. These phenomena are different not only fromthe behaviors of optimally doped samples but also from those of the conventional Fermiliquid-like metal (superconductor) expected in the overdoped regime. The next interest ishow these anomalies develop with doping, and how they link to the normal state properties2r the phase diagram.To explore this issue, in the present study, we examined a precise doping dependenceof Raman scattering spectra between p =0.16 and 0.22. We also measured a - and c -axisresistivity to monitor the normal state for the same series of crystals. When we discusssomething related to the doping level in HTSC, it is very important to collect the data ofvarious physical quantities for the same series of samples by fixing a material. Here we havechosen the Y123 system, and prepared a series of detwinned crystals of Y − x Ca x Ba Cu O y (Y/Ca123) with various x and y . Comparing the spectra for a certain doping level p butdifferent y , we can distinguish the CuO-chain contribution from the response of the CuO plane. It has been uncovered that the spectral changes are not monotonic with p but showan abrupt change near p =0.19 where the resistivity suggests the closing of pseudogap. Thepossibility for the CuO chain contribution to the observed anomalies was completely ruledout. II. EXPERIMENTS
Single crystals of Y/Ca123 were grown by a pulling technique [14] for various Ca con-tents. Rectangular shaped samples were cut from as-grown crystals and detwinned underuniaxial pressure, followed by post-annealing in oxygen atmosphere to adjust oxygen con-tent. Carrier doping level ( p ) was controlled by both Ca content ( x ) and oxygen content( y ). Ca content was determined by an inductively coupled plasma analysis, while oxygencontent was estimated from annealing temperature, using the literature data [15] given foreach Ca content. Fifteen samples with different combination of x and y were prepared forRaman measurement, and 26 for resistivity measurement in total. The value of x variesfrom 0 to 0.12, while y is from 6.74 to 6.92. The carrier concentration p was estimated fromthe empirical relation between T c and p [16].Raman scattering spectra were measured in the pseudo-backscattering configuration forvarious polarizations with using a triple monochromator equipped with a refrigerator cryo-stat. Although the crystal structure of Y/Ca-123 is orthorhombic, all symmetries refer to atetragonal D h point group in the present study. X and Y axis are indexed perpendicularto and along the Cu-O chains, while X ′ and Y ′ are rotated by 45 degree from X and Y ,respectively. In order to extract the electronic Raman response, we fit the spectra in the3ame way as ref.[17].Resistivity was measured by means of a standard four probe technique. ρ a was measuredfor detwinned samples, while crystals for ρ c -measurements were not detwinned. So far, therehas been no available result of ρ c for heavily overdoped Y/Ca123, because the measurementsfor c -axis properties are difficult with polycrystalline samples or thin single crystals grown bya flux method. It should be mentioned that Y123 single crystals grown by a pulling techniqueis as long as a few millimeter along c -axis, which enables us to measure ρ c accurately. III. RESULTSA. Raman scattering spectra with A g and B g symmetries FIG. 1: Raman scattering spectra of Y − x Ca x Ba Cu O y for x =0.10, y =6.83, and p =0.179 with(a) A g and (b) B g polarizations. Solid (blue in color) curves are the fitting results by the Green’sfunction method and the light solid (greed in color) is the extracted electronic responses. Insetsshow electronic response (solid line, cyan in color) and differences between the spectra at 10K and100K, I(10K)-I(100K) (dotted line, pink in color). Figure 1 shows the Raman scattering spectra of Y/Ca-123 for x =0.103 and y =6.83 with A g ( X ′ X ′ − XY ) and B g ( X ′ Y ′ ) polarizations at 10 K. Compared to the spectra of op-timally doped Y123 ( x =0 and y =6.88)[18], there appear several sharp peaks ascribed tothe phonons induced by oxygen deficiencies. The obtained A g and B g electronic Ramanspectra (green curves) show broad peaks (pair-breaking peaks) centered at around 300 cm − and 400 cm − respectively, which are due to the modification of the electronic component4 IG. 2: Doping dependence of the electronic responses in the (a) A g and (b) B g Raman scattering(T=10K). Phonon peaks are subtracted by fitting. below superconducting transition temperature T c . The inset of Fig.1 compares the elec-tronic component at 10 K and the difference of the raw spectra at 100K and 10K. A goodcorrespondence between the two curves justifies our fitting procedure.Figure 2 shows gradual changes of the 10K-electronic responses with carrier doping forthe A g and B g polarizations. In B g spectra the pair-breaking peak shifts more rapidly tolower energies than in A g spectra. This decrease is, as expected from the suppression ofT c , partly due to the decease of superconducting gap energy itself, but is too large to beexplained with such a usual mechanism. The difference between B g and A g pair-breakingpeak energies becomes small with carrier doping. In the electronic Raman scattering ofcuprates, the difference between the polarizations is explained by the screening effect, whichis usually effective only for A g polarization [19]. But in the present case, some mechanism5re necessary to suppress the peak energy in B g polarization. Another remarkable changeappears in peak intensity. The intensity of A g peak decreases with doping, while that of B g peak increases. All these changes were reported in our previous paper [12] and werediscussed as the effect of s -wave component mixing ( ∼
20 % at p =0.22) into a d -wave gap[20]. FIG. 3: (a) Doping (p) dependence of the pair-breaking peak energies for A g and B g spectra.Inset shows the peak energies as a function of oxygen deficiency δ =7- y . Squares and triangles arethe data for B g and A g peaks, respectively. (b) Doping dependence of the peak intensity ratioI( A g )/I( B g ). The B g and A g peak energies and the peak intensity ratio I( A g )/I( B g ) are plotted inFigures 3(a) and (b). One can find a clear kink at p ∼ A g peak energy, whilethe B g peak energy rapidly decreases with doping and merges to the A g line at p > − y , nosystematic change is observed, as demonstrated in the inset. This implies that the observedphenomena are caused only by carrier doping but neither related to the CuO chain structurenor the oxygen deficiency in it. The peak intensity ratio also drops with doping and reachesabout 0.5 at p ∼ p < p > . Raman scattering spectra with XX - and Y Y -polarizations
Another marked effect of carrier overdoping is the quantum interference between Ramanscattering of CuO chains and CuO planes [13]. It manifests itself as a strong suppression ofthe pair-breaking peak in Y Y -polarization spectrum. As is typically seen in the Fano lineshape for the electron-phonon coupling system, the interference between two electronic Ra-man scattering processes modifies a Raman spectrum, if the coupling of these two electronicchannels is strong. Therefore, the suppression of pair-breaking peak in the
Y Y -spectrumis an indication of a large transfer matrix between the CuO -plane and CuO-chain in theheavily overdoped Y/Ca123. FIG. 4: XX - and Y Y -polarized Raman scattering spectra at 10K for various doping levels. Thedark (blue in color) and the light (red in color) curves represent the XX - and , Y Y -spectra,respectively. Phonon peaks are subtracted by fitting.
A precise doping dependence of the electronic Raman spectra of XX and Y Y polariza-tions are demonstrated in Figure 4. It is seen that the suppression of
Y Y -polarization peaksets in at around p =0.19, and then grows with further doping. The suppression in Y Y -polarization is not caused by oxygen deficiency in the CuO chain but develops as a function7f doping level. Namely, this quantum interference effect is enhanced by the increase of holeconcentration on CuO planes. This is another support for the electronic change at p ∼ B g peak in the tetragonal framework is not an ar-tifact caused by the XY -anisotropy. It is because the XY -anisotropy becomes remarkableat p > B g peak is observed at p < C. Resistivity in the a - and c -directions FIG. 5: Resistivities of Y/Ca-123. (a) In-plane resistivities ρ a . Arrows indicate T ∗ where temper-ature dependence deviates from T-linear dependence. (b) c -axis resistivities ρ c . Arrows indicatesT ∗ where low-temperature upturn of resisvitities starts. It is important that the doping level p ∼ A g / B g spectra and the XX/Y Y spectra. This implies that some distinct changein the electronic state is behind them. To discuss the change at ∼ a - and c -axes of Y/Ca123 crystals. Since it is a collection of the data for samples withvarious Ca contents, the doping level does not correlate with oxygen content. Both ρ a and ρ c monotonically decrease with doping. It is rather surprising that ρ c is not much affected byoxygen deficiency. A signature of pseudogap opening can be seen in the upward deviationof ρ c (T) from the T-linear relation as well as the downward deviation of ρ a (T) from the8-linear relation[21]. Figure 5 demonstrates that the pseudogap temperature T ∗ is loweredwith doping and becomes invisible above p ∼ ∗ ( p ) line below T c in the phase diagram, it is expected to reach zero at p ∼ IV. DISCUSSION
Since a strong two-dimensionality beyond the band theory in HTSC is predominantlydue to strong electron correlation but enhanced by the pseudogap opening, the close ofpseudogap is expected to weaken two dimensionality by increasing interlayer coupling. Onone hand, the close of pseudogap at p ∼ T ∗ ( p ) in Fig.5. On the other hand, the negative quantum interference seen in Fig.4 iscaused by an increase of transfer matrix between CuO chain and CuO plane, namely threedimensional coupling between the layers. Therefore, it is likely that the negative quantuminterference starting at p =0.19 is caused by the close of the pseudogap. It can be consideredas the evidence for recovering of three dimensionality above p =0.19.Here it should be noted that even after the pseudogap disappears anisotropy in the normalstate cannot be described by an effective mass model. This can be seen, for example, inthe temperature dependence of the resistivity ratio ρ c /ρ a which should be constant in aFermi liquid metal. The value of resistivity ratio ( ∼ c -direction [22, 23], which results in a large anisotropy ratio γ of upper critical fields. As we reported in reference [24], γ rapidly decreases with overdopingand reaches the band calculation value ( ∼
3) at p ∼ Y Y -spectrum and for the presence ofcritical doping at p =0.19 where the pseudogap closes.9or the anomalous doping dependence of A g and B g pair-breaking peaks, we need morecareful discussion. Four possible factors can be listed up as origins for the decrease in thepair-breaking peak energies: (i) decrease in the maximum gap energy ∆ with doping, dueto T c suppression, (ii) mixing of the s -wave component with doping, (iii) change of thetopology of Fermi surface (FS) with doping, (iv) change of the Fermi surface around (0, ± π )and ( ± π ,0) by collapse of the pseudogap. It is clear that the first one is not the sole originto explain the observed rapid decrease of pair-breaking peaks. Some or all of the other threemay contribute to this phenomenon. The second origin, the s -wave mixing is currently themost plausible explanation to reconcile with the observed rapid change of Raman spectra,although the origin of s -wave component is unclear yet. As the s -wave component increaseswith doping, the energy of B g pair-breaking radically decreases because of the appearanceof the smaller gap maximum as well as the screening effect in the B g channel[20]. Thescreening effect also suppresses the A g peak intensity.The third one, the FS topology should also be taken into account, because the k -dependence of superconducting gap energy depends on the shape of FS even for the case ofsimple d -wave gap. Moreover, the B g Raman vertex is quite sensitive to the FS topology inthe antinodal direction where van Hove singularity is present. According to the calculationby Branch and Carbotte, the B g peak energy changes with the second nearest hopping t ′ because the FS topology changes with t ′ from hole-like to electron-like one [25]. The changeof hole-like FS to electron-like one was reported by ARPES for La − x Sr x CuO with x ∼ B g peak energy is 30 % at most bythe change of FS topology.Since the B g Raman spectrum is sensitive to the FS around ( ± π ,0) and (0, ± π ), disap-pearance of the pseudogap (the fourth factor) must seriously affect the B g spectrum. Thenext question is which of these four factors can cause the non-monotonic change in the A g and B g pair-breaking peaks. The first factor (decrease in ∆ ) can be ruled out, because itis unlikely that ∆ abruptly changes at p =0.19. The observed spectral change at p ∼ Ba CuO z [27, 28, 29], and thus this should be common among HTSC. Althoughone may expect that the collapse of pseudogap in overdoped regime leads to a simple d -wavesuperconductivity, the observed anomaly in this study is quite distinct from such a simplesuperconducting state. Here we may take into consideration the existence of unpaired carri-ers in the overdoped regime. For example, a large amount of unpaired carriers are observedin far-infrared spectra[30], specific heat[31], and magnetic susceptibility[32]. If a supercon-ducting phase and unpaired carriers coexist, a proximity effect between the two phases mustbe taken into account. This could induce an anomaly such as an s -wave component. Anabrupt change at p =0.19 suggests that this proximity effect may change where the FS isfully recovered. V. SUMMARY
In order to examine the phase diagram from the viewpoint of superconducting response,we studied the electronic Raman spectra of overdoped (Y,Ca)Ba Cu O y as a function ofdoping level p . By a precise and systematic study on a series of detwinned crystals withvarious Ca and oxygen contents, we were able to remove the contribution of oxygen deficiencyin our discussion and to extract a pure doping effect.It was found that the changes of superconducting responses in XX/Y Y - and A g /B g -polarizations are not monotonic but show abrupt changes at around p =0.19, where theclosing of pseudogap is suggested by both of ρ a (T) and ρ c (T). These changes at p =0.19 areattributed to an essential change of the electronic state such as the closing of pseudogapand the change of Fermi surface topology. Our results support the picture in which thepseudogap line T ∗ ( p ) hits to zero at p ∼ p =0.19, while the normal state resistivityindicates a persistence of unusual charge dynamics along the c -axis.This work is supported by New Energy and Industrial Technology Development Organi-zation (NEDO) as Collaborate Research and Development of Fundamental Technologies for11uperconductivity Applications. [1] J.B. Torrance, Y. Tokura, A.I. Nazzal, A. Bezinge, T.C. Huang, and S.S. P. Parkin, Phys.Rev. Lett. , 1127 (1988).[2] T. Timusk and B. Statt, Rep. Prog. Phys. , 61 (1999).[3] J. L. Tallon and J. W. Loram, Physica C , 53 (2001).[4] S. Pailhes, C. Ulrich, B. Fauque, V. Hinkov, Y. Sidis, A. Ivanov, C.T. Lin, B. Keimer, P.Bourges, Phys. Rev. Lett. , 257001 (2006) .[5] D. van der Marel, H.J.A. Molegraaf, J. Zaanen, Z. Nussinov, F. Carbone, A. Damascelli, H.Eisaki, M. Greven, P. H. Kes, M. Li, Nature , 271 (2003).[6] N. Gedik, M. Langner, J. Orenstein, S. Ono, Y. Abe, Y. Ando, Phys. Rev. Lett. , 117005(2005).[7] G.S. Boebinger, Y. Ando, A. Passner, T. Kimura, M. Okuya, J. Shimoyama, K. Kishio, K.Tamasaku, N. Ichikawa, S. Uchida, Phys. Rev. Lett. , 5417 (1996).[8] N. Nagaosa and P.A. Lee, Phys. Rev. Lett. , 2450 (1990).[9] T. Tanamoto, H. Kohno and H. Fukuyama, J. Phys. Soc. Jpn. , 2739 (1994).[10] V.J. Emery and S.A. Kivelson, Nature (London) , 434 (1995).[11] T. Staufer, R. Nemetschek, R. Hackl, P. M¨uller, H. Veith, Phys. Rev. Lett. , 1069 (1992).[12] T. Masui, M. Limonov, H. Uchiyama, S. Lee, S. Tajima, A. Yamanaka, Phys. Rev. B ,060506(R) (2003).[13] T. Masui, M. Limonov, H. Uchiyama, S. Tajima, A. Yamanaka, Phys. Rev. Lett. , 207001(2005).[14] Y. Yamada, Y. Shiohara, Physica C , 182 (1993).[15] B. Fisher, J. Genossar, C.G. Kuper, L. Patlagan, G.M. Reisner, A. Knizhnik, Phys. Rev. B , 6054 (1993).[16] J.L.Tallon, C. Bernhard, H. Shaked, R.L. Hitterman, J.D. Jorgensen, Phys. Rev. B , 12911(1995).[17] M. Limonov, D. Shantsev, S. Tajima, A. Yamanaka, Phys. Rev. B , 024515 (2001).[18] X.K. Chen, E. Altendorf, J.C. Irwin, R. Liang, W.N. Hardy, Phys. Rev. B , 10530 (1993).[19] T. P. Devereaux and D. Einzel, Phys. Rev. B , 16336 (1995).
20] R. Nemetschek, R. Hackl, M. Opel, R. Philipp, M.T. B´eal-Monod, J.B. Bieri, K. Maki, A.Erb and E. Walker, Eur. Phys. J. B , 495 (1998).[21] K. Takenaka, K. Mizuhashi, H. Takagi and S. Uchida, Phys. Rev. B bf50, 6534(R) (1994).[22] K. Semba, A. Matsuda, T. Ishii, Phys. Rev. B bf49 10043 (1994).[23] K. Tomimoto, I. Terasaki, A.I. Rykov, T. Mimura, S. Tajima, Phys. Rev. B bf60 114 (1999).[24] K. Nagasao, T. Masui, S. Tajima, Physica C , 1188 (2008).[25] D. Branch and J. P. Carbotte, Phys. Rev. B , 13288 (1996).[26] A. Ino, C. Kim, M. Nakamura, T. Yoshida, T. Mizokawa, A. Fujimori, Z.-X. Shen, T.Kakeshita, H. Eisaki, S. Uchida, Phys. Rev. B , 094504 (2002).[27] C. Kendziora, R.J. Kelley, M. Onellion, Phys. Rev. Lett. , 727 (1996).[28] L.V. Gasparov, P. Lemmens, N.N. Kolesnikov, G. G¨untherodt, Phys. Rev. B , 11753 (1998),[29] T. Nishikawa, T. Masui, S. Tajima, H. Eisaki, H. Kito, A. Iyo, Journal of Physics and Chem-istry of Solids (2008), doi:10.1016/j.jpcs.2008.06.022.[30] J. Sch¨utzmann, S. Tajima, S. Miyamoto, S. Tanaka, Phys. Rev. Lett. , 174 (1994); J.Sch¨utzmann, S. Tajima, S. Miyamoto, Y. Sato, I. Terasaki, Solid State Commun. , 293(1995).[31] J. W. Loram, J. L. Tallon and W. Y. Liang, Phys. Rev. B , 060502(R) (2004).[32] Y. Tanabe, T. Adachi, T. Noji, Y. Koike, J. Phys. Soc. Jpn. , 2893 (2005)., 2893 (2005).