Pair breaking versus symmetry breaking: Origin of the Raman modes in superconducting cuprates N. Munnikes,1 B. Muschler,1 F. Venturini,1,∗ L. Tassini,1 W. Prestel,1 Shimpei Ono,2 9 Yoichi Ando,3 A. Damascelli,4 H. Eisaki,5 M. Greven,6 A. Erb,1 and R. Hackl1 0 0 1Walther Meissner Institute, Bavarian Academy of Sciences, 85748 Garching, Germany 2 n 2CRIEPI, Komae, Tokyo 201-8511, Japan a J 3Institute of Scientific and Industrial Research, 2 2 Osaka University, Ibaraki, Osaka 567-0047, Japan ] 4Department of Physics & Astronomy, n o University of British Columbia, Vancouver, BC V6T1Z4, Canada c - r 5Nanoelectronic Research Institute, AIST, Tsukuba 305-8568, Japan p u 6Department of Applied Physics and Photon Science, s . t a Stanford University, Stanford, CA 94305, USA m - (Dated: January 22, 2009) d n Abstract o c [ We performedRaman experiments on superconductingBi2Sr2(Ca1−xYx)Cu2O8+δ (Bi-2212) and 1 YBa Cu O (Y-123) single crystals. These results in combination with earlier ones enable us v 2 3 6+x 8 to analyze systematically the spectral features in the doping range 0.07 ≤ p ≤ 0.23. In B (xy) 4 2g 4 3 symmetry we find universal spectra and the maximal gap energy ∆0 to follow the superconducting . 1 transition temperatureT . TheB (x2−y2) spectra in Bi-2212 show an anomalous increase of the 0 c 1g 9 intensity towards overdoping, indicating that the corresponding energy scale is neither related to 0 : v the pairing energy nor to the pseudogap, but possibly stems from a symmetry breaking transition i X at the onset point of superconductivity at p ≃ 0.27. r sc2 a PACS numbers: 78.30.-j, 74.72.-h,74.20.Mn, 74.25.Gz 1 Energy scales play an important role in solids whenever various ground states are in close proximity. The copper-oxygen superconductors are paradigmatic of competing order controlled by doping p. Yet, the phases and relevant energies are still intensively debated [1, 2, 3, 4, 5, 6, 7, 8]. For example, in the underdoped range, p ≤ 0.16 holes per CuO 2 formula unit, the variation with p of the superconducting gap ∆k(p) is not settled. In some experiments the maximum of the d-wave gap, ∆ (p), is found to increase or stay 0 constant [7, 8]. Other experiments indicate ∆ (p) to follow the superconducting transition 0 ∗ ∗ temperature T [2, 3, 4, 9, 10, 11, 12, 13]. A second energy ∆ appears already at T > T . c c ∗ ∆ is the typical range over which spectral weight is suppressed in the vicinity of (π,0) and equivalent points in the Brillouin zone (anti-node) and is usually referred to as the ∗ pseudogap [6, 14, 15, 16]. T and T merge for 0.16 < p < 0.20 while there are still two c m energy scales exhibiting different doping dependences [1, 5, 6, 10, 11, 13, 16]. There is general agreement that the one observed close to the Brillouin zone diagonal (node) follows T . The anti-nodal one is approximately proportional to (1−p/p ) with 0.16 < p < 0.30, c 0 0 ∗ similarly as ∆ (p). However, above T there is no suppression of spectral weight any more c [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17] and coherence peaks are observed everywhere on the Fermi surface by angle-resolved photoemission (ARPES) [1] and in real space by scanning tunneling spectroscopy [5, 7]. The wide ranges of p and p indicate systematic variations m 0 with both experiment and material. In a recent Raman experiment the energy of the anti- nodalpair-breakingpeakwasobservedtodecreasemuchfasterthanT uponappliedpressure c [18]. Particularly thelast result castsdoubtontheprevailing interpretationoftheanti-nodal energy in terms of a direct relationship to the pairing energy or the pseudogap. In this paper, we present new electronic Raman scattering experiments and put them into context with earlier results. We systematically study the sample dependence and, as an additional variable, the intensity of the superconductivity-induced features for doping levels 0.07 ≤ p ≤ 0.23. The results show that the momentum dependence of the supercon- ducting gap, f(k) = ∆k/∆0, hardly depends on doping for both Y-123 and Bi-2212. At p > 0.16, the anti-nodal spectra of Bi-2212 neither reflect the pseudogap nor the super- conducting gap. Rather, the doping dependence of both the intensity and the energy of the superconductivity-induced modes suggests that they are intimately related to the onset point of superconductivity at p = 0.27 on the very overdoped side of the phase diagram. sc2 Momentum-dependent electron dynamics such as gaps in superconductors or collective 2 modes can be studied by Raman scattering.By appropriately adjusting the polarizations of the incoming and outgoing photons different parts of the Brillouin zone can be projected out independently [19]. In the cuprates, B and B spectra emphasize anti-nodal and nodal 1g 2g electrons, respectively, with the form factors shown in the insets of Fig. 1 (a) and (b). In the superconducting state the condensate is directly probed since the anomalous part of the Green function is measured in addition to the normal one. The spectra were measured with standard Raman equipment using the Ar+ line at 458 nm. The temperatures generally refer to the illuminated spot and are typically between 5 and 10 K above those of the holder. In Fig. 1 we plot raw data of new measurements on high-quality (Y Ca )Ba Cu O 0.92 0.08 2 3 6.3 (Y-UD28, T = 28 K) (a,b), Bi Sr CaCu O (Bi-OPT94, T = 94 K) (e,f), and c 2 2 2 8+δ c Bi Sr (Ca Y )Cu O (Bi-OPT96, T = 96 K; Bi-OD87, T = 87 K) (c,d,g,h) sin- 2 2 0.92 0.08 2 8+δ c c gle crystals. In spite of the almost identical T s, the two optimally doped Bi-2212 samples c B1g (Fig. 1 (c–f)) show substantial differences in the B spectra. The peak energy Ω of sam- 1g peak ple Bi-OPT96 is approximately 25% higher than that of Bi-OPT94 while T changes only c by 2%. The variation of the peak position is accompanied by a change in the amplitude A , sc i.e. the difference between the superconducting and the normal-state spectra at the peak maximum, by a factor of 2.7. These variations appear to be a result of subtle differences in hole concentration and of quenched disorder [20] leading to local strain fields. In the B 2g spectra there are only minor changes in shape, amplitude, and peak energy. The overdoped sample Bi-OD87 [Fig. 1 (g,h)] was prepared from Bi-OPT96 by oxygen annealing. Both peak frequencies move downwards along with T with a tendency of the B c 1g peak to move more rapidly than the B peak as observed earlier in Bi-2212 [9, 12, 17, 21], 2g Y-123 [10, 12, 22, 23] and HgBa CuO [2]. 2 6+δ On the underdoped side we studied Y-123 for its superior crystal quality [24]. We find superconductivity to be observable only in B symmetry. The peak energy is at approx- 2g imately one third of that observed at optimal doping and follows T . The absence of c superconductivity-induced peaks in B symmetry appears to be a generic feature of un- 1g derdoped cuprates with p ≤ 0.13 (for a discussion see ref. [19]) which occurs in the same doping range as the loss of coherence close to the anti-nodal points observed in many exper- iments [1, 25]. It has been noticed earlier that the B peak energies in the superconducting state follow 2g T [9, 10, 12, 13, 19, 21, 22]. Beyond that we demonstrate here that the entire B spectra c 2g 3 12 6 (a) (b) G G 8 17K 4 17K 53K B1g X M 53K B2gX M 4 2 W) Y-UD28 (Y0.92Ca 0.08)Ba2Cu3O6.3 m 0 0 s/ (c) 23K (d) 23K p ’’ (c 8 113K 4 113K R e 4 2 ns Bi-OPT96 Bi2Sr2(Ca 1.92Y0.08)Cu2O8+ o 0 0 sp (e) 23K (f) 23K e n r 8 112K 4 112K a m a 4 2 R Bi-OPT94 Bi2Sr2Ca2 Cu2O8+ 0 0 (g) 15K (h) 15K 8 95K 4 95K 4 2 Bi-OD87 Bi2Sr2(Ca1.92Y0.08)Cu2O8+ 0 0 0 200 400 600 800 10000 200 400 600 800 1000 -1 Raman shift (cm ) ′′ FIG. 1: Raman response Rχ (Ω,T) (raw data) of (Y Ca )Ba Cu O (Y-UD28) (a,b) and 0.92 0.08 2 3 6.3 Bi2Sr2(Ca1−xYx)Cu2O8+δ (Bi-OPT94, Bi-OPT96, Bi-OD87) (c–h) in B1g and B2g symmetries as indicated. The corresponding light polarizations and sensitivities in the Brillouin zone are shown in the insets with copper and oxygen atoms displayed in red and blue, respectively. In (e) a double-headed arrow indicates the amplitude A of the superconductivity-induced peak. sc Whenever applicable a down-pointing arrow gives the approximate position, where normal-state and superconducting spectra merge. can be scaled by normalizing the energy axis of each sample to the respective T and the c intensityto1atenergiesintherange1000cm−1. AsshowninFig.2,thesuperconductingB 2g spectra collapse on universal curves for both Y-123 and Bi-2212. The low-energy part of the normalized spectra can be described quantitatively in terms of a dx2−y2 gap [19]. Naturally, the description fails at higher energies since only the weak coupling limit is considered which neglects the strong interactions responsible for the large self energy of the electrons [1] and, hence, the Raman spectra at high energies [19]. With the gap represented by ∆k = ∆0[coskx −cosky]/2 we find agreement between theory and experiment up to the B2g pair-breaking peak (see Fig. 2). While the B maximum Ω (p) itself scales as 6 k T 2g peak B c consistent with previous reports [9, 10, 12, 19, 21], the gap maximum ∆ from the d-wave 0 4 2 G Y-123 (a) B2g X M 1 T ~ 15K ) Y-OD87 W Y-OPT92 m Y-UD60 s/ Y-UD28 p ’’ (c00 G Bi-2212 (b) se B2g n X M o T ~ 15K sp1 e c r oni Bi-UD57 ctr0 ed ele B1gX MG BBBiii---OOODDD557668 (c) z3 Bi-OD82 ali T ~ 15K Bi-OD87 m Bi-OPT94 r o Bi-OPT92 N2 1 Bi-OPT96 Bi-UD92 0 0 2 4 6 8 10 12 14 / kBTc ′′ FIG. 2: Normalized electronic Raman response χ0(Ω,p) of (Y1−yCay)Ba2Cu3O6+x in B2g symme- try (a) and Bi2Sr2(Ca1−xYx)Cu2O8+δ in B2g (b) and B1g symmetry (c). Spectra from samples other than those shown in Fig. 1 are taken from our published work [10, 12, 21, 23]. For clarity, the phonons have been subtracted. The energy axes are normalized to the individual transition temperatures. All superconducting spectra merge with the normal-state response in the shaded range. fit in Fig. 2 follows T as 2∆ = 9.0±0.5 k T . This demonstrates that both the gap ratio c 0 B c ∆ /k T and the momentum dependence f(k) remain unchanged in the entire doping range 0 B c studied and, hence, solves a long-standing controversy. The B results pose constraints on the interpretation of the B spectra since the two 2g 1g symmetries are linked by the form factors: a potential change of f(k) would inevitably leave animprint onbothB andB spectra. Inturn, since the B pair-breaking features remain 1g 2g 2g invariant down to very low doping the disappearance of the B gap structures for p < 0.15 1g [Fig. 1 (a)] cannot simply be traced back to the gradual loss of quasiparticle coherence around the anti-nodal parts of the Fermi surface [4, 5, 7] as proposed earlier [2, 22]. In a 5 sense, symmetry seems to protect the nodal electrons. In Fig.2 (c) we plot electronic B spectra of Bi-2212. As a general trend, the peaks move 1g from 9.0 to 4.5 k T for p increasing from 0.15 to 0.23. While the variation of the peaks B c is not monotonic, all normal and superconducting spectra still merge in the same range of approximately 12–14 k T just as in B symmetry. B c 2g In order to make connection to previous work [2, 9, 10, 12, 17, 19, 23] we plot the peak energies Ω (p) for B and B symmetry in Fig. 3 (a). Also shown are 2∆ (p) and a peak 1g 2g 0 B1g linear fit to the B data. Clearly, Ω (p) is unrelated to 2∆ (p) while the peak energies 1g peak 0 in B symmetry scale approximately as 1.4∆ (p) as expected from theory [19]. 2g 0 As a new variable we analyze the amplitudes A (p). In Fig. 3 (b) we compile results sc for A (p) from the present study and our earlier results in Y-123 [10, 12, 23] and Bi-2212 sc [10, 12, 21] with all amplitudes given in absolute units. The differences between Y-123 and Bi-2212 are small indicating little individual variation for these two double-layer compounds and little influence of resonantly enhanced scattering with excitation in the visible spectral range [21]. For B symmetry A (p) is practically doping independent with an average 2g sc close to 1 cps/mW. The variations of order ±50% between individual samples not only reflect impurity effects [26] but also variations of the overall cross section which are not yet understood. Similarsample-dependent changesarealsoobservedinB symmetry. However, 1g the largebasis of results allows us to derive two significant trends: (i) below p ≃ 0.13, A (p), sc i.e. any superconductivity-induced spectral change, vanishes in B symmetry (cf. Fig. 1 1g (a)). This goes along with the rapid decrease of the coherence peaks in tunneling [5] and in ARPES at the anti-nodal Fermi surface crossing [1, 3, 4]. (ii) In Bi-2212 A (p) increases sc strongly for p > 0.18 which has not been appreciated yet. The two points from Y-123 follow the same trend. If we plot [A (p)]−1 (Fig. 3 (c)) we find a divergence point at 0.26±0.03 sc close to p = 0.27 where superconductivity disappears (or appears, depending on the point sc2 of view). Given the universality of f(k) and 2∆ /k T , the variation of ΩB1g (p)/k T by a factor 0 B c peak B c of two, and the tendency of AB1g(p) to diverge, it is hard to identify the B maximum with sc 1g ∆ . What are the alternatives? 0 An explanation in terms of an exciton-like bound state below 2∆ (Bardasis-Schrieffer 0 mode)hasbeenproposedrecently[27,28]. Atfirstglance,theenergyandintensityvariations predicted on the basis of a spin-fluctuation model are similar to those observed here with 6 -1 m)800 c (a) (6peak00 y 2 0 erg400 n e ak 200 e p W) 0 m Bi-2212 B1g (b) cps/ 10 Bi-2212 B2g A (sc Y-123 B1g e Y-123 B2g d 5 u plit m a 0 ps) (c) c 0.4 W/ m 0.3 -1 A ] (sc0.2 [ 0.1 Bi-2212 B1g 0 0.05 0.10 0.15 0.20 0.25 doping p(holes/CuO2) FIG. 3: Doping dependence of the superconductivity-induced features in Y-123 (full symbols) and B2g Bi-2212 (open symbols). (a) Peak energies Ω . Ω (squares) is smaller than 2∆ (dashes). peak peak 0 B1g ThesameholdstrueforΩ (diamonds)atp > 0.16. Alinearfit(straightfullline)representedby peak ΩB1g = 1294(1−p/0.275) cm−1 extrapolates to the upper critical doping p ≃ 0.27 terminating peak sc2 the superconductingdome. (b) Amplitudes A (p) in B and B symmetries. The horizontal line sc 1g 2g at 1.03 cps/mW is the average of the amplitudes in B symmetry. (c) Inverse B amplitudes 2g 1g [A (p)]−1 of Bi-2212. The linear fit extrapolates to zero at p ≃ 0.26 close to p . sc sc2 a simultaneous increase of both amplitude and split-off below 2∆ . However, the doping 0 dependence of the B Raman mode is just opposite to what one expects for the spin 1g channel. Similar arguments apply for a bound state induced by charge ordering [29]. At present we are not aware of an interaction with dramatically increasing coupling strength towards high doping. Alternatively, band structure effects may play a role. However, the quite complicated multi-sheeted Fermi surface of Y-123 seems to have only little influence on the spectra in the superconducting state. Since these more traditional possibilities fail to provide a qualitatively correct description of the experiments we explore a scenario which rests on the unconventional evolution with 7 doping of the B intensity in Bi-2212. If individual variations between the samples are 1g neglected, AB1g(p) diverges approximately as AB1g(p) ∝ [1−p/p ]−1. Although there is sc sc sc2 a substantial increase of anti-nodal coherence in the ARPES single-particle spectra upon overdoping, such as in the case of heavily overdoped Tl-2201 [30], the evolution of the B Raman response can hardly be explained in this way. If this were the case, the B 1g 1g maximum would just become sharper while conserving the integrated area. The observed B1g intensity increase along with the reduction of Ω (p) [Fig. 3 (a)]is instead more compatible peak with the behavior of a Goldstone modeappearing when a continuous symmetry is broken. In fact, we find not only AB1g(p) to diverge at p = 0.26±0.03 but also ΩB1g (p) to extrapolate sc peak linearly to zero at p = 0.27±0.02 as expected for a symmetry-breaking mode. In this scenario the B spectrum is a superposition of the weak coupling pair-breaking 1g feature and an additional mode with B symmetry originating from a broken symmetry. 1g The mode depends on doping and, in close correspondence to the variation with pressure of B1g Ω /k T [18] on sample details [20]. The microscopic origin remains open yet. A spin- peak B c density modulation with q = (π,π) would not appear in B but, rather, in A symmetry 1g 1g [31]. A Pomeranchuk instability of the Fermi surface [32] or spin and/or charge ordering fluctuations with (0.2π,0) [33, 34] have the proper symmetry. In conclusion, the doping independence of the normalized B pair-breaking spectra pins 2g down the superconducting gap’s momentum dependence. The variations of energy and amplitude of the superconductivity induced B spectra cannot originate from a doping 1g dependence of the gap, since there should also be an influence on the B spectra. For 2g p > 0.16 we are dealing apparently with a mode of well defined B symmetry (typical for a 1g collective mode) rather than a projection of the gap as in B symmetry. We speculate that 2g at least in Bi-2212 the mode indicates a broken continuous symmetry at the onset point of superconductivity at p ≃ 0.27. sc2 Acknowledgements: We thank Guichuan Yu for valuable discussions and comments. We acknowledge support by the DFG under grant numbers HA 2071/3 and ER 342/1 via Research Unit FOR538. The crystal growth work at Osaka and Stanford was supported by KAKENHI 19674002 and by DOE under Contracts No. DE-FG03-99ER45773 and No. DE-AC03-76SF00515, respectively. 8 ∗ Permanent address: Mettler-Toledo (Schweiz) GmbH, 8606 Greifensee, Switzerland [1] A. Damascelli, Z. Hussain, and Z.-X. Shen, Rev. Mod. Phys. 75, 473 (2003). [2] M. Le Tacon et al., Nature Physics 2, 537 (2006). [3] K. Tanaka et al., Science 314, 1910 (2006). [4] W. S. Lee et al., Nature 450, 81 (2007). [5] K. K. Gomes et al., Nature 447, 569 (2007). [6] S. Huefner, M. A. Hossain, A. Damascelli, and G. A. Sawatzky, Rep. Prog. Phys. 71, 062501 (2008). [7] J. W. Alldredge et al., Nature Physics 4, 319 (2008). [8] T. Yoshida et al., preprint, arXiv:0812.0155 (2008). [9] S. Sugai and T. Hosokawa, Phys. Rev. Lett. 85, 1112 (2000). [10] R. Nemetschek et al., Phys. Rev. Lett. 78, 4837 (1997). [11] C. Panagopoulos and T. Xiang, Phys. Rev. Lett. 81, 2336 (1998). [12] M. Opel et al., Phys. Rev. B 61, 9752 (2000). [13] G. Deutscher, Nature 397, 410 (1999). [14] C. C. Homes et al., Phys. Rev. Lett. 71, 1645 (1993). [15] A. G. Loeser et al., Science 273, 325 (1996). [16] T. Timusk and B. Statt, Rep. Prog. Phys. 62, 61 (1999). [17] C. Kendziora and A. Rosenberg, Phys. Rev. B 52, R9867 (1995). [18] A. F. Goncharov and V. V. Struzhkin, J. Raman Spectrosc. 34, 532 (2003). [19] T. P. Devereaux and R. Hackl, Rev. Mod. Phys. 79, 175 (2007). [20] H. Eisaki et al., Phys. Rev. B 69, 064512 (2004). [21] F. Venturini et al., J. Phys. Chem. Solids 63, 2345 (2002). [22] X. K. Chen et al., Phys. Rev. B 56, R513 (1997). [23] R. Nemetschek et al., Eur. Phys. J. B 5, 495 (1998). [24] A. Erb, E. Walker, and R. Flu¨kiger, Physica C 258, 9 (1996). [25] F. Venturini et al., Phys. Rev. Lett. 89, 107003 (2002). [26] T. P. Devereaux, Phys. Rev. Lett. 74, 4313 (1995). [27] A. V. Chubukov, T. P. Devereaux, and M. V. Klein, Phys. Rev. B 73, 094512 (2006). 9 [28] A. V. Chubukov and M. R. Norman, Phys. Rev. B 77, 214529 (2008). [29] R. Zeyher and A. Greco, Phys. Rev. Lett. 89, 177004 (2004). [30] M. Plat´e et al., Phys. Rev. Lett. 95, 077001 (2005). [31] F. Venturini et al., Phys. Rev. B 62, 15204 (2000). [32] W. Metzner, D. Rohe, and S. Andergassen, Phys. Rev. Lett. 91, 066402 (2003). [33] S. Caprara et al., Phys. Rev. Lett. 95, 117004 (2005). [34] S. Wakimoto et al., Phys. Rev. Lett. 92, 217004 (2004). 10