ARPES studies of c-axis intracell coupling in Bi 2 Sr 2 CaCu 2 O 8þd

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1 Journal of Physics and Chemistry of Solids 63 (2002) ARPES studies of c-axis intracell coupling in Bi 2 Sr 2 CaCu 2 O 8þd A.D. Gromko a, Y.-D. Chuang a,b, A.V. Fedorov a,b, Y. Aiura c, Y. Yamaguchi c, K. Oka c, Y. Ando d, D.S. Dessau a, * a Department of Physics, University of Colorado, Boulder, CO , USA b Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA c National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba Central 2, Umezono, Tsukuba, Ibaraki , Japan d Central Research Institute of Electric Power Industry (CRIEPI), Iwato Kita, Komae, Tokyo , Japan Abstract Using angle-resolved photoemission spectroscopy we have performed a detailed study of bilayer splitting in Bi 2 Sr 2 CaCu 2- O 8þd as a function of doping level and temperature. In heavily overdoped samples where the splitting is the clearest, we extract an intracell coupling t, 55 mev. As a function of photon energy the intensity ratio of the bonding and antibonding bands varies, allowing us to detect the bilayer splitting effect in the optimal and underdoped regimes. Surprisingly, with reduced doping the intracell coupling is not measurably reduced. Upon cooling to the superconducting state, a gap D opens in both bands yet the magnitude of the splitting remains unchanged. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: C. Photoelectron spectroscopy; D. Electronic structure; D. Fermi surface; D. Superconductivity 1. Introduction One of the hallmarks of the physics of cuprate hightemperature superconductors is that the superconducting transition temperature T 0 is strongly dependent upon the number of Cu O planes per unit cell [1]. This would seem to indicate that the physics of the coupling between Cu O planes within a unit cell is important to the mechanism of high-t c superconductivity. However, until recently there have been no direct observations of any type of c-axis coupling (intracell or intercell) in the cuprates. Transport measurements, optical conductivity, and interlayer tunneling all indicate that coherent charge transport along the c-axis is severely reduced from that in the a b plane [2 4]. Following, the vast majority of theoretical models treat the cuprates in the limit of zero intracell and intercell coupling, i.e. as a single Cu O plane. Here we report on angle-resolved photoemission (ARPES) measurements showing a clear splitting of the near-e F electronic bands in Bi 2 Sr 2 CaCu 2 O 8þd (Bi2212) * Corresponding author. Tel.: þ ; fax: þ address: dessau@spot.colorado.edu (D.S. Dessau). for doping levels ranging from heavily overdoped to underdoped. All evidence points to intracell c-axis coupling as the responsible agent for this splitting. The splitting goes to zero along the (0,0) (p,p) symmetry line, and is maximal near the (p,0) point of the (Brillouin) zone, consistent with the predicted symmetry [5,6]. For overdoped levels we extract an intracell coupling value t, 55 mev, which is reduced from LDA calculations by a factor of 3, confirming that the correlation effects do exist in the overdoped regime. However, this value is on the order of other important energy scales (T c, T p, J ), meaning the physics of this coupling cannot be ignored in theoretical models. Even with the observation of a substantial c-axis intercell coupling in overdoped samples, one may be tempted to argue away its importance with the educated guess that it is limited to a small Fermi liquid-like region of the phase diagram. In underdoped samples we approach the Mott insulator limit where correlations are expected to become stronger, as evidenced by the observed non-fermi liquid behavior, for review see Ref. [7]. The c-axis conductivity has also been found to be reduced in underdoped samples [2,4], and is usually interpreted as increased two-dimensional confinement as /02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S (02)

2 2300 A.D. Gromko et al. / Journal of Physics and Chemistry of Solids 63 (2002) one moves away from the overdoped regime. However, our direct measurements of the intrabilayer coupling indicate that this is not the case. Near (p,0) where the splitting is the strongest, we find that the linewidth of spectral features grows with underdoping but the magnitude of the bilayer splitting remains nearly unchanged. We also find that the magnitude of t is essentially the same in both the normal and superconducting states for these samples. 2. Experimental The experiments were carried out at the Stanford Synchrotron Laboratory, Stanford, CA, the Advanced Light Source, Berkeley, CA, and the Synchrotron Radiation Center, Stoughton, WI. Details of the experimental setups can be found elsewhere [8]. The data shown here were taken on four samples with a naming convention based on T c : OD55 (overdoped, T c ¼ 55 K), OD85 (overdoped, T c ¼ 85 K). OP91 (optimally doped, T c ¼ 91 K), and UD78 (underdoped, T c ¼ 78 K). An important variable in the experiment was photon energy, which we used to empirically adjust the relative intensity of the antibonding (A) and bonding (B) bands. This effect is due to photoemission matrix elements and has been calculated independently by Lindroos et al. [9]. The photon energies utilized were 22, 24.7, and 47 ev. For all photon energies the experimental energy resolution was kept below 20 mev as determined by the 10 90% width of a gold Fermi edge. For the data of Fig. 1 the in-plane component of the photon polarization was along the (0,0) (p,p) symmetry line. For Figs. 2 and 3 the polarization was along the (0,0) (p,0) direction. 3. Results and discussion Data showing the first determination of normal-state bilayer splitting in overdoped Bi2212 samples [10] is shown in Fig Fig. 1(a) shows a schematic of the commonly accepted Fermi surface (FS) in Bi2212 [12]. Thick yellow lines represent the main FS (M) and the thin yellow lines represent the superstructure FS (SS) produced by the crystal distortion. Panel (b) shows a 2D intensity plot of ARPES spectral weight at hn ¼ 24:7 ev in a 10 mev window centered on E F, as a function of the emission angles u and f from overdoped sample OD85 in the normal state. In such a plot the high-intensity locus determines the FS, modulo matrix element effects. This plot clearly shows two main FS features, labeled A and B. Two branches are also faintly visible in the superstructure FS as well. This behavior is not 1 A simultaneous, independent measurement of bilayer splitting in overdoped Bi2212 was made by Feng et al. Ref. [11]. expected within the generic FS topology shown by a comparison of the ARPES intensity plot and the yellow lines in panel (a). From the intensity plot we can see that the highintensity locus is split into two segments as we move along the FS from the (0,0) (p,p) symmetry line towards (p,0), with one segment matching the expected FS, and another segment closer to the (0,0) (p,0) line. In the bilayer splitting scenario, the electronic states from each of the two CuO planes per unit cell will couple, breaking their degeneracy. One set of states will increase in energy (antibonding) while the other set will decrease (bonding). Within this picture we make the assignment that feature A is the antibonding and feature B the bonding. An essential observation is that the splitting goes to zero along the (0,0) (p,p) symmetry line, as predicted [5,6]. Also, it appears that previous ARPES experiments were mainly sampling the B band, while the A band remained undetected. In the following discussion we will see that this was largely due to the photon energy used and matrix element effects associated with it. In Fig. 2 we present ARPES data showing the bilayer splitting effect for doping levels ranging from heavily overdoped to underdoped [13]. Here we show spectra along the (p,0) (p,p) symmetry line (green bar, Fig. 2(g)), where the geometry is such that we are cutting along the gradient of the E vs. k band dispersion. This allows us to resolve the bilayer splitting directly at (p,0), whereas the geometry of Fig. 1 was better suited to resolving the splitting near the (0,0) (p,p) line. Panel (a) shows the clearest splitting, in data on sample OD55 taken at the photon energy of 22 ev. Again we show a 2D intensity plot, this time of raw ARPES spectral weight as a function of k y (vertical axis) and binding energy (horizontal axis). This geometry beautifully displays the B band dispersion from the bottom of the band at energies as deep as,110 mev all the way up to E F. Meanwhile, the bottom of the A band is exceedingly close to E F (,10 mev). From this we would expect the A band to be much more electronically active than the B band. This observation may prove important to theories which attempt to explain the physics of these compounds in term of a van Hove singularity, for review see Ref. [14]. When we tune the photon energy to 47 ev, panel (b), we see that the intensity ratio of A to B is greatly increased so that the B band is barely visible. This is verified by EDCs and MDCs from the data, shown in panels (h) and (i). At 22 ev (red curves), both EDCs and MDCs show both A and B features. However, at 47 ev the B features are essentially absent. As previously mentioned, this can be wholly accounted for by the photoemission matrix elements [9], which is consistent with the fact that the A band MDC and EDC lineshapes remain relatively unchanged with photon energy. We can use this large matrix element modulation to our advantage in deconvolving the contribution of the A and B bands to the ARPES lineshape in optimal and underdoped samples, where the broadening of individual features is relatively large. Fig. 2(c) (f) show data from samples OP91

3 A.D. Gromko et al. / Journal of Physics and Chemistry of Solids 63 (2002) Fig. 1. ARPES intensity map within ^5 mev of E F from the normal state (T ¼ 100 K) of sample OD85 (panel (b)) at hn ¼ 24:7eV: The intensity plot is also overlaid with the commonly accepted FS from Ding et al. [12] (panel (a)) consisting of hole-like main FS segments (thick yellow) plus superstructure replicas (thin yellow). The white dots are FS crossings determined from MDC derived dispersion. Bands are labeled A ¼ antibonding and B ¼ bonding. and UD78 at photon energies of 22 and 47 ev. Compared to OD55, it is much harder to resolve two independent features in the data. However, it is clear that in going from 47 to 22 ev there is a relative enhancement of the spectral weight at deeper binding energy. That this is again a matrix element effect sampling the A and B bands is proved by the EDCs and MDCs in panels (j) (m). In going from 47 to 22 ev, these curves show a large relative increase in spectral weight at binding energies greater than,100 mev, consistent with the effect seen in OD55. This data is directly relevant for the tissue of FS topology, which has been intensely debated recently. In particular, there has been a discussion about whether the FS exhibits an electron-like character at certain photon energies [15], or whether there is a single unchanging hole-like FS plus superstructure, with no photon-energy dependent effects other than matrix elements [16]. The data here shows that two FS topologies can be seen on any one sample depending on the photon energy used, due to the matrix element modulation of the relative intensity of the bilayer bands. We believe that this should close the debate over whether two FS segments can exist in Bi2212. However, since the linewidth of the antibonding feature is larger than its distance from E F at (p,0), we cannot use the current data to convincingly determine whether the antibonding band is above or below E F. Initial measurements [17] indicate that in addition to the photon energy intensity modulation shown here, the location of the antibonding band appears to change with photon energy. Whether this is an artifact of final-state effects or due to coherent c-axis coupling between unit cells is difficult to determine and requires further study. Having observed bilayer splitting in the raw ARPES data with no fitting or modeling required, we now extract quantitative information on the splitting size using EDC and MDC fitting of the data. Near E F, where the dispersion is steep, we fit each set of MDCs with two Lorentzian peaks and a linear background. Near the bottom of the band, where the dispersion is flat, we fit the EDCs with two Lorentzian peaks and a linear background multiplied by a Fermi cutoff. The overdoped samples lend themselves well to this fitting, as the separation of the A and B bands is large compared to their widths. Optimal and underdoped samples can also be fit with two features, where in fact the data cannot be reliably fit with a single feature. Figs. 3(a) (c) show the MDC (closed circles) and EDC (open circles) centroids for OD55, OP91, and UD78 under identical conditions (47 ev, k x ¼ 1:27p; normal state). The dashed lines are quadratic fits to the centroids of the A and B bands, implying approximately parabolic band dispersion (here we do not address any slight deviations from the parabolic dispersion due for example to self-energy effects). In practice, we found the splitting of the quadratic curves from OD55, and then overlaid these curves with the data for OP91 and UD78 and shifted the curves in energy while holding the splitting fixed. For OP91 the offset was 30 mev, and for UD78 the offset was 40 mev. In doing this we are neglecting any possible doping dependences to the shape of these bands. The reasonable agreement between the data and the chosen fitting routine is more than sufficient for concluding that the shape and size of the splitting (,70 mev) do not drastically decrease as a function of doping. These offsets can be understood as resulting from a rigid-band filling effect in this doping range. Using the theoretically proposed bilayer splitting parameterization DðkÞ, 0:5t ðcosðk x aþ cosðk x aþþ [2], the splitting extrapolates to 114 ^ 8meV at (p,0) or t < 57 ^ 4 mev, obtained from the 47 ev data. Using the same procedure on the 22 ev data we extract a (p,0)

4 2302 A.D. Gromko et al. / Journal of Physics and Chemistry of Solids 63 (2002) Fig. 2. Raw ARPES data along the (0,0) (p,p) symmetry line (panel (g), inset) at photon energies of 22 and 47 ev for samples OD55 (panels (a) and (b)), OP91 (panels (c) and (d)), and UD78 (panels (e) and (f). For each of the three doping levels, we also show EDCs at (p,0) (panels (h,j,l)) and MDCs at E F (panels (l,k,m)). Red and blue curves represent 22 and 47 ev data, respectively. splitting value of t < 54 mev, which is in excellent agreement with the splitting of 55 mev we originally reported in OD85 at the photon energy of 25 ev [13]. Thus we conclude that t has at most a very weak dependence on photon energy, and does not decrease with doping. Although our experiment only directly addresses the doping dependence of the intracell c-axis coupling strengths, an extrapolation of this data makes a severe doping dependence of the intercell c-axis coupling constant appear unlikely. This is surprising in conjunction with the c-axis normal state resistivity r c, which goes from metallic behavior in the overdoped regime to insulating behavior in the underdoped regime [2]. Such data has been widely taken to indicate 2D confinement in the underdoped samples, which would be consistent with exotic behaviors such as marginal Fermi liquid theory [18] and spin charge separation [19]. In light of the strong intracell t persisting to the underdoped regime observed here, we suggest that these data instead reflect a lack of coherent coupling between unit cells, which is consistent with the ARPES measurements. It is possible that a factor other than 2D confinement may explain the anomalous transport behavior, such as the onset of the pseudogap or an increased scattering rate near (p,0) due to electronic inhomogeneity [20]. Having explored the bilayer splitting effect as a function of doping and photon energy in the normal state, the question remaining is the effect of superconductivity on t. Fig. 3(d) and (f) show data from OD55 taken in the normal (T ¼ 80 K) and superconducting (T ¼ 30 K) states under identical conditions (22 ev, k x ¼ 1.0p). Here we show a reduced energy range of 300 mev to accentuate the bilayer splitting. In the normal state, we see both A and B bands extend to E F, as evidenced from the EDCs shown in panel (e). From the stack of EDCs we see that the leading edges of both A and B bands clearly reach E F, indicating an FS crossing. Upon cooling to the superconducting state, a gap clearly opens in both the A and B bands, so that the EDC peaks shown in panel (g) only reach a binding energy D ¼ 18 mev. This is a further indication that the A and B bands are intrinsic to Bi2212, not to mention indicating their relevance to superconductivity. Focusing

5 A.D. Gromko et al. / Journal of Physics and Chemistry of Solids 63 (2002) Fig. 3. Quadratic fitting results to the MDC and EDC derived dispersions of the A and B bands at 47 ev and k x ¼ 1:27p for samples OD55 (panel (a)), OP91 (panel (b)), and UD78 (panel (c)). We also show normal (panel (d)) and superconducting state (panel (f)) intensity plots at 22 ev and k x ¼ 1:0p for sample OD55. The data is also presented as EDC stacks (panels (e) and (g)). on the bonding band, for binding energies near E ¼ D the spectra are clearly changed in going to the superconducting state. However, for deeper binding energies the changes appear minimal, with the bonding band bottom relatively unchanged (, 100 mev), indicating that t is unchanged by the onset of superconductivity. 2 The observation of bilayer splitting with a constant t has important implications for the famous peak dip hump (PDH) structure [21], which has been found to occur in the superconducting state ARPES spectrum and has been interpreted in terms of coupling to the (p,p) neutron resonance mode [22] and in terms of a condensate fraction [23]. The PDH structure was reported to develop out of a single, broad normal state feature, which upon cooling to the superconducting state would exhibit a sharper low-energy feature separated from the hump at higher binding energies by a spectral dip. Bilayer splitting provides a very natural explanation for this PDH structure, wherein the peak and hump are the A and B bands, and the strength of the dip is proportional to the clarity of the two features. From Fig. 2(j) and (l) which were taken with improved resolution and sample quality, it is not surprising that previous studies of 2 This conflicts with the results of Feng et al. Ref. [11]. optimal and underdoped samples missed the bilayer PDH in the normal state. New high-resolution data shows that the sharpening of the bilayer features in the superconducting state for all doping levels is consistent with previous PDH observations and is a strong evidence that the PDH is due solely to bilayer splitting [24]. In conclusion, we have investigated bilayer splitting in Bi 2 Sr 2 CaCu 2 O 8þd across the doping phase diagram, where we have taken advantage of photon-energy dependent matrix element effects to observe the splitting as doping is reduced and the antibonding and bonding features are broadened. We measure an intracell coupling t, 55 mev which is surprisingly robust as a function of doping level, indicating that confinement to a single CuO 2 plane does not increase in the underdoped regime. In the superconducting state both the bonding and antibonding bands are gapped by an energy D without any indications of a change in intercell coupling. Acknowledgments We acknowledge sample preparation help from J. Koralek and M. Varney and beamline support from X.J.

6 2304 A.D. Gromko et al. / Journal of Physics and Chemistry of Solids 63 (2002) Zhou, P. Bogdanov, Z. Hussain, D.H. Liu, and H. Hochst. We gratefully acknowledge the help of R. Goldfarb at NIST for the use of the SQUID magnetometer. This work was supported by the NSF Career-DMR and the DOE DE-FG03-00ER ALS and SSRL are operated by the DOE, Office of Basic Energy Sciences, and the SRC is supported by the NSF. References [1] J.M. Tarascon, et al., Phys. Rev. B 38 (1992) [2] T. Watanabe, T. Fujii, A. Matshda, Phys. Rev. Lett. 79 (1997) [3] C.E. Gough, et al., cond-mat/ [4] A.V. Puchkov, et al., Phys. Rev. Lett. 77 (1996) [5] S. Chakravarty, et al., Science 261 (1993) 337. [6] O.K. Anderson, et al., J. Phys. Chem. Solids 56 (1995) [7] B. Battlog, C. Varma, Phys. World February (33) (2000) 45. [8] Y.-D. Chuang, et al., Science 292 (2001) [9] M. Lindroos, S. Sahrakorpi, A. Bansil, cond-mat/ [10] Y.-D. Chuang, et al., Phys. Rev. Lett. 87 (2001) [11] D. Feng, et al., Phys. Rev. Lett. 86 (2001) [12] H. Ding, et al., Phys. Rev. Lett. 76 (1996) [13] Y.-D. Chuang, et al., cond-mat/ [14] R.S. Markiewicz, J. Phys. Chem. Solids 58 (1997) [15] Y.-D. Chuang, et al., Phys. Rev. Lett. 83 (1999) [16] S.V. Borisenko, et al., Phys. Rev. Lett. 84 (2000) [17] A. Gromko, et al., unpublished data. [18] C.M. Varma, et al., Phys. Rev. Lett. 63 (1989) [19] P.W. Anderson (Eds.), The Theory of Superconductivity in the High-T c Cuprates, Princeton Series in Physics, Princeton University Press, NJ, [20] S.H. Pan, et al., Nature 413 (2001) 282. [21] D.S. Dessau, et al., Phys. Rev. Lett. 66 (1991) [22] J.C. Campuzano, et al., Phys. Rev. Lett. 83 (1999) [23] D.L. Feng, et al., Science 289 (2000) 277. [24] A.D. Gromko, et al., in preparation.