A ug 1 99 8 C-axis Electronic Raman Scattering in Bi 2 Sr 2 CaCu 2 O

We report a c-axis-polarized electronic Raman scattering study of Bi2Sr2CaCu2O8+δ single crystals. In the normal state, a resonant electronic continuum extends to 1.5 eV and gains significant intensity as the incoming photon energy increases. In the superconducting state, a coherence 2∆ peak appears around 50 meV, with a suppression of the scattering intensity at frequencies below the peak position. The peak energy, which is higher than that seen with in-plane polarizations, signifies distinctly different dynamics of quasiparticle excitations created with out-of-plane polarization. PACS numbers: 74.72.Hs, 78.20.-e, 78.30.-j Typeset using REVTEX 1 One of the peculiar aspects of the high-Tc cuprates is the incoherent nature of the charge transport perpendicular to the CuO2 planes [1]. Early on it was established experimentally that the normal-state in-plane resistivity typically varies linearly with temperature, whereas the out-of-plane resistivity almost universally displays semiconducting behavior [2]. The c-axis optical conductivity of the most cuprates [3,4] shows an electronic background with a very large scattering rate – that is the mean free path appears to be less than the lattice spacing. These results suggest that there is no coherent electronic transport in the c-direction: all motions are inelastic. A number of models have been proposed to explain the important mechanisms contributing to c-axis transport in high-Tc superconductors, including localization along the c-axis [5], carrier confinement in the resonating valence bond (RVB) theory [6], and interlayer tunneling (ILT) or hopping [7,8]. However, there is currently no consensus as to the clear picture of the origin of incoherent c-axis transport. Among all cuprate superconductors, the double-layered Bi2Sr2CaCu2O8+δ (Bi-2212) crystal is the most decoupled material. In Bi-2212, the ratio of the out-of-plane to in-plane resistivity ρc/ρab can be as high as 10 5 [9]. Optical response shows that the c-axis reflectivity of Bi-2212 is highly insulating, while the in-plane reflectivity is metallic [3]. The corresponding plasma frequency anisotropy in Bi-2212, ωpab/ωpc > 100, is substantially larger than that observed in other cuprates. These data provide evidence that the c-axis transport of Bi-2212 is incoherent, with the extremely small energy scale set by the hopping interaction between the adjacent CuO2 bilayers. In the superconducting state, the two-dimensional character of Bi-2212 also manifests itself strongly in the penetration depth measurements. The c-axis penetration depth is extremely large (λc ≈ 100 μm) [10]. The large anisotropy between λab and λc of Bi-2212 was shown to be best described within a picture of strongly superconducting CuO2 layers weakly coupled by Josephson interaction along the c-axis [11]. The purpose of this study is to investigate, in the context of electronic Raman scattering spectroscopy, the role of c-axis polarizability in the Bi-2212 cuprates. Raman scattering has been proved to be a valuable technique for understanding the quasiparticle dynamics on different regions of the Fermi surface in the cuprate systems by orienting incoming and 2 outgoing photon polarizations [12]. The electronic Raman spectra polarized in the ab-plane of Bi-2212 have been extensively studied [13]. In contrast, Raman data on the electronic scattering of Bi-2212 for photons polarized along the c-axis are rare [14]. Our new results show that the electronic continuum in zz-polarization does exist and is not small. Notably, this continuum intensity resonates towards near ultraviolet (UV) photon excitation. Below Tc, there is a measurable superconductivity-induced redistribution of the zz-polarized continuum and the presence of a 2∆ peak-like feature, similar to those observed in the ab-plane Raman response. Single crystals of Bi-2212 were grown near-stoichiometric using a solvent-free Floating Zone process in a double-mirror image furnace modified for very slow growth. In this letter, we used an as-grown, un-annealed single crystal of dimensions 5×1×0.5 mm with a superconducting transition onset at 87 K (dc magnetization) and onset-to-saturation midpoint at 85 K. The Raman measurements were performed on two faces of the crystal. One face (labeled I in Fig. 1) contains both the c-axis and either the aor bdirection. The second face, face II, provided the aand b-axis response. We have also studied another sample (Tc = 93 K, ∆Tc = 1.5 K) with less surface quality of face I and obtained similar results. Throughout this study, x and y are indexed along the Bi-O bonds, rotated by 45 with respect to the Cu-O bonds. All symmetries refer to a tetragonal D4h point group. The low-frequency Raman spectra were taken in pseudobackscattering geometry with h̄ωi = 1.92 eV photons from a Kr + laser. The laser excitation of less than 10 W/cm was focused into a 50 μm diameter spot on the sample surface. The temperatures referred to in this paper are the nominal temperatures inside the cryostat. The spectra were analyzed by a triple grating spectrometer with a liquid-nitrogen cooled charge-coupled device detector. To investigate further the resonance property, we have used several excitation lines from Ar and Kr lasers ranging from visible red to near UV. All the Raman spectra were corrected for the spectral response of the spectrometer and detector, the optical absorption of the sample as well as the refraction at the sample-gas interface [15]. The imaginary parts of the c-axis-polarized Raman response functions, obtained by di3 viding the original spectra by the Bose-Einstein thermal factor, are shown in Fig. 1 for two different temperatures, 100 K (T > Tc) and 5 K (T ≪ Tc). In the normal state, the most prominent features of the spectra are the electronic continuum and several q ≈ 0 Raman allowed phonon modes, whose overall character is in good agreement with that reported previously [16–18]. We focus on the temperature behavior of the electronic Raman scattering response. Well below Tc, it can seen in Fig. 1 that for the zz continuum there is a loss of scattering strength at low frequencies which redistributes into the weak and broad peak at higher frequencies. Above 700 cm, the 5 K and 100 K spectra appear to be essentially identical. These data were reproducibly observed at three different spots on the sample. We emphasize that the redistribution of the scattering intensity itself is not of phononic origin. The low energy (red) excitation is used primarily to reduce the intensity of phononic scattering. Furthermore, a similar feature has been reported for other less anisotropic members of the high-Tc superconductors, including YBa2Cu3O7−δ (YBCO) [19] and NdBa2Cu3O7−δ [20]. In order to observe the superconductivity-induced redistribution of the electronic continuum better, in the inset of Fig. 1 we present the change between the normal and superconducting spectra in an enhanced manner, where the 5 K spectrum is normalized by (1) dividing by the 100 K spectrum (top curve), (2) subtracting the 100 K spectrum (middle curve), and (3) the difference of Raman spectra, as in (2), after first subtracting the phonon contributions (bottom curve). We believe that sharp features in difference spectra are due to temperature dependence of phononic scatterings. It is nevertheless clear that in all cases below Tc a broad peak forms in the electronic continuum which is accompanied by reduced scattering at the lowest Raman shift. The difference vanishes at sufficiently high frequencies. It is instructive to compare the c-axis electronic continuum with results for other scattering configurations, which are shown in Fig. 2. As can be seen in the Fig. 2(a), a depolarized zx spectrum has an even smaller continuum intensity compared with that from the zz component. Furthermore, the normal and superconducting spectra are indistinguishable. In contrast, the superconducting transition leads to the redistribution of the continuum into 4 a broad peak in xx polarization (Fig. 2(b)). It is interesting to note that the out-of-plane and in-plane xx spectra (Fig. 2(c)) look almost identical. We have also found that there is an x-y anisotropy clearly demonstrated by the phonon modes between in-plane xx and yy (Fig. 2(f)) polarizations [17]. Referring to the Fig. 2(e), the B1g contribution is predominant in xy geometry, and gives an electronic continuum that is much stronger than that in any other polarization. Below Tc, the strong suppression of the continuum is observed, and the low-frequency intensity varies roughly as ω, while it is quite linear in xy (Fig. 2(d)) polarization (B2g + A2g symmetry). At the same time, the magnitude of superconductivityinduced peak is much less intense in B2g + A2g symmetry than that found in B1g symmetry. Such ω dependences in both scattering geometries are consistent with an order parameter of d-wave symmetry [d(x − y) when referred to Cu-O bonds] [21]. The results presented in Figs. 1 and 2 clearly show that the intensity of the c-polarized continuum is not negligible compared with that of the in-plane symmetries. We regard these observations as truly extraordinary, for c-axis transport is incoherent. To examine what microscopic origins might produce the zz continuum in Bi-2212, we first discuss our data in terms of the conventional model of light scattering from a superconductor [21,22]. In this model, the strength of the electronic Raman scattering is proportional to the square of the Raman vertex. For nonresonant excitation, the Raman vertex at a point k in reciprocal space is given approximately by the inverse effective mass (the curvature of the energy band dispersion), γij ∝ 1 m ij ∝ ∂ǫ(k) ∂ki∂kj . In Bi-2212, both transport [3,9] and band structure calculations [23] reflect the fact that the c-axis effective mass is in general very heavy. Consequently, the c-axis nonresonant Raman scattering should be truly small. We see, instead, an ordinary size for