Bulk electronic structures and strong electron–phonon interactions in an electron-doped high-temperature superconductor

M Tsunekawa^1,4,5, A Sekiyama¹, S Kasai¹, S Imada¹, H Fujiwara¹, T Muro², Y Onose³, Y Tokura³ and S Suga¹

¹ Department of Materials Physics, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
² Japan Synchrotron Radiation Research Institute, Hyogo 679-5198, Japan
³ Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan

⁴ Present address: Research Center for Materials Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan.

⁵ Author to whom any correspondence should be addressed.

E-mail: tsunekawa.masanori@d.mbox.nagoya-u.ac.jp

Received 4 October 2007
Published 1 July 2008

Contents

• 1. Introduction
• 2. Experimental
• 3. Surface and bulk electronic structures probed by soft x-ray PES for quasi-two-dimensional
• 4. Strong electron-phonon contribution to the quasiparticle dispersion: nodal `kink' and suppressed antinodal `kink' behavior
• 5. FS mapping by high-hν ARPES
• 6. Conclusions
• Acknowledgments
• References

1. Introduction

It is generally accepted that collective excitations play essential roles in the superconducting state of the high-temperature superconducting cuprates (HTSCs). Low-hν (photon energy) angle-resolved photoemission spectroscopy (ARPES) studies [1] have elucidated the anisotropic `kink' feature (abrupt change of the electron velocity) in the quasiparticle dispersions (QD) for the HTSCs. Since the `kink' will be observed at binding energies corresponding to the collective mode, its observation is regarded as evidence for the strong coupling of the electron with a collective mode. For the hole-doped HTSCs, the `kink' behavior along the nodal [(0, 0)- (π, π)] direction is interpreted as indicating strong coupling with longitudinal optical phonons, because it is observed even for La<sub>2–x</sub>Sr<sub>x</sub>CuO<sub>4</sub> where the magnetic mode does not exist [2]–[4]. For the electron-doped HTSCs, on the other hand, no `kink' behavior is observed along the nodal direction while the finite `kink' or the antiferromagnetic `pseudo-gap' behavior is seen along the antinodal [(π, 0)-(π, π)] and off-nodal directions by low-hν ARPES [5]–[9]. For both the hole- and electron-doped HTSCs, it is considered that the `kink' behavior along the antinodal and off-nodal directions is depicted by the magnetic excitation mode because the electrons near (π, 0) are easily coupled to the magnetic mode with a Q vector of (π, π) [7, 10, 11].

So far, low-hν ARPES results reported for Nd_2–xCe_xCuO₄ (NCCO) have shown the suppression of the spectral weight around (~0.7π and ~0.3π) and (~0.3π and ~0.7π) (`hot spots' [11]–[13]), which are located at the intersections between the Fermi surface (FS) and the antiferromagnetic Brillouin zone (AFBZ) boundary. Such suppression has been believed to correspond to the pseudogap in the optical conductivity, which is estimated as ~200 meV, and to the peak of the two-magnon Raman scattering [14]. It has been considered that the pseudogap in the optical conductivity in the underdoped region, which becomes smeared out for x = 0.15, is related to the evolution of the antiferromagnetic spin correlation [14]. The suppression of the spectral weight at the `hot spots', however, is confirmed not only in underdoped antiferromagnetic NCCO, but also in optimally doped superconducting Nd_1.85Ce_0.15CuO₄ in the low-hν ARPES reported so far [11]. Meanwhile, there are several reports claiming strong electron–phonon interactions in the electron-doped HTSCs leading to the `kink' in the scattering rate derived from the optical reflectance [14], the softening of a mode in the inelastic x-ray scattering [15] and so on. However, there is thought to be no direct evidence for the strong electron–phonon interactions in the electron-doped HTSCs contributing to the superconductivity [16]. In hole-doped HTSCs, on the other hand, the isotope effect [17] and the anisotropic `kink' along the nodal direction in QD [2, 3] are often thought to be directly reflecting the contribution of the electron–phonon interactions to their superconductivity.

Photoemission spectroscopy (PES) is very powerful to directly probe electronic structures of solids. However, the high surface-sensitivity of low-hν PES has often prevented one from probing genuine bulk electronic structures [18]–[20]. For quasi-two-dimensional electron systems such as HTSCs, it has long been thought that the electronic structures of the top (or surface) conducting layer are equivalent to those of the bulk layers, which are responsible for the superconductivity. High-hν core-level PES studies [21]–[26], however, recently suggested that the electronic structures of the bulk CuO₂ layers, in particular for optimally doped Nd_1.85Ce_0.15CuO₄, are noticeably different from those of the surface CuO₂ layer, which are mainly detected by low-hν ARPES [6, 8, 22]. High-hν ARPES [23, 24] is therefore essential for directly revealing the bulk QD.

In this paper, we demonstrate by means of bulk-sensitive high-hν ARPES that the electron–phonon interactions are strong enough along the nodal direction in the bulk of optimally electron-doped Nd_1.85Ce_0.15CuO₄ , even though the electron–phonon coupling is suppressed in the underdoped region. Our results imply that the effect of anisotropic electron–phonon interactions is `universal' in the HTSCs.

2. Experimental

High-hν ARPES and angle-integrated PES of single crystals of Nd_2–xCe_xCuO₄ (x = 0.075 and 0.15) [27] were performed at SPring-8 BL25SU [28] by using a GAMMADATA-SCIENTA SES-200 electron energy analyzer. The energy resolution was set to either 200 (for the FS mapping as later shown in figure 4) or 100 meV (for the ARPES along the high-symmetry lines as shown in figures 2 and 3). The momentum resolution parallel (perpendicular) to the analyzer slit was set to ±0.02(±0.03) Å^–1. The emission angle for ARPES was approximately set to normal to the sample surface. The energy resolution for the angle-integrated Cu 2p core-level PES was set to be better than ~350 meV. Clean surfaces were obtained by cleaving the sample in situ at the measuring temperature of 20 K. The base pressure was 3.0×10^–8 Pa.

3. Surface and bulk electronic structures probed by soft x-ray PES for quasi-two-dimensional

It has been widely believed that the electronic structures are similar in the bulk and at the surface in the case of quasi-two-dimensional systems, for instance, HTSCs. Recently, hard x-ray PES has, however, revealed a noticeable difference of the electronic structures between the bulk and the surface [29]. Soft x-ray PES is useful enough to estimate both the contributions of the topmost and the bulk layers in PES spectra [23] by changing the emission angle θ from the normal, resulting in a change of the probing depth. We have performed Cu 2p core-level PES in order to confirm that the electronic structures derived from the surface's topmost layer are remarkably different from those in the bulk even for quasi-two-dimensional Nd_1.85Ce_0.15CuO₄.

The inelastic mean free path of photoelectrons (IMFPP) is typically estimated as ~5 and 11–15 Å at the kinetic energies of photoelectrons (E_k) of 55 and 400–700 eV, respectively [30]. Figure 1(a) shows the angle-integrated PES spectra of the Cu 2p core-level for different detection polar-angles (θ) of the emitted photoelectrons with E_k~ 530–570 eV at hν = 1504 eV, where the acceptance angle is about ±5°. The surface sensitivity of the PES spectra increases with θ. In addition to a broad peak centered at 933 eV, a shoulder structure is observed at 931–932 eV in figure 1(a). The relative intensity of the shoulder structure to the broad peak is clearly reduced with increasing θ, namely with increasing surface sensitivity. The spectral weight of the `Bulk' component in the PES spectra can then be estimated as

where s = 6.035 Å and λ(E_k~570 eV) = 14.5 Å are the thickness of the `Surface' as assumed in figure 1(c) (the distance between the Nd(Ce)-O layers) and the IMFPP [30] at the kinetic energy E<sub>k</sub>. We have deconvoluted the Cu 2p core-level spectra for the polar angles θ = 0° and 60° into the `Bulk' and `Surface' components as in figure 1(b). The intensity ratio of the `Bulk':`Surface' is derived from equation (1) as 66:34 at θ = 0° and 44:56 at θ = 60°. The Cu 2p core-level spectrum at θ = 34° is well reproduced by the weighted sum of the `Bulk' and `Surface' spectra in figure 1(b) with the predicted intensity ratio of `Bulk' and `Surface'  = 61 : 39 at this θ in figure 1(d). It is obvious that the spectral feature in the `Bulk' is drastically different from that at the `Surface'. The structure at 931–932 eV in figure 1(b) corresponds to the feature induced by the non-local screening effect reported by hard x-ray PES [21] for the core–hole excitation. Thus, the `Bulk' components are confirmed to be dominant in our high-hν near-normal emission PES spectra with a kinetic energy of around 500 eV.

4. Strong electron–phonon contribution to the quasiparticle dispersion: nodal `kink' and suppressed antinodal `kink' behavior

The high-hν ARPES-intensity plots along the antinodal and nodal directions at hν = 500 eV are displayed in figures 2(a) and (c), respectively. The anisotropy of the `kink' behavior revealed by the high-hν ARPES is in striking contrast to that reported by low-hν ARPES [5]. No clear `kink' is observed in our high-hν ARPES for Nd_1.85Ce_0.15CuO₄ along the antinodal direction as shown in figures 2(a) and (b), although an antinodal `kink' was suggested by the low-hν ARPES for NCCO [5]. It has recently been suggested that the antinodal `kink' behavior is related to the antiferromagnetic `pseudo-gap' at the `hot spots' for NCCO [6]. Stronger antiferromagnetic `pseudo-gap' and `hot spot' effects are reported in the other electron-doped HTSC, Sm_1.86Ce_0.14CuO₄ [9]. It is found that the quasiparticle effective mass near the Fermi level (E_F) is most strongly enhanced in the close vicinity of the `hot spot' due to the opening of the antiferromagnetic `pseudo-gap' for those electron-doped HTSCs. Such an enhancement of the quasiparticle effective mass near E_F is gradually suppressed due to their movement away from the `hot spot' toward (π, 0) [6]. Neither the antiferromagnetic `pseudo-gap' behavior nor the near-E_F quasiparticle mass enhancement are clearly seen along the antinodal direction by our high-hν ARPES in figures 2(a) and (b), which implies that both effects are weak in the bulk. Nevertheless, from the experimental point of view, it remains slightly unclear at present whether both the effects are really negligible along the antinodal direction in the bulk. The suppression of the spectral weight at the `hot spots' is described in chapter 5.

On the other hand, the striking nodal `kink' is observed by high-hν ARPES, here in the QD at 50–80 meV and 0.46–0.49 Å<sup>–1</sup> (figure 2(d)), although no clear `kink' at 50–80 meV has been detected by low-hν ARPES. Insets of figures 2(b) and (d) show the energy dependence of the real part of the self-energy derived from the QD at hν = 500 eV. Although no significant feature is observed in the inset of figure 2(b) along the antinodal direction, a clear feature is observed in the inset of figure 2(d) near the nodal `kink'. This energy for electron-doped Nd<sub>1.85</sub>Ce<sub>0.15</sub>CuO<sub>4</sub> (50–80 meV) is close to those of the kinks reported for several families of hole-doped HTSCs. The nodal `kink' in figures 2(c) and (d) for the electron-doped Nd_1.85Ce_0.15CuO₄ is similar to those [2, 3, 16] observed for the hole-doped HTSCs with respect to both k-direction and energy scale. The nodal `kink' feature was also observed in the high-hν ARPES spectra at different hν( = 460 eV) as shown in figures 2(e) and (f) beyond the statistic fluctuation as recognized in the inset of figure 2(f). Therefore, the nodal `kink' observed here for high-energy excitations is neither due to any possible extrinsic effect nor due to matrix element effects, but due to an intrinsic effect, being a characteristic of bulk Nd_1.85Ce_0.15CuO₄. The presence (absence) of the nodal (antinodal) `kink' in QD observed by the present high-hν ARPES is much different from the results of low-hν ARPES so far reported for NCCO [5, 6].

First, the electron–phonon coupling is considered as an origin of the `kink' behavior, while other scenarios are also proposed for the `kink' behavior. The electron–phonon coupling constant λ ' estimated from the low-hν ARPES results for optimally doped NCCO is definitely smaller than that for the hole-doped HTSC families, suggesting that the superconducting mechanism for the HTSCs depends on the type of the doped carriers [16]. However, the bulk λ ' is estimated here as ~ 1.2–1.6 for Nd_1.85Ce_0.15CuO₄ in a way similar to that in [2] by assuming a bare band shown in figure 2(d). This value is comparable to λ ' for the hole-doped HTSCs with a similar carrier concentration [2]. Our results have thus revealed that the electron–phonon coupling intensity for the electron-doped Nd_1.85Ce_0.15CuO₄ is not smaller than those in the hole-doped HTSCs [2] in the superconducting phase, implying that the existence of the anisotropic nodal `kink' behavior is inherent in the HTSCs irrespective of the type of doped carriers.

There have been several reports supporting a strong electron–phonon contribution to the superconductivity in the electron-doped HTSCs in the following respects. (i) The `kink' in the scattering rate derived from optical reflectance lies in a similar energy region to our `kink' and is assigned to electron–phonon coupling [14]. (ii) The inelastic x-ray scattering reported by d'Astuto et al  [15] suggests that the softening of a mode at ~55–75 meV is ascribable to the oxygen half-breathing mode as reported for the hole-doped HTSCs. (iii) The neutron scattering reported by Kang et al has revealed changes with doping in the generalized phonon density of structures around 70 meV [31]. (iv) While the nodal `kink' energy of 50–80 meV estimated from our high-hν ARPES is much smaller than the energy of ~200 meV for the pseudogap in the optical conductivity [14] associated with the antiferromagnetic spin correlation model, it corresponds well to the characteristic energy of the electron–phonon interactions. Therefore, the antiferromagnetic spin correlation [14] cannot be the leading candidate for the origin of the nodal `kink' behavior here. The nodal `kink' reported here is consistently understandable with the other bulk-sensitive results mentioned above [14, 15, 31]. It is possible that the surface electronic structures deviated much from the bulk could induce the stability of the antiferromagnetism in the surface region even for optimally doped NCCO. Then, the electron–phonon interactions would be masked at the surface. There can be another possible scenario [32] as the s and d wave superconductivity coexists in HTSCs, whereas the contribution from the s wave superconductivity is suppressed at the surface. The superconductivity gap symmetry in the bulk cannot be resolved, however, in the present high-hν ARPES due to the limited energy resolution.

We discuss now the competition between the electron–phonon coupling and the spin correlation along the nodal direction in both superconducting and antiferromagnetic phases. The energy distribution curves (EDCs) for x = 0.075 and 0.15 are integrated around the Fermi wave vector (k_F) and (0, 0) (4.1% of the half of the Brillouin zone (BZ) along the nodal direction) at hν = 500 eV in figure 3(a). The EDCs near (0, 0) are shown as reference for discussing the intrinsic spectral shape near the k_F point beyond the background spectral shape. The spectral weight around k_F is drastically suppressed for x = 0.075 compared with that for x = 0.15. In the difference spectra between the near-k_F and near-(0, 0) spectra in figure 3(b), the intensity for x = 0.075 decreases monotonically from 200 meV toward E_F, consistently with the pseudogap in the optical conductivity for 0 ≤x≤0.125. Such a pseudogap behavior is not seen for x = 0.15 in figure 3(b). These results have revealed that the electron–phonon coupling overwhelms the antiferromagnetic spin correlation in the superconducting bulk NCCO with x = 0.15 along the nodal direction. Our result for x = 0.075 suggests, on the other hand, that the antiferromagnetic spin correlation is certainly playing important roles in the antiferromaginetic phase in the underdoped region. The behavior of the quasiparticle spectral weight revealed here near E_F along the nodal direction (even though broadened by the instrumental resolution) is similar to the doping dependence of the pseudogap in the optical conductivity for 0≤x≤0.15. This scenario is consistent with the report that both the pseudogap in the optical conductivity and the two-magnon peak in the Raman scattering spectra are not discerned for x = 0.15 in the superconducting phase, but are seen for x≤0.125 in the antiferromagnetic phase [14].

5. FS mapping by high-hν ARPES

The near-E_F ARPES-intensity plot for x = 0.15 at hν = 500 eV is shown in figure 4(a) indicating a hole-like FS centered at (π, π). The k_Fs estimated from the EDCs and momentum distribution curves (MDCs) are shown in figure 4(b) by black full circles with error bars. Since the k_z dependence of the FS topology was recently found for Ca-doped Sr₂RuO₄ [33], a typical layered compound, the measurement of Nd_1.85Ce_0.15CuO₄ was additionally performed at hν = 460 eV with different k_z. The results are shown in figures 4(c) and (d). In figures 4(b) and (d), the FS topology fitted to the hν = 55 eV ARPES are added [34]. It is found that the shape of the FS resolved at hν = 500 and 460 eV is not as different as theoretically suggested [34]. Although its shape is rather circular, noticeable deviation from the FS at hν = 55 eV is recognized near the antinodal direction [13, 34]. Namely, k_F is closer to the (–π, 0)-(π, 0) and (0, –π)-(0, π) axes in the high-hν ARPES, when the center of gravity of the k_F distribution is taken into account. For further discussions, however, higher resolutions with respect to the energy and wave number are required. Still it is very clear that the FS shape is much different from the square-like FS shape along the AFBZ boundary reported by Claesson et al  [35] at hν = 400 eV after symmetrization. The results in figures 4(a)–(d) are raw data measured over the full BZ without any symmetrization procedure. In figures 4(c) and (d), the spectral weight is not fully suppressed in the k region corresponding to the `hot spots' in the lower part of the BZ, implying that the suppressed spectral weight on the `hot spots' could be due to matrix element effects and/or the difference in k_z.

6. Conclusions

We have carried out soft x-ray ARPES for the electron-doped HTSCs Nd_2–xCe_xCuO₄ (x = 0.075 and 0.15) at hν = 500 eV. Our high-hν bulk-sensitive ARPES results have revealed a bulk-originated nodal `kink' derived from the electron–phonon coupling in electron-doped Nd<sub>1.85</sub>Ce<sub>0.15</sub>CuO<sub>4</sub>. This result confirms that the electron–phonon interactions prevail in the bulk but are suppressed at the surface in electron-doped superconducting Nd<sub>1.85</sub>Ce<sub>0.15</sub>CuO<sub>4</sub>. The nodal `kink' behavior is equivalent to that observed in hole-doped HTSCs. The doping dependence of the spectral weight near E_F in the nodal EDCs suggests that the electron–phonon interactions overwhelm the spin correlation in the superconducting bulk Nd_1.85Ce_0.15CuO₄, even though the spin correlation is certainly playing some important roles in the antiferromagnetic phase in the underdoped region. The electron–hole symmetry in the HTSCs is confirmed with respect to the nodal `kink' behavior due to the electron–phonon coupling.

Acknowledgments

We are grateful to M Sing for his enlightening discussions. We thank Y Ishida, T Hamasaki, and the staff of SPring-8, especially Y Saitoh and T Matsushita for supporting the experiments. This work was supported by the Grant-in-Aid for Creative Scientific Research (15G213), COE Research and a Grant-in-Aid for 21st century COE `Core Research and Advanced Education Center for Materials Science and Nano Engineering' (G18) and a Grant-in-Aid for the Scientific Research (18104007, 18684015 and 18860048) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. The experiments were performed under the approval of SPring-8 (2002B3009, 2003A4009, 2003B5009 and 2004A6009).

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