One of the most important issues related to the mechanism of superconductivity in HTSCs is the role of electron-phonon (el-ph) interaction in this mechanism for such a strongly correlated electron systems. A group of scientists from the US and Japan have revealed a strong experimental evidence for existence of the strong electron-phonon interaction in these systems, however its role in the mechanism of superconductivity has not been cleared yet. They have measured ARPES spectra of different HTSCs families LSCO, Pb-Bi2212 (Pb doped) and Pb-Bi2201 in the nodal direction (0,0)-(π,π) in a vide range of temperature and doping concentration.
Experimental results:
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There is a clear kink in the electronic dispersion curves around 50-80 meV (Fig. 1) for all the samples in different values of doping and temperature (below and above Tc). This kink clearly persists above Tc but a thermal broadening is present.
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The energy dispersive curves (EDC) of Bi2212 in the nodal direction and for different doping are in good agreement with the corresponding data for Be (0001) surface which has strong el-ph interaction, and simulated spectra (Fig. 2).
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There is also a dip feature in all the spectra in Fig. 2 near 55-70 meV. Fig. 3b sows the doping dependence of this dip energy in the (0,π) direction.
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The quasiparticle width decrease more rapidly below the relevant energy (Fig. 3a), which corresponds to the kink position in the dispersion.
Discussion:
The change of electron self-energy below ~70 meV (i.e. kink) indicates electrons have an interaction with a collective boson mode with this energy. The similar energy scales in systems with different energy gap ranging from 10-20 meV for LSCO and Bi2201, to 30-50 meV for Bi-2212, rules out the superconducting gap as the origin. Also coupling with the magnetic mode at 41 meV can be ruled out, because the kink has been observed in LSCO where the magnetic mode dose not exist and also well above Tc in all samples, while the magnetic mode sets at Tc for optimal and overdoped systems.
These experimental evidences leave the phonon as the only possible candidates, although there are also some reasons that this kink could be originated from el-ph interaction: 1) there is bond stretching phonon mode with energy ~50-80 meV (highest energy phonon mode) in nearly all HTSCs, 2) neutron scattering of LSCO indicates strong coupling of this phonon mode to charge, 3) the kink persist in all temperature but thermally broaden in higher temperature, 4) the EDC curves are very similar to Be (0001) surface which has strong el-ph with a dip energy which could be related to phonon energy, 5) the rapidly decreasing of quasiparticle width below phonon energy is also in consistent with el-ph coupled systems.
By estimating el-ph coupling strength (λ) by simple model (the ratio of the velocities below and above the kink in Fig. 1 ~ λ+1) the doping (Fig. 1f) and momentum (Fig. 4a) dependence of λ’ can be determined. λ’ is different but proportional to λ, and is an overestimate for λ because there is also strong el-el interaction in these systems. Fig. 4a shows that λ’ is not very anisotropic (change by a factor of <2) and not temperature dependence, both in consistent with phonon interpretation of the data.
The authors have addressed that the magnetic mode (41 meV) explanation of the kink and dip in EDC not only are inconsistent with the data presented here, but also has some serious weakness such as: 1) the small percent of this mode in the total spectral spin fluctuation weight is not enough to produce large changes in EDC above and below Tc, 2) calculations show strong anisotropy for λ’ near (0,π) which is inconsistent with these data (inset of Fig. 4a). A problem with considering strong el-ph in HTSCs is that there are not clear resistivity dropping or saturation near phonon frequency Ω and T≈(0.3-0.5)Ω, respectively.
In Summary, this study indicates existence of strong el-ph interaction in HTSCs and suggests including it in any microscopic theory of superconductivity.
Ref.: A. Lanzara, P. V. Bogdanov, X. J. Zhou, S. A. Kellar, D. L. Feng, E. D. Lu, T. Yoshida, H. Eisaki, A. Fujimori, K. Kishio, J.-I. Shimoyama, T. Nodak, S. Uchidak, Z. Hussain & Z.-X. Shen, Nature 412 (2001) 510.
