The isotope effect (IE) on Tc of optimally doped HTSCs (α=dlnTc/dlnM <0.1) is small in comparison with the conventional BCS superconductors (α~0.5), an evidence that usually used against the phonon mediated pairing in HTSCs. However, the ARPES kink is one of the strongest evidence that there is strong electron-phonon coupling in HTSCs. To confirm this, a group of the US in collaboration with Japanese Scientists has measured the oxygen IE effect of the ARPES pattern for the optimally-doped Bi2212 system by substitution 16Oà18Oà16OR (re-substituted again to confirm the pure IE). They have found a very strong and energy dependent (unusual) IE which is in contrast with the IE on Tc of this system.
Both energy and momentum dispersive curves (EDCs & MDCs) show strong phonon renormalization of the electron dynamics in the 100–300 meV range, while the renormalization is very small for the low energy (<100 meV) and coherent peak (Fig. 1). This energy dependence IE and the dominant effect in energy higher than the kink energy (~ phonon frequencies of this system) go well beyond the Migdal–Eliashberg model.
Isotope shift of the low energy is strongly anisotropic (k dependence) such that it changes from ~15 to -30 meV (stronger near the antinodal-cuts) with a subtle sign change through cuts 2-6 in Fig. 2d, while the kink shift is small ~(5-10)±5 meV for all cuts. Data shows a linear correlation of the isotope shift with the magnitude of superconducting gap along the Fermi surface (inset of Fig. 2a).
The changes of the superconducting gap are small and random in both magnitude and sign. It varies by ~5 meV from one sample to another (for measuring different samples) regardless of the isotope mass.
Both EDCs an MDCs data shows strong temperature dependence of the isotope shift below (T=20 K) and above (100 K) of Tc (Fig.3).
At first the author have discussed that the experimental error such as unintentional doping change induced by the substitution process or sample misalignment could be ruled out, because the temperature dependence, the reversibility and the reproducibility of the observed effects upon repeated measurements. The large IE not only confirms the phonon-originated of the ARPES kink, but also indicates strong electron-phonon interaction in this system. The strong E, k and T dependence of isotope shift are well beyond the usual electron-phonon coupling theory such as Migdal-Eliashberg theory for the strong coupling superconductivity.
The much stronger IE below Tc suggests a picture where pairing of electrons enhances their coupling to the lattice and vice versa, as in spin-Peierls physics. In this picture, the motion of electron pairs modifies the lattice distortion locally and vice versa. If the coupling is too strong: the pair will be localized, the lattice distortion becomes static, and finally the system becomes an insulator. Where the coupling is not strong enough, the dynamic spin-Peierls distortion follows the coherent motion of electron pairs in a superconducting state. The significant isotope dependences of pseudogap temperature T*, J and various low-temperature spin properties support this scenario.
Ref.: G.-H. Gweon, T. Sasagawa, S.Y. Zhou, J. Graf, H. Takagi, D.-H. Lee & A. Lanzara, Nature 430 (2004) 187.
Based on the inconsistency of the IE on ARPES data and on Tc of optimally doped Bi-2212 of the above study, Douglas et al. have re-studied this effect in the almost identical material and experimental conditions. They are unable to detect the unusual IE on their new data and only a small average isotope shift of ~2 ± 3 meV has been found for 10 cuts (inset of Fig. 1b), inconsistent with the previous results of ~40 meV (by Gweon et al.). This small IE has been confirmed by using three different facilities, samples with multiple doping levels, including the optimal doping, and with various photon energies. The errors related to the sample misalignments, which is crucial for creating apparent energy shifts (probably the origin of the observed unusual IE by Gweon et al.), has been removed by collecting data on both sides of the (0,0) point (with ~0.1 degrees accuracy). Although, this study does not confirm the unusual large-scale IE, this result does not invalidate electron–phonon coupling as a potential pairing mechanism for HTSCs.
Ref.: J. F. Douglas, H. Iwasawa, Z. Sun, A. V. Fedorov, M. Ishikado, T. Saitoh, H. Eisaki,H. Bando, T. Iwase, A. Ino, M. Arita, K. Shimada, H. Namatame, M. Taniguchi, T. Masui, S. Tajima, K. Fujita, S. I Uchida, Y. Aiura, D. S. Dessau; Nature 446 (2007) E5.