For the cuprate high temperature superconductivity (high-Tc) research over the past three decades, the biggest challenge is to identify the relevant low energy degrees of freedom that are critical to formulating the correct theoretical model for high-Tc superconductivity. The main difficulty lies in the closeness between various relevant energy scales. For low energy processes that are comparable to the superconducting gap energy ∆sc, there are the spin exchange energy J, the lattice vibration (phonon) energy Ωph, and the van Hove singularity energy E(π,0). However, anomalous isotope effects on Tc and superfluid density in the cuprates cannot be captured by traditional phonon-mediated superconductivity theories. Historically, a purely electronic Hamiltonian – the Hubbard model – was widely regarded to encapsulate all the core physics of the high-Tc phenomena.
In a recent paper published in Science, scientists from Stanford University and from Stanford Institute for Materials and Energy Sciences (SIMES), in collaboration with material scientists from Japan and theoreticians from Japan, the Netherlands, and Berkeley, reinstated the substantial role of the lattice vibration in the cuprate high-Tc superconductivity – however, in a subtle way that is highly intertwined with the electronic correlations. They finely straddled 18 differently hole-doped high-Tc compound Bi2Sr2CaCu2O8+δ within 8% change of hole carrier concentration, a doping range where Tc evolves from 47 K to 95 K through a putative quantum critical point, around which the electronic correlation effect experiences a sudden change. Then systematic experiments were carried out using the angle-resolved photoemission spectroscopy (ARPES) facility at SSRL Beam Line 5-4. Here, the high-resolution ARPES end station provided critical information of both the superconducting gap and the electron-lattice coupling.
As shown in Fig. 1, the electron-lattice coupling at (π, 0) – the momentum where the superconducting gap is maximum – suddenly increases in strength when the doping is sensitively reduced from 22% to 19%, indicated by the rapid growth of the spectral “dip” shaded in grey. In the meantime, the superconducting gap quadruples, superconducting Tc doubles, and various electronic correlation effects become prominent. The phonon energy extracted from the ARPES spectra is around 37 meV, which agrees with a particular type of out-of-plane copper-oxygen bond buckling phonon. What is peculiar is the positive feedback between the development of superconductivity and the lattice coupling when the temperature is lowered, which cannot be simply explained under conventional single-particle framework. This phonon was predicted to be capable of enhancing the superconducting Tc by as much as 50% at moderate coupling, and is now experimentally demonstrated to show lock-step evolution with the growth of the superconductivity.
Fig. 2 also unifies the layer-dependence of Tc with the doping dependent perspective. For single-layer cuprate (e.g. Bi-2201) where the CuO2 plane sits on the crystal mirror plane, this phonon is practically decoupled from the superconducting electrons as forbidden by symmetry. Indeed, single-layer cuprate spectra lack the coupling feature, and its Tc is much lower than its multi-layer counterparts, whose lattice symmetry allows the aforementioned coupling. Intriguingly, the correlation effects are also accordingly stronger in the multi-layer systems, which supports the self-consistent conjecture – the electronic correlation and the lattice coupling cooperatively feedback to each other, where the latter, with correct properties, enhances the superconductivity.
Y. He, M. Hashimoto, D. Song, S.-D. Chen, J. He, I. M. Vishik, B. Moritz, D.-H. Lee, N. Nagaosa, J. Zaanen, T. P. Devereaux, Y. Yoshida, H. Eisaki, D. H. Lu and Z.-X. Shen, "Rapid Change of Superconductivity and Electron-phonon Coupling through Critical Doping in Bi-2212", Science 362, 62 (2018) doi: 10.1126/science.aar3394