What do we know about the strength of the electron-phonon coupling in high-temperature superconductors? I would like to clarify the situation of the electron-phonon coupling in high-temperature superconductors (or considering only the cuprates). The main question is what do we know about the strength of the electron-phonon coupling in terms of the experiments. The naive question is that does it exist a universal equation which is an expression of the critical temperature depending on the strength (similar to Mc.Millan formalism), and if it does, is it consistent with the typical ~ 100 K critical temperature of the cuprates.
 A: You are probably aware that the underlying mechanism responsible for superconductivity in cuprates or Fe-based superconductors is still subject to intense debate and research. The usual BCS electron-phonon coupling (EPC) is too weak to account for superconductivity at temperatures of order $100$ K, and produces a gap of s-wave symmetry which is incompatible with the gap symmetry observed in many materials. Several models including nematicity, magnetic or spin fluctuations, charge and spin density waves... have been proposed, all suported by experimental data.
However, people are still considering the role of EPC in the emergence of superconductivity in the $p$ or $d$-wave channel, such as in this paper. Its references links to experimental results supporting their idea.
There is also a nice review about the possible pairing coming from the Friedel oscillations of the Coulomb potential.
A: One way to estimate electron-phonon coupling is to take a look on the hot-electron relaxation rate, which can be more or less directly probed by pump-probe spectroscopy. The values for $\lambda$ are around 0.2-0.5. There are few articles on this topic from C. Gadermaier.
Here are the links
http://dx.doi.org/10.1063/1.4726164
http://link.aps.org/doi/10.1103/PhysRevLett.105.257001
http://link.aps.org/doi/10.1103/PhysRevX.4.011056
