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After looking at these two RevModPhys articles, I have found myself perplexed by the current state of high $T_c$ superconductivity research. Seeing as I cannot find any SE articles more recent than 5 years or so, I thought I'd ask this question.

What is the current state of research on high-Tc superconductors? In particular, this question I think has two major points, but perhaps an expert can correct me about other angles?

  1. Have people managed to rule out electron-phonon interactions as a pairing mechanism? Is there any strong evidence either way?

  2. Do we have more conclusive evidence for or against antiferromagnetic ordering contributing to pairing? There seems to more and more discussion about entanglement in the strange metal regime described by holographic conjectures as contributing to a more exotic pairing mechanism? What evidence would you need for this argument?

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    $\begingroup$ "We wanted the paper to represent ... a progress report on where we had gotten so far, the things that could be agreed as a basis for further work. When we submitted it ... we were shocked to discover that although the editor was eager to publish it, he could find only a tiny minority of referees in the field who would agree, ... we did not expect that the field was so poisoned by self-interest and factionalism that no one outside our group could be found who wanted to see such a progress report published." P.W.Anderson, "Personal History ...", 2010. Same now, methinks. $\endgroup$
    – Andrea Alciato
    Commented Nov 22, 2021 at 11:56
  • $\begingroup$ What do you mean "pairing" ? Are covalent single bonds (each contains a pair of electrons) in insulators considered as "electron-phonon" interaction as well? $\endgroup$
    – Paul Kolk
    Commented Aug 2 at 22:00

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Probably, the problem is much deeper than it seems; the low temperature superconductivity (SC) is poorly understood, so a further evolution in the high temperature SC is locked. The dominating theories cannot explain not only latest facts, such as high-temperature SC, SC in two dimensional systems, SC in heterostructures etc., but also the “conventional” experiments. For example the BCS theory contradicts many effects in conventional metals: inverse/weak/giant isotope effect, Tc dome at high pressure, superconductor-insulator transitions, stable electronic pairs without SC, existence of persistent (for many years!) supercurrents, existence of permanent SC pairs. A plausible solution of these old questions will open a road to correct solutions for new superconductors.

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