I would say it's the former --- there are some (two or three) theories which give the correct qualitative picture. However, experiments on these materials are actually very difficult, because the observed phenomenon (in the quantitative aspects) are actually very sensitive to things like impurities or disorder of grains, surface effects, etc. It's very difficult to even achieve consensus about what experimental effects are actually seen, and what they mean --- for example, the famous "linear resistivity" of the strange metal phase is actually very rarely that linear, but simply something close to linearity, and not even over a very large range of temperatures; this isn't to say that there isn't a linear scaling regime, but just that in practise to demonstrate it experimentally is challenging. When we move on to more sophisticated measurements such as ARPES or STM tunnelling experiments, people get even more agitated about what the experiments are really measuring.As an outsider, I'd like to ask a question about the status of research on high-Tc superconductors. Is there a lack of convincing theories, or is there an abundance of promising theories but no good experimental probe to pick out the correct one?
I wouldn't raise my hopes up if I were you. It seems very unethical to try ro explain one unexplained phenomenon by using an unproven theory from a completely different field.Lately there have been lots of talk about string theory shedding light on high-Tc through gauge/gravity duality, i.e. AdS/CFT.
A book is not a very good source to quote for the progress in the field of High-Tc superconductors. This is because things change very dramatically. As an example, the apical oxygen half-breathing phonon mode is now considered to be a serious candidate as the source of pairing mechanism.Here is from a book I read
"...the characteristics of high- superconductors
deviate from the predictions of the BCS theory as those of organic supercon-
ductors and heavy fermions. For example, the BCS isotope effect is almost ab-
sent in cuprates. As a consequence, this has prompted the exploration of non-
phonon electronic coupling mechanisms. Ph. Anderson was probably the first
to suggest a theoretical model which did not incorporate phonon-electron inter-
actions. Between 1987 and 2002, more than 100 theoretical models of high-
superconductivity were proposed. Most of these models consider phonons ir-
relevant. Looking ahead, it is worth noting that, as established by now, none of
them can be fully applied to high- superconductors; however, the combina-
tion of two proposed models, namely, the bisoliton theory and the theory based
on spin-fluctuations, can in the first approximation describe the phenomenon
of high- superconductivity"
Could you introduce some newest review papers (or any documents) on this field. I really want to know what is happening with high-Tc superconductivity. Thanks!A book is not a very good source to quote for the progress in the field of High-Tc superconductors. This is because things change very dramatically. As an example, the apical oxygen half-breathing phonon mode is now considered to be a serious candidate as the source of pairing mechanism.