Leading theories of the cuprate superconductivity: a critique

Abstract

We present a review of the leading theoretical approaches in the field of cuprate high temperature superconductivity. We start out by defining the problem and ask the question: whether an overarching theory possible (which is capable of explaining not only the mechanism of unconventional superconductivity but also a coherent understanding of the strange metal phase and the pseudogap phase)? If it is possible, what should we expect from the overarching theory? We list various experimental facts, and point out what can we learn from them and where do current theories stand in addressing them? Next, we present a critique of the current leading approaches. We conclude that although progress in the field has been unprecedented, but we still lack a coherent understanding.

arXiv comment13 pages, and 9 figures; A new section on the cluster-DMFT based approaches is added. Some typos corrected. Comments/criticism is most welcomed!

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• A short review of the recent progresses in the study of the cuprate superconductivity
• Two $T$-linear scattering rate regimes in the triangular lattice Hubbard model
• Exploring charge and spin fluctuations in infinite-layer cuprate SrCuO${}_2$ from a phonon perspective
• Emergence and tunability of Fermi-pocket and electronic instabilities in layered Nickelates
• Non-Fermi Liquid Behavior of the $t$-$J$ Model in the Strange Metal Phase: $U(1)$ Gauge Theory Consistent with Local Constraints
• Condensation mechanism of high-$T_c$ cuprates: the key role of pairon excitations