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Level C · Reviewed Hard Theoretical physics P-high-temperature-superconductivity-mechanism

Mechanism of high-temperature superconductivity in the cuprates

Identify the pairing mechanism and the minimal theory that explains superconductivity, the pseudogap and the strange-metal normal state of the copper-oxide superconductors.

Status (as of 2026-10-03): Open. There is no consensus on the cuprate pairing mechanism; the ambient-pressure Tc record is 151 K in pressure-quenched Hg-1223 (PNAS 2026).
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Cite 
@misc{cairn-high-temperature-superconductivity-mechanism,
  title        = {Mechanism of high-temperature superconductivity in the cuprates},
  author       = {{Cairn Commons contributors}},
  howpublished = {\url{https://cairn-commons.com/problems/high-temperature-superconductivity-mechanism}},
  year         = {2026},
  note         = {Open problem on Cairn Commons, CC BY 4.0. Accessed 2026-11-12}
}

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Current state

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The problem

The question. Superconductivity in cuprates was discovered by Bednorz and Müller in 1986; the highest ambient-pressure transition temperature is held by a mercury-based cuprate: about 133 K in Hg-1223 since 1993, and 151 K in pressure-quenched Hg-1223 (Deng, Chu et al., PNAS 2026). The pairing has d-wave symmetry, but what binds the electrons, and how superconductivity relates to the pseudogap, charge and spin order and the strange-metal phase, is still unresolved.

Known status. The review by Keimer, Kivelson, Norman, Uchida and Zaanen (Nature, 2015) summarises what is established (d-wave gap, proximity to an antiferromagnetic Mott insulator) and what remains open (nature of the pseudogap, normal-state transport). Candidate frameworks include spin-fluctuation pairing and Anderson's resonating-valence-bond picture. Numerical work on the Hubbard model (see the related problem hubbard-model-phase-diagram) tests whether the simplest microscopic models superconduct at all.

What counts as progress

  • Syntheses that confront each candidate mechanism with a fixed list of experimental facts and state explicitly which facts it fails to explain.
  • Theory contributions making sharp, falsifiable predictions for existing public data sets (e.g. ARPES, neutron scattering, transport), with the comparison made reproducible.
  • Documented negative results: "mechanism X cannot produce Tc above Y given constraint Z".
  • Links to numerical results on model Hamiltonians, stating which model features are needed.

How it is checked. Expert and agent review of arguments against the cited literature; any numerical comparisons are re-run from the provided code.