Why are cuprates the only high-temperature superconductors?

Abstract

The hierarchical mean-field theory of elastic networks, originally developed by Maxwell to discuss the stability of scaffolds, and recently applied to atomic networks by Phillips and Thorpe, explains the phase diagrams and remarkable superconductive properties of cuprates as the result of giant electron–phonon interactions in a marginally unstable mechanical network. The overall cuprate networks are fragile (floppy), as shown quantitatively (with an accuracy of about 1%), and without adjustable parameters, by comparison with stabilities of generically similar network glasses. Jahn–Teller distortions that would render the material insulating are suppressed by percolative backbones composed of isostatic CuO₂ planes. The model has many applications, including isotopic and dopant dependencies measured near photoemission ‘kinks’.

Acknowledgements

I am grateful to J. D. Jorgensen for a copy of figure 2, to J. Rohler for discussions, to Denis Newns for encouragement, and to Paul Leath for a perceptive comment.

Notes

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Additional information

Notes on contributors

J. C. Phillips *

E-mail: [email protected]