Why Are Cuprates the Only High-Temperature Superconductors?

TL;DR

This paper explains the unique high-temperature superconductivity of cuprates through a hierarchical mean-field theory of elastic networks, highlighting the role of giant electron-phonon interactions in marginally unstable, fragile networks stabilized by CuO2 planes.

Contribution

It applies a hierarchical mean-field theory to demonstrate how giant electron-phonon interactions in fragile, marginally unstable networks account for cuprates' superconducting properties.

Findings

Cuprate networks are fragile and floppy, with stability accurately quantified.

Superconductivity arises from giant electron-phonon interactions in these networks.

CuO2 planes form percolative backbones stabilizing the overall structure.

Abstract

The heirarchical 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 ~1 percent), and without adjustable parameters, by comparison with stabilities of generically similar network glasses, and are stabilized by percolative backbones composed of CuO2 planes.