# Cooper pairs without 'glue' in high-$T_c$ superconductors

## TL;DR

This paper proposes that in high-$T_c$ cuprates, Cooper pairs form spontaneously without a mediating 'glue', driven by mutual pair interactions, leading to a new understanding of the superconducting phase and its properties.

## Contribution

It introduces the concept of 'pairons' formed by itinerant holes in an antiferromagnetic background and explains superconductivity without traditional pairing mechanisms.

## Key findings

- Pairs form spontaneously without 'glue'
- The phase diagram is explained by a single energy scale $\,J$
- The excitation gap is determined by carrier concentration and $J$

## Abstract

We address the origin of the Cooper pairs in high-$T_c$ cuprates and the unique nature of the superconducting (SC) condensate. Itinerant holes in an antiferromagnetic background form pairs spontaneously, without any `glue', defining a new quantum object the `pairon'. In the incoherent pseudogap phase, above $T_c$ or within the vortex core, the pairon binding energies are distributed statistically, forming a `Cooper-pair glass'. Contrary to conventional SC, it is the mutual pair-pair interaction that is responsable for the condensation. We give a natural explanation for the {\it ergodic rigidity} of the excitation gap, being uniquely determined by the carrier concentration $p$ and $J$. The phase diagram can be understood, without spin fluctuations, in terms of a single energy scale $\sim J$, the exchange energy at the metal-insulator transition.