# Dynamic d-symmetry Bose condensate of a planar-large-bipolaron-liquid in cuprate superconductors

## TL;DR

This paper models a large-bipolaron liquid in cuprate superconductors, demonstrating how phonon-mediated attraction and Bose condensation of d-symmetry bipolarons can lead to superconductivity with distinctive properties.

## Contribution

It introduces a model of large-bipolaron liquids in cuprates, highlighting the role of phonon-mediated attraction and dynamic d-symmetry Bose condensation in superconductivity.

## Key findings

- Large-bipolarons form in cuprates due to dielectric constant ratios.
- Phonon-mediated attraction leads to bipolaron condensation into a liquid.
- Superconductivity arises from Bose condensation of d-symmetry bipolarons.

## Abstract

Planar large-bipolarons can form if the ratio of the surrounding mediums static to high-frequency dielectric constants is especially large. A large-bipolaron in p-doped La2CuO4 is modeled as two electrons being removed from the out-of-plane orbitals of four oxygen ions circumscribed by four copper ions of a CuO2 layer. These oxygen dianions relax inwardly as they donate electrons to the surrounding outwardly relaxing copper cations. This charge transfer generates the strong in-plane electron-lattice interaction needed to stabilize a large-bipolaron with respect to decomposing into polarons. The lowest-energy radial in-plane optic vibration of a large-bipolarons four core oxygen ions with their associated electronic charges has d-symmetry. Electronic relaxation in response to multiple large-bipolarons atomic vibrations lowers their frequencies to generate a phonon-mediated attraction among them which fosters their condensation into a liquid. This liquid features distinctive transport and optical properties. A large-bipolaron liquids superconductivity can result when it undergoes a Bose condensation yielding macroscopic occupation of its ground-state. The synchronized vibrations of large-bipolarons core-oxygen ions with their electronic charges generate this Bose condensates dynamic global d-symmetry.

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Source: https://tomesphere.com/paper/1705.10335