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

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.