Parity of the order parameter in high-temperature superconductors with respect to aπ2rotation

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Abstract
In order to establish the parity of the order parameter in the model based on the idea of a strong phonon-mediated long-range attraction, enhanced by the extended saddle-point singularities in the electron spectrum, plus a weak short-range repulsion, a comparison of critical temperatures and free energies of the even and odd solutions for the order parameter is performed. A criterion is established distinguishing the two options. It is shown, particularly, that superconductivity, induced by phonons, can, nevertheless, lead to an odd order parameter. On the other hand, contrary to the previous statements, this is the only possibility for the order parameter to change its sign within this model. The theory is influenced by the latest experimental results.