A strong polaron pairing model of high-temperature cuprate superconductors is presented. The normal and anomalous one-particle Green’s functions are derived from a system with strong electron-phonon coupling. Self-consistent equation for the superconducting order parameter ( ) is derived using Green’s function technique and following Lang and Firsov transformations. Expressions for specific heat, density of states, free energy, and critical field based on this model have been derived. The theory is applied to explain the experimental results in the system . There is convincing evidence that the theory is fully compatible with the key experiments. 1. Introduction Strikingly, after 26 years of enormous experimental and theoretical efforts followed by the discovery, there is still little consensus on the pairing mechanism of high-temperature superconductivity (HTSC) in cuprates [1–12]. HTSCs have unique physical properties in both the normal state and superconducting one. To comprehend the physics of these complex compounds is one of the main tasks of the theory of superconductivity, whose solution may allow one to explain the pairing mechanism ensuring HTSC. At present, there exists no mechanism which would explain the totality of thermodynamical, magnetic, and superconductive properties of HTSCs from a single point of view. The electron-phonon pairing mechanism [13–16], being the principal one in low-temperature superconductors, makes a considerable contribution to the establishment of the superconducting state in HTSCs. But in order to obtain proper description, it is necessary to consider the other mechanism inherent in HTSCs [3, 5, 7, 8, 10]. To explain HTSC, a lot of models and mechanisms of this unique phenomenon have been proposed [1–5, 10, 11]. The key question is the nature of the mechanism of pairing of carriers. There are many different models of superconductivity available, for example, magnon model, exciton model, model of resonant valence bonds, bipolaronic model, bisoliton model, anharmonic model, model of local pairs, and plasmon model, [17]. All these models use the concept of pairing with a subsequent formation of a Bose condensate at temperature irrespective of the nature of the resulting attraction. Some recent theoretical models postulate the mechanism of antiferromagnetic spin fluctuations [18, 19], so that the electron scattering on them can be the reason for the pairing of electrons. In order to comprehend the nature of the superconducting state, it is necessary to construct a consistent microscopic theory which should be able to
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