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Cooperative Electronic and Phononic Mechanism of the High Temperature Superconductivity in Cuprates

In conventional superconductors, phonons glue two electrons with opposite spins to form Cooper pairs and condensation of these pairs leads to the superconductivity. Identifying the underlying mechanism of the high temperature superconductivity in cuprates is among the most important problems in physics. Even quarter of a century after the first report of high temperature superconductor by Bednorz and Muller in 1986, there is still no general consensus on the pairing mechanism of superconductivity in these materials. So far, many theories have been developed to explain the exotic properties of cuprates, but they can explain only a limited number of experiments. In this article, we present a new pairing mechanism that incorporates both strong correlation and phonon mediated interaction on an equal footing to produce superconductivity. In this framework, strong correlation and anti-ferromagnetic interaction between electrons, create RVB pairs and phonons provide the phase coherence between these RVB pairs. Both of these are required in this approach to obtain the superconductivity. This approach resolves three limitations of the U(1) slave boson method. We achieve a better estimation of $T_c$, we only predict $\frac{h}{2ec}$ vortices and the linear $T$ coefficient of the superfluid is not sensitive to the doping. This formalism provides a framework that connects Anderson's idea of preformed Cooper pairs and phonon based theories.