The Specific Heat of a Spin-Fluctuated Cuprate superconductors with strong electronic-Phonon Correlations

Strongly correlated electronic models such as the Hubbard, are often used to describe the properties of cuprates. In most cases, the projected Hubbard operators are normally used to study this models. The Hubbard operators normally give rise to a specific kinematical interaction of electrons with spin and charge fluctuations. These interaction is induced by the intraband hopping with a coupling parameter, W=8t, of the order of the kinetic energy of electrons which is much larger than the antiferromagnetic exchange interaction J induced by the interband hopping. This study presents a theoretical approach to specific heat of a spin fluctuated superconductivity in electron-doped Niodium Cellenium Copper Oxide (Nd2-xCexCuO4 -NCCO) and Praseodymium Cellenium Copper Oxide (Pr2-xCexCuO4-PCCO) and hole-doped Yitrium Barium Copper Oxide (YBa2CuO7-YBCO) and Lanthanum Strontium Copper Oxide (La2-xSrxCuO4-LSCO) where these interactions are taken into account within the Hubbard operator technique. The low-energy spin excitations are considered for the Heisenberg model, while the electronic properties are studied using the two-dimensional Hubbard-Holstein model.