Coexistência de supercondutividade e charge density wave em um regime correlacionado - Prauchner, Leonardo Costa (2021)
The strongly correlated electron systems raise the interest of researchers from different areas. However, one of the main categories of those are the unconventional superconductors, also known as high-Tc superconductors. Characterized by a critical temperature above 32 K, predicted by the BCS theory, those systems generally show typical strongly correlated systems behaviors, such as in cuprates. This category of systems have a rich phase diagram, with many phases and coexistence regimes. The case of cuprates is an example where both charge density wave and superconductivity coexist, while also showing the antiferromagnetic and spin density wave phases. There exists a consensus that the mechanisms that generate the superconductivity on systems like cuprates are directly associated to the other, neighbouring phases to the superconductivity. Thanks to that, studying those phases and their coexistence is of utmost importance to the understanding of those systems. The main objective of this work is to analyze the effects of the repulsive coulomb interaction U on the coexistence between superconductivity and charge density wave phases region. The main characteristic of the superconductor phase is the null resistance below a certain temperature, while the charge density wave is characterized by a periodic charge modulation on the lattice. With the intent of perform this study, a BCS-like model was used, which considers both the CDW and superconductivity phases. To be able to study the model, the Green's functions technique was used, alongside the Matsubara's formalism. However, the utilized model does not consider strong correlations. The fact that the Matsubara's formalism is invariant towards correlations allows the introduction of correlations by replacing the normal state uncorrelated Green's function by a new Green's function, obtained through the Hubbard-I approximation. The Hubbard model is traditionally used to study strongly correlated systems. Utilizing the combination from those analytical techniques, together with programs developed in the Fortan 95 language, the effects of U on the superconductor and charge density wave gaps were studied, on their pure and coexistence regime. The main effect of U that was observed is a suppression on both phases, that tends to destroy the coexistence of them. The effect of the second nearest neighbor hopping t1 and U on the gaps was also verified, where both suffered a partial suppression. On the high values of U limit, there is a stabilization of the values of the occupation, which is equivalent to the half-filling regime, that causes U to have a saturation tendency above a certain U value. It has been observed that a rise on the value of U also requires a rise on the V values, to stabilize both phases.