Explorando fases em óxidos de cobre: ajustes de dados numéricos em investigação de supercondutividade

Abstract

In this dissertation we investigate superconductivity in strongly correlated systems, with a specific focus on copper oxides, known as cuprates. These materials exhibit a variety of emerging phases as we vary parameters such as temperature, doping, and pressure. In addition to the superconducting phase, other phases, such as the pseudogap, remain poorly understood. The pseudogap phase is characterized by a suppression of spectral weight in certain directions in momentum space. Understanding this phase is fundamental to understanding superconductivity, as it is believed that there are signatures of the superconducting phase in the pseudogap phase. The Hubbard model is used to describe strongly correlated systems, as it well describes the competition between the kinetic energy and the Coulomb interaction of electrons. It is believed that much can be learned about cuprates considering the Hubbard model in two spatial dimensions, corresponding to the planes of copper and oxygen, in the presence of doping, arising from the other atoms. However, the model does not have an exact solution in two dimensions, requiring the use of a numerical method for its resolution. In previous work by the group, the model was solved numerically without considering superconductivity via extensions of Dynamical Mean Field Theory (DMFT). This technique maps the Hubbard model onto the Anderson impurity problem, simplifying the resolution. The results obtained revealed two distinct metallic phases, conventional and pseudogap, as the system doping varied. The objective of this dissertation is to verify whether the different metallic phases mentioned above give rise to different superconducting phases. For this, an electron pair formation term was added to the Hamiltonian and new numerical DMFT results were obtained. These results are difficult to understand; to analyze them, we use a phenomenological model that describes electron dynamics at low energies. We built a code that simultaneously adjusts the DMFT curves for the real and imaginary parts of the normal and anomalous self-energies to the phenomenological model for each doping value, allowing the analysis of the model parameters starting from the different metallic regions. Our preliminary results show fluctuations in these parameters when we vary the doping, suggesting that it would be desirable to obtain more accurate DMFT results, which is in progress, so that new adjustments to the phenomenological model can be made.