Highly correlated systems and superconductivity at high critical temperatures

In this project, we made a theoretical and experimental study on solids wit h strong electronic correlations. From a theoretical point of view we studi ed mainly systems with low electronic density, in order to obtain an exact solution, using the generalized Hubbard model and the mapping method in rea l space. We found a solution for the problem of one hole and one doblon in an antiferromagnetic background, besides the solution for the problem of th ree body in a one dimensional lattice. To find the solution of these two pr oblems, we made an extension of the mapping method to include the effects o f the charge density on the hopping parameter. On the other hand, from an e xperimental point of view we made the synthesis by the solid state reaction method of the series of compounds with a general formula ABCuO(x) [A=(Sr,C a); B=(Na.K)], where we obtained the synthesis conditions ones the thermody namical equilibrium of the different phases was reached. We found the solub ility limit. of the solid solution and characterized our samples using diff erent techniques, X-ray powder diffraction, differential thermal analysis a nd scanning electron microscopy. It is important to say that the theoretica l studies give us mainly the base to have a physical discussion of the expe rimental results and not necessarily a model to explain those results.