Defeitos em matéria condensada: de twistons a skyrmions.

Abstract

Topological defects are characterized as stable equation of motion solutions in one or more spatial dimensions and play an important role in nonlinear science. In this study, space-time (1 + 1) and (2 + 1) dimension defects are emphasized. In the first case, configurations known as twistons (kink-like topological solutions) present in polyethylene crystals are assessed. In this first approach, previous works were reviewed and new families of potentials that adequately describe these types of systems were constructed from the extension method, presenting analytical topological solutions that do not display infinite degeneracy problems. In the second case, structures known as skyrmions were studied based on their description in magnetic materials, where they are denoted as topologically stable nanoscale magnetization configurations. The extension method was applied and a potential from which such magnetic structures can be modelled, function of two coupled scalar fields was presented. In addition, the new two-field model possesses known analytical solutions, allowing for interesting analyses, such as the determination of a conserved topological quantity, the study of the different magnetization configurations and calculation of mean matter radius.