Dynamics, topological defects and phase transitions in two-dimensional systems.

Abstract

The physical properties of ordered media depend strongly on the existence of topological defects. Such defects are a consequence of the periodicity and stiffness of the ordered media and are also responsible for the mechanism that produces symmetric-breaking phase transitions. In turn, a wide variety of ordered media emerges through this symmetry breaking.In systems with continuous symmetry, for example, as in crystalline atomic lattices, topological defects in the form of dislocations determine most of the plastic properties, both in dynamic and static behavior. In superconductors, vortices are the most relevant topological defects. When the symmetry is discrete, as in the case of adsorbed atomic layers on a substrate the relevant topological defect consists of a domain wall or interface, separating different ordered regions of the system. In two-dimensional materials, such as graphene and other monolayer materials, the presence of such defects in the form domain-wall structures have important effects on the friction properties. The purpose of the present project is to develop theoretical research on dynamic, topological defects and phase transitions in two-dimensional systems. The central focus is on phenomena that occur mainly in superconducting arrays and crystal surfaces. The common feature of these apparently distinct systems is the existence of competition between elasticity, periodicity of ordered media and external force. The periodicity of the system allows the formation of topological defects that determine both the dynamics and phase transitions in the system. (AU)