Férmions de Dirac não massivos em (2+1) dimensões sob deformações com simetria angular

Abstract

The fundamental objective of this research is to investigate the joint effects of curvatures and deformations (strains) of surfaces on the behavior of systems made up of fermionic fields and particles confined to them. Two-dimensional materials such as graphene lead to an effective description of conduction electrons in terms of massless Dirac fermions. We are therefore initially motivated by this type of system. In carrying out this study, we are, in principle, considering two different approaches. The first, and of main interest, aims to use techniques of relativistic quantum mechanics and differential geometry to perform the coupling of the Dirac equation with the geometry of the curved surface, to study the effective potentials that arise by changing the metric, in which we introduce deformation terms via elasticity theory. It should be noted that, in this approach, we consider the limit to be continuous, i.e., we treat the system as a continuous surface. We are relying on the fact that in these systems the particles behave in a way analogous to bodies subject to a gravitational field, i.e., they feel the deformations in the space to which they are confined in a way analogous to the minimum coupling in gravitation. This differentiates it from the second approach, which is based on results using the tight-binding method, considering the surface to be a crystalline network.