Efeitos da curvatura localizada na dinâmica de férmions de Dirac sem massa (2+1) dimensões

Abstract

In this work, we investigate how a localized curvature affects the dynamics of massless Dirac fermions propagating on a curved surface. We use graphene as the physical system of interest, since due to its crystalline structure, the electrons in this material effectively behave as massless relativistic particles in a (2+1)-dimensional spacetime, allowing their dynamics to be described by the Dirac equation. We consider smooth protrusions on curved surfaces with axial symmetry, adopting two specific geometric models: a Gaussian-type bump and a volcano-type bump. By incorporating the minimal coupling between the spinor and the geometry of the surface, described using vielbeins and the spin connection, we study the behavior of the wavefunction over these geometries. As the curvature vanishes asymptotically, we find that the electronic states behave like free waves far from the protrusions. However, in regions with pronounced curvature, there is a significant increase in the probability density of finding the electron in that region. Finally, we introduce an external magnetic field to analyze the differences between the curvature-induced pseudogauge field and the effects of a real field, which allows us to identify the emergence of bound states and the formation of Landau levels.