Revisiting the electronic properties of disclinated graphene sheets

Abstract

The interplay between topological defects, such as dislocations or disclinations, and the electronic degrees of freedom in graphene have been extensively studied. In the literature, for the study of this kind of problems, it is in general used either a gauge theory or a curved spatial Riemannian geometry approach, where, in the geometric case, the information about the defects is contained in the metric and the spin-connection. However, these topological defects can also be associated with a Riemann–Cartan geometry where curvature and torsion plays an important role. In this article, we study the interplay between a wedge disclination in a planar graphene sheet and the properties of its electronic degrees of freedom. Our approach relies on its relation with elasticity theory through the so called elastic-gauge, where their typical coefficients, as for example the Poisson’s ratio, appear directly in the metric, and consequently also in the electronic spectrum.