Holonomy transformations and application in the curved structure of graphene

Abstract

In this contribution we show that holonomy transformations are an efficient method to describe some geometrical characteristics. This approach is an alternative proceeding the Gauss-Bonnet theorem to get the deficit angle and it also permits to obtain the phase factor acquired by a vector which was parallel transported through a medium with topological defects. We have applied the holonomy transformation to the system described by Gonzalez and Herrero formed by two sheets of graphene connected by a carbon nanotube. The result confirms that the angle endowed is equivalent to 12 heptagonal carbon rings, which was shown by the authors.