Eur. Phys. J. Plus (2013) 128: 60
https://doi.org/10.1140/epjp/i2013-13060-x

Regular Article

Holonomy transformations and application in the curved structure of graphene

¹ Instituto de Física, Universidade Federal de Alagoas, Campus A. C. Simões - Av. Lourival Melo Mota, s/n, CEP: 57072-970, Tabuleiro do Martins - Maceió - AL, Brazil
² Departamento de Física, Universidade Estadual de Feira de Santana, 44031-460, Feira de Santana, BA, Brazil
³ Departamento de Física, CCEN, Universidade Federal da Paraíba, Cidade Universitária, 58051-970, João Pessoa, PB, Brazil

Received: 15 March 2013
Accepted: 6 May 2013
Published online: 7 June 2013

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 González 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.