Eur. Phys. J. Plus (2017) 132: 183
https://doi.org/10.1140/epjp/i2017-11457-1

Regular Article

The geometric theory of defects description for C₆₀ fullerenes in a rotating frame

¹ Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-970, João Pessoa, PB, Brazil
² Centro de Ciências Exatas e Sociais Aplicadas, Universidade Estadual da Paraíba, Patos, PB, Brazil
³ Instituto de Física, Universidade Federal de Alagoas, Campus A. C. Simões, Av. Lourival Melo Mota, s/n, Tabuleiro do Martins, 57072-970, Maceió, AL, Brazil
⁴ Departamento de Física, CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-970, João Pessoa, PB, Brazil

^* e-mail: furtado@fisica.ufpb.br

Received: 5 February 2017
Accepted: 16 March 2017
Published online: 25 April 2017

Abstract

In this paper we investigate a rotating fullerene molecule. We use a geometric theory to describe the fullerene as a two-dimensional spherical space in a rotating frame with topological defects submitted to a non-Abelian gauge field. We write an effective metric describing the fullerene molecule in a rotating frame. We solve the massless Dirac equation in this model and obtain exactly the eigenvalues and eigenfunction of the Hamiltonian. The fullerene molecule is placed in the presence of an Aharanov-Bohm flux and the Hamiltonian for this case is solved exactly. Also, we obtain the analogue of the Aharonov-Carmi phase for this system in a rotating frame and find that the energy depends on the parameters characterizing the disclination, the non-Abelian gauge field and the angular velocity of the molecule. The influence of the rotation on the energy spectrum, eigenvalues, eigenvectors and geometric phase is discussed.