In this paper a geometric approach to describe a rotating fullerene molecule with Ih symmetry is developed. We study the quantum dynamics of quasiparticles in a continuum limit considering a description of fullerene in a spherical solution of the Godel-type space-time with a topological defect. Therefore, we study the molecule in a rotating frame. Also we combine the well-known non-Abelian monopole approach with this geometric description, including the case of the presence of the external Aharonov-Bohm flux. The energy levels and the persistent current for this study are obtained, and we show that they depend on the geometrical and topological properties of the fullerene. Also, we verify recovering of the well-known results for limiting cases.

Description for rotating C 60 fullerenes via an analogue of Gödel-type metric

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.

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

The present paper describes rotations of C60 fullerene molecules in the solid phase of a fullerite. The conducted studies show that these relatively large molecules rotate according to the same laws as macroscopic bodies, i.e., according to the laws of classical mechanics. The performed calculations confirm that fullerene rotations do not cause friction. We suggest a method for a strong increase in the internal energy of the material that does not lead to its destruction. It is theoretically shown that in standard fullerite, in the absence of electric and magnetic fields, fullerene rotations occur with an average angular frequency of 0.34·× 1012 rad·s−1, which is consistent with the experimental data obtained using nuclear magnetic resonance. By means of calculations, we found that alternating magnetic fields of a certain configuration wind fullerenes encapsulated by iron. In this case, two temperatures arise in the fullerite crystal: a high rotational temperature and a vibrational temperature close to normal. For the purpose of determining this velocity, as well as the nature of rotations, the present paper suggests a way of integrating the dynamic Euler equations for the projections of a molecule’s angular velocity vector onto the coordinate axes associated with the fullerene. The stages of computer simulation of fullerene movements, which was carried out without using previously developed packages of molecular-dynamic modelling, are consistently described.

Md-Simulation of Fullerene Rotations in Molecular Crystal Fullerite

In this paper, we study Weyl fermions in a family of Godel-type geometries in Einstein general relativity. We also consider that these solutions are embedded in a topological defect background. We solve the Weyl equation and find the energy eigenvalues and eigenspinors for all three cases of Godel-type geometries where a topological defect is passing through them. We show that the presence of a topological defect in these geometries contributes to the modification of the spectrum of energy. The energy zero modes for all three cases of the Godel geometries are discussed.

Weyl fermions in a family of Gödel-type geometries with a topological defect

In this paper, motivated by the possibility of experimental realization, we study the low-energy electronic states of a rotating carbon nanotube within a continuum model. An effective Dirac equation in the rotating reference frame is derived and exact analytical solutions for the eigenfunctions and energy spectrum are obtained. A Zeeman-like splitting results from the coupling of rotation to total angular momentum and the previously known static results are obtained in the no rotation limit.

Spin splitting at the Fermi level in carbon nanotubes in the absence of a magnetic field

In this paper, motivated by the experimental evidence of rapidly rotating C60 molecules in fullerite, we study the low-energy electronic states of rotating fullerene within a continuum model. In this model, the low-energy spectrum is obtained from an effective Dirac equation including non-Abelian gauge fields that simulate the pentagonal rings of the molecule. Rotation is incorporated into the model by solving the effective Dirac equation in the rotating referential frame. The exact analytical solution for the eigenfunctions and energy spectrum is obtained, yielding the previously known static results in the no rotation limit. Due to the coupling between rotation and total angular momentum, that appears naturally in the rotating frame, the zero modes of static C60 are shifted and also suffer a Zeeman splitting whithout the presence of a magnetic field.

Jonas R. F. Lima

Papers

Effects of rotation in the energy spectrum of C60