Spheroidal geometry approach to fullerene molecules

Graphite is an example of a layered material that can be bent to form fullerenes which promise important applications in electronic nanodevices. The spheroidal geometry of a slightly elliptically deformed sphere was used as a possible approach to fullerenes. We assumed that for a small deformation the eccentricity of the spheroid e≪1. We are interested in the elliptically deformed fullerenes C70 as well as in C60 and its spherical generalizations like big C240 and C540 molecules. The low-lying electronic levels are described by the Dirac equation in (2+1) dimensions. We show how a small deformation of spherical geometry evokes a shift of the electronic spectra compared to the sphere. The flux of a monopole field was included inside the surface to describe the fullerenes. Both the electronic spectrum of spherical and the shift of spheroidal fullerenes were derived.