Electronic Structure of Spheroidal Fullerenes

Both the eigenfunctions and the local density of states (DOS) near the pentagonal defects on the fullerenes was calculated analytically as a numerically. The results shows that the low-energy DOS has a cusp which drops to zero at the Fermi energy for any number of pentagons at the tip except three. For three pentagons, the nonzero DOS across the Fermi level is formed. 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 is much more smaller then one. 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 and both the electronic spectrum of spherical and the shift of spheroidal fullerenes were derived. In the next study the expanded field-theory model was proposed to study the electronic states near the Fermi energy in spheroidal fullerenes. The low energy electronic wave functions obey a two-dimensional Dirac equation on a spheroid with two kinds of gauge fluxes taken into account. The first one is so-called K spin flux which describes the exchange of two different Dirac spinors in the presence of a conical singularity. The second flux (included in a form of the Dirac monopole field) is a variant of the effective field approximation for elastic flow due to twelve disclination defects through the surface of a spheroid. We consider the case of a slightly elliptically deformed sphere which allows us to apply the perturbation scheme. We shown exactly how a small deformation of spherical fullerenes provokes an appearance of fine structure in the electronic energy spectrum as compared to the spherical case. In particular, two quasi-zero modes in addition to the true zero mode are predicted to emerge in spheroidal fullerenes. The effect of a weak uniform magnetic field on the electronic structure of slightly deformed fullerene molecules was also studied. It was shown how the existing due to spheroidal