Low energy electronic states in spheroidal fullerenes

The field-theory model is proposed to study the electronic states near the Fermi energy in spheroidal fullerenes. The low energy electronic wavefunctions 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. It is 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. An additional 'hyperfine' splitting of the levels (except the quasi-zero-mode states) is found.Comment: 9 page

Electronic structure of spheroidal fullerenes in a weak uniform magnetic field: a continuum field-theory model

The effect of a weak uniform magnetic field on the electronic structure of slightly deformed fullerene molecules is studied within the continuum field-theory model. It is shown how the existing due to spheroidal deformation fine structure of the electronic energy spectrum modifies in the presence of the magnetic field. Hyperfine splitting of the energy-levels dictated by the topological defects is also influenced by the weak external magnetic field. Exact analytical solutions for zero-energy modes are found.Comment: 8 page

The continuum gauge field-theory model for low-energy electronic states of icosahedral fullerenes

The low-energy electronic structure of icosahedral fullerenes is studied within the field-theory model. In the field model, the pentagonal rings in the fullerene are simulated by two kinds of gauge fields. The first one, non-abelian field, follows from so-called K spin rotation invariance for the spinor field while the second one describes the elastic flow due to pentagonal apical disclinations. For fullerene molecule, these fluxes are taken into account by introducing an effective field due to magnetic monopole placed at the center of a sphere. Additionally, the spherical geometry of the fullerene is incorporated via the spin connection term. The exact analytical solution of the problem (both for the eigenfunctions and the energy spectrum) is found.Comment: 9 pages, 2 figures, submitted to European Physical Journal

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 is smaller than one. We are interested here in the big elliptically deformed fullerenes.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.Comment: 12 pages, 2 figure