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 wave functions obey a two-dimensional Dirac equation on a spheroid with two kinds of gauge fluxes taken into account. The first one is the 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 quasizero modes in addition to the true zero mode are predicted to emerge in spheroidal fullerenes. An additional “hyperfine” splitting of the levels (except the quasizero-mode states) is found.

Figure 1

The schematic picture of the first positive electronic level $E_{jn}^{\delta }$ for spheroidal fullerenes.

Figure 2

The schematic picture of the second positive electronic level $E_{jn}^{\delta }$ for spheroidal fullerenes.