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.
73.22.-f Electronic structure of nanoscale materials: clusters,
nanoparticles, nanotubes, and nanocrystals
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