Zero modes for Dirac fermions on a sphere with fractional vortex

Osipov V.A., Kochetov E.A.

PACS: .40.-k, 11.15.-q, 73.61.Wp

**Normalized zero-energy states are shown to emerge for massless Dirac fermions in an external gauge field that gives rise to non-quantized vortices on a sphere. A field-theory model is used to describe electronic states of a fullerene-like molecule. In particular, we predict an existence of exactly one zero-energy mode due to a disclination. For 60° disclination the normalized electron density at zero energy is found to behave as Д**^{-5}/^{3 }with *R *being the fullerene radius.