Fullerenes, zero-modes and self-adjoint extensions

A. Roy, M. Stone

Research output: Contribution to journalArticlepeer-review


We consider the low-energy electronic properties of graphene cones in the presence of a global Fries-Kekulé Peierls distortion. Such cones occur in fullerenes as the geometric response to the disclination associated with pentagon rings. It is well known that the long-range effect of the disclination deficit-angle can be modelled in the continuum Dirac-equation approximation by a spin connection and a non-Abelian gauge field. We show here that to understand the bound states localized in the vicinity of a pair of pentagons one must, in addition to the long-range topological effects of the curvature and gauge flux, consider the effect of the short-range lattice disruption near the defect. In particular, the radial Dirac equation for the lowest angular-momentum channel sees the defect as a singular endpoint at the origin, and the resulting operator possesses deficiency indices (2, 2). The radial equation therefore admits a four-parameter set of self-adjoint boundary conditions. The values of the four parameters depend on how the pentagons are distributed and determine whether or not there are zero modes or other bound states.

Original languageEnglish (US)
Article number015203
JournalJournal of Physics A: Mathematical and Theoretical
Issue number1
StatePublished - 2010

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)


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