Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2009-09-08
J.Phys.A43:015203,2010
Physics
Condensed Matter
Other Condensed Matter
20 pages LaTeX, 7 figures
Scientific paper
10.1088/1751-8113/43/1/015203
We consider the low-energy electronic properties of graphene cones in the presence of a global Fries-Kekul\'e 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 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.
Roy Abhishek
Stone Michael
No associations
LandOfFree
Fullerenes, Zero-modes, and Self-adjoint Extensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Fullerenes, Zero-modes, and Self-adjoint Extensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fullerenes, Zero-modes, and Self-adjoint Extensions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-384888