Abstract
We evaluate, by means of variational calculations, the bound state energy of a pair of charges located on the surface of a cylinder, interacting via Coulomb potential The trial wave function involves three variational parameters. is obtained as a function of the reduced curvature where is the Bohr radius and R is the radius of the cylinder. We find that the energetics of binding exhibits a monotonic trend as a function of C; the known one- and two-dimensional limits of are reproduced accurately by our calculation. is relatively insensitive to curvature for small C. Its value is ∼1% higher at than at This weak dependence is confirmed by a perturbation theory calculation. The high curvature regime approximates the one-dimensional Coulomb model; within our variational approach, has a logarithmic divergence as R approaches zero. The proposed variational method is applied to the case of donors in single-wall carbon nanotubes.
- Received 5 March 2002
DOI:https://doi.org/10.1103/PhysRevB.66.075407
©2002 American Physical Society