Variational approach to the Coulomb problem on a cylinder

Article

关键词: TIGHT-BINDING MODEL;    CARBON NANOTUBES;    BOUND-STATES;    DEFECTS;   

DOI  :  10.1103/PhysRevB.66.075407

来源: SCIE

【 摘 要 】

We evaluate, by means of variational calculations, the bound state energy E-B of a pair of charges located on the surface of a cylinder, interacting via Coulomb potential -e(2)/r. The trial wave function involves three variational parameters. E-B is obtained as a function of the reduced curvature C=a(0)/R, where a(0) 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 E-B are reproduced accurately by our calculation. E-B is relatively insensitive to curvature for small C. Its value is similar to1% higher at C=1 than at C=0. This weak dependence is confirmed by a perturbation theory calculation. The high curvature regime approximates the one-dimensional Coulomb model; within our variational approach, E-B has a logarithmic divergence as R approaches zero. The proposed variational method is applied to the case of donors in single-wall carbon nanotubes.

【 授权许可】

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