Atomic and electronic structures of large and small carbon tori

The stability of large carbon tori is examined within the elasticity theory. Tori of diameter larger than 200 nm obtained by bending a single-wall nanotube and connecting the two ends together are proved to be stable. Molecular mechanics is used for optimizing the structure of a small polygonal torus $\left({\mathrm{C}}_{1960}\right)$ obtained by connecting short portions of (6,6) and (10,0) nanotubes with ten pairs of pentagons and heptagons. The electronic structures of both small and large tori are determined within the framework of a tight-binding Hamiltonian, and their energies are compared. By application of London theory, it is shown that a magnetic field deeply influences the electronic structure of the carbon tori.