Electronic structure of single-wall, multiwall, and filled carbon nanotubes

We determine the electronic structure of single-wall, multiwall, and filled carbon nanotubes using the local-density-functional formalism. In order to handle these extremely inhomogeneous systems of nested graphene cylinders with ${10}^3$–${10}^4$ valence electrons, we adopt a technique that discretizes the eigenvalue problem on a grid and yields simultaneously all occupied and unoccupied states. We apply this formalism to nanotubes, where the ionic background can be described by infinitely thin structureless cylindrical walls, and the electron distribution is subsequently obtained in a self-consistent manner. Comparison with parametrized calculations, which consider explicitly the atomic positions, proves that the essential features of the electronic structure in these systems do not depend on the exact atomic positions.