Nearly free electron superatom states of carbon and boron nitride nanotubes

By first-principles theory we study the nearly free electron (NFE) states of carbon and boron nitride nanotubes. In addition to the well-known π bands, we found a series of one-dimensional (1D) NFE bands with on-axis spatial distributions, which resemble atomic orbitals projected onto a plane. These bands are 1D counterparts of the recently discovered superatom orbitals of 0D fullerenes. In addition to the previously reported lowest energy NFE state with the angular quantum number l = 0 corresponding to s atomic orbital character, we find higher energy NFE bands with l > 0 corresponding to the p, d, etc., orbitals. We show that these atom-like states of nanotubes originate from the many-body screening, which is responsible for the image potential of the parent two-dimensional (2D) graphene or BN sheets. With a model potential that combines the short-range exchange-correlation and the long-range Coulomb interactions, we reproduce the energies and radial wave function profiles of the NFE states from the density functional theory calculations. When the nanotube radius exceeds the radial extent on NFE states, the NFE state energies converge to those of image potential states of the parent 2D molecular sheets. To explore possible applications in molecular electronics that take advantage of the NFE properties of nanotube building blocks, we investigate the modification of NFE states by transverse electric fields, alkali metal encapsulation, and lateral and concentric nanotube dimerization.