Electronic structure of silicon-based nanostructures

We have developed an unifying tight-binding Hamiltonian that can account for the electronic properties of recently proposed Si-based nanostructures, namely, Si graphene-like sheets and Si nanotubes. We considered the $sp^3s^*$ and $sp^{3}$ models up to first- and second-nearest neighbors, respectively. Our results show that the Si graphene-like sheets considered here are metals or zero-gap semiconductors, and that the corresponding Si nanotubes follow the so-called Hamada's rule [Phys. Rev. Lett. {\bf 68}, 1579 1992]. Comparison to a recent {\it ab initio} calculation is made.