Interwall interaction and electronic structure of double-walled BN nanotubes

We report first-principles total-energy electronic-structure calculations that provide energetics and electronic structures of double-walled BN nanotubes, $\mathrm{}(n,0\mathrm{})\mathrm{}$@(15,0) and $\mathrm{}(m,0\mathrm{})\mathrm{}$@(20,0). We find that the most favorable double-walled nanotubes studied here are (7,0)@(15,0) and (12,0)@(20,0) in which the interwall distances are about $3\hspace{0.5em}\AA .$ The electronic energy bands around the Fermi energy depend interestingly on the tube radii due to the hybridization between $\sigma$ and $\pi$ states. We also find that the nearly-free-electron states of the nanotubes induce peculiar charge redistribution in the interwall region.