Electronic properties of tubule forms of hexagonal ${\mathrm{BC}}_3$

First-principles and tight-binding electronic-structure calculations of hypothetical tubule forms of hexagonal ${\mathrm{BC}}_3$ have been performed. According to the total-energy and force calculations, stable atomic geometries of the ${\mathrm{BC}}_3$ tubules can be obtained by rolling hexagonal ${\mathrm{BC}}_3$ sheets keeping the C—C and C—B lengths at 1.42 and 1.55 Å, respectively. Since the energy increase upon tubule formation is smaller than that of carbon tubules, we conclude that the ${\mathrm{BC}}_3$ tubules are likely to form. The planar ${\mathrm{BC}}_3$ sheet has π and ${\mathrm{\pi }}^{\mathrm{*}}$ bands above the Fermi level, and this feature is retained in the electronic structures of the ${\mathrm{BC}}_3$ tubules. The influence of concentric formations of the ${\mathrm{BC}}_3$ tubules on their conductivities is also discussed.