  We investigate the stability of boron nitride conical sheets of nanometer
size, using first-principles calculations. Our results indicate that cones with
an antiphase boundary (a line defect that contains either B-B or N-N bonds) can
be more stable than those without one. We also find that doping the antiphase
boundaries with carbon can enhance their stability, leading also to the
appearance of localized states in the bandgap. Among the structures we
considered, the one with the smallest formation energy is a cone with a
carbon-modified antiphase boundary that presents a spin splitting of about 0.5
eV at the Fermi level.
