We apply first-principles calculations to study the electronic structure of boron nitride nanocones with disclinations of different angles $theta=npi/3$. Nanocones with odd values of $n$ present antiphase boundaries that cause a reduction of the work function of the nanocones, relative to the bulk BN value, by as much as 2 eV. In contrast, nanocones with even values of $n$ do not have such defects and present work functions that are very similar to the BN bulk value. These results should have strong consequences for the field emission properties of boron nitride nanocones and nanotubes.
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