Density-functional calculations predict half-metallicity in zigzag single-walled carbon nanotubes of finite length with the two ends saturated with hydrogen. We have analyzed the change of the $\alpha$- and $\beta$-spin electronic gaps under the influence of an electric field applied along the nanotube axis. The half-metallic behavior, in which the electronic gap is zero for one spin flavor and nonzero for the other, is obtained for a critical electric field of $3.0/w\text{V}/\text{Å}$, where $w$ is the length of the nanotube. This critical field is the same as that predicted for graphene nanoribbons. By a detailed analysis of the spin structure of the ground state, we show the relevance of the edge states, electronic states spatially localized at the carbon atoms of the nanotube boundaries, on the on-set of half-metallicity, and on the magnetic properties of the finite semiconducting zigzag nanotubes.

• Received 7 March 2008

DOI:https://doi.org/10.1103/PhysRevB.78.035432