Smallest Nanotube: Breaking the Symmetry of ${\mathit{sp}}^3$ Bonds in Tubular Geometries

We describe how $s{p}^2$ carbon, threefold coordinated by other carbons, can be replaced by $s{p}^3$ carbon, also threefold carbon coordinated, to produce extremely small-diameter ( $\sim 0.4\mathrm{nm}$) carbon nanowires with only minimal bond-angle distortion. Under a naming convention analogous to that for ordinary carbon nanotubes, the smallest $s{p}^3$ tubes have wrapping indices $(3,0)$ and $(2,2)$. These systems have large band gaps and a stiffness larger even than that of traditional $s{p}^2$-bonded carbon nanotubes. They therefore form the stiffest one-dimensional systems known.