Primary metallic or small-gap semiconducting nanotubes are tubes with band
gaps that arise solely from breaking the bond symmetry due to curvature. We
derive an analytic expression for these gaps by considering how a general
symmetry breaking opens a gap in nanotubes with a well-defined chiral wrapp
ing vector. This approach provides a straightforward way to include all typ
es of symmetry-breaking effects, resulting in a simple unified gap equation
as a function of chirality and deformations.