Why does carbon nanotube index determine whether it is metallic?

[gravenewworld]

We briefly got an intro to carbon nanotubes in our nanomaterials class, and the professor only briefly introduced carbon nanotubes and the ways to describe the different types of tubes via their indices. Why is it that if the indices of the carbon nanotube have the property such that n-m = 3*integer or (n,0) , the carbon nanotube is metallic, otherwise it is a semiconductor. I find it quite fascinating how the folding geometry can affect the properties of the material. It was never explained to us why, however.

 

[miketout]

While I haven't seen a complete physics-based explanation anywhere, it seems clear that the armchair and zigzag CNTs are metallic and the others are varying degrees of semiconductor.

I do have a hypothesis, which is that since a conjugated, conductive bond has the most electron mobility when it is planar, the armchair and zigzag CNTs have vertical bonds, aligned with the length of the CNT, allowing them to be completely planar. Different chiralities have varying degrees of ability to manifest planar bonds, which I suspect has a lot to do with their conductivity characteristics.

Like I said, I haven't seen the reason explained in academic literature, though it likely is somewhere, but I happened to be in a discussion about this today, and we agreed that this explanation would make sense.