Band gap scaling laws in group IV nanotubes

By using the first-principles calculations, the band gap properties of nanotubes formed by group IV elements have been investigated systemically. Our results reveal that for armchair nanotubes, the energy gaps at K points in the Brillouin zone decrease as 1/r scaling law with the radii (r) increasing, while they are scaled by -1/r ² + C at Γ points, here, C is a constant. Further studies show that such scaling law of K points is independent of both the chiral vector and the type of elements. Therefore, the band gaps of nanotubes for a given radius can be determined by these scaling laws easily. Interestingly, we also predict the existence of indirect band gap for both germanium and tin nanotubes. Our new findings provide an efficient way to determine the band gaps of group IV element nanotubes by knowing the radii, as well as to facilitate the design of functional nanodevices.