Analytical relation of band gaps to both chirality and diameter of single-wall carbon nanotubes

We present a tight-binding model of single-wall carbon nanotubes with curvature-modified hopping parameter ${\gamma }_i,$ from which an analytical relation of band gaps to both chirality and diameter is derived by developing a transfer matrix method. The results are in agreement with the experimental results obtained from scanning tunneling microscopy and scanning tunneling spectroscopy measurements by three groups.