Self-consistent calculations of strain-induced band gap changes in semiconducting (n,0) carbon nanotubes

First-principles density-functional calculations of the electronic structure, energy band gaps (E-g), and strain-induced band gap changes in moderate-gap single-walled (n,0) carbon nanotubes (SWNTs) are presented. It is confirmed that (n,0) SWNTs fall into two classes depending upon n mod 3=1 or 2. E-g is always lower for "mod 1" than for "mod 2" SWNTs of similar diameter. For n < 10, strong curvature effects dominate E-g; from n=10 to 17, the E-g oscillations, amplified due to sigma-pi mixing, decrease and can be explained very well with a tight-binding model which includes trigonal warping. Under strain, the two families of semiconducting SWNTs are distinguished by equal and opposite energy shifts for these gaps. For (10,0) and (20,0) tubes, the potential surface and band gap changes are explored up to approximately +/- 6% strain or compression. For each strain value, full internal geometry relaxation is allowed. The calculated band gap changes are +/-(115 +/- 10) meV per 1% strain, positive for the mod 1 and negative for the mod 2 family, about 10% larger than the tight-binding result of +/- 97 meV and twice as large as the shift predicted from a tight-binding model that includes internal sublattice relaxation.