Universal band gap modulation by radial deformation in semiconductor single-walled carbon nanotubes

We report on a universal band gap modulation by radial deformation found for semiconductor single-walled carbon nanotubes (SWNTs). The plausible radial deformation of an individual SWNT under hydrostatic pressure is predicted using the method developed in the previous work [M. Hasegawa and K. Nishidate, Phys. Rev. B 74, 115401 (2006)]. It is found by ab initio electronic-structure calculations that the band gap of zigzag SWNTs is dictated by the shape of the high-curvature edge region of a deformed cross section perpendicular to the tube axis: If we let Rₘᵢₙ be an averaged curvature radius in that region, the band gap at the Γ point remains almost unchanged when Rₘᵢₙ≥3.2, and its closure occurs at Rₘᵢₙ≈2.4 irrespective of tube size and cross-sectional shape as a whole. It is also confirmed that the band gap closure is accompanied by the concentration, in the high-curvature region, of the lowest conduction state at the Γ point. Possible implications of these results are discussed.