Curvature, hybridization, and STM images of carbon nanotubes

The curvature effects in carbon nanotubes are studied analytically as a function of chirality. The $\pi$ orbitals are found to be significantly rehybridized in all tubes, so that they are never normal to the tubes’ surface. This results in a curvature induced gap in the electronic band structure, which turns out to be larger than previous estimates. The tilting of the $\pi$ orbitals should be observable by atomic resolution scanning tunneling microscopy measurements.