Analytical approach to optical absorption in carbon nanotubes

We derive an analytic expression for the optical matrix elements of carbon nanotubes and calculate their optical absorption spectra within the tight-binding approximation. For zigzag nanotubes we present an analytical result for the absorption coefficient. Metallic nanotubes have an optical band gap regardless of their chiral angle. The optical absorption intensity increases by up to 10% from zigzag to armchair nanotubes. This trend is in agreement with experiment, although its magnitude is underestimated. We predict a strong absorption peak in the high-energy spectra of certain zigzag nanotubes that can be used to identify the tubes experimentally.