Inhomogeneous optical absorption around the K point in graphite and carbon nanotubes

The optical absorption spectra of π electrons are calculated for graphite and carbon nanotubes. Particular attention is paid to the processes contributing to the optical absorption as a function of the electron wave vector k and light polarization direction. The optical absorption amplitude around the K point in the Brillouin zone has a node in the two-dimensional Brillouin zone of graphite. The formula for the absorption scattering matrix around the K point is given analytically by expanding the matrix element into a Taylor series. The chirality dependence of the absorption matrix element of a single-wall carbon nanotube is presented.