Polarization-dependent optical excitations in AB-stacked graphite

The band structure of AB-stacked graphite exhibits two pairs of parabolic bands, where the band-edge states induce the peaks and shoulders in the density of states and in the joint density of states (JDOS). The dipole matrix element M$^{cv}$ plays an important role in the relationship between the spectral function A($\omega$) and JDOS. It is strongly dependent on the polarization directions ${\bf {\hat{E}}}$ of the laser beams, showing a anisotropic property. The optical excitations do not fully reflect the special structures of JDOS. For ${\bf {\hat {E}}}$ on the graphene plane, A($\omega$)$'$s are isotropic and include one sharp peak and some shoulders. As for ${\bf {\hat {E}}}$ along the stacking direction, A($\omega$) is much weaker, and only shows a broadened peak. The spectra contrast sharply with those of AA-stacked graphite.