  The band structures and optical properties of AAB-stacked trilayer graphenes
(AAB-TLG) are calculated by the tight-binding model and gradient approximation.
Three pairs of the energy bands exhibit very different energy dispersions at
low energy and saddle points at the middle energy. At zero electric field,
$3$$^2$ excitation channels exist in both the low and middle frequencies, and
cause the very rich joint density of states (JDOS). However, the structures in
the JDOS do not appear in the absorption spectra completely. Due to the
different contributions from the velocity metric elements, some excitation
transitions disappear in the spectra. Furthermore, the frequency and the
existence of the absorption structures are affected by the increase of the
electric field from zero.
