  We developed the generalized tight-binding model to study the
magneto-electronic properties of AAB-stacked trilayer graphene. Three groups of
Landau levels (LLs) are characterized by the dominating subenvelope function on
distinct sublattices. Each LL group could be further divided into two
sub-groups in which the wavefunctions are, respectively, localized at 2/6 (5/6)
and 4/6 (1/6) of the total length of the enlarged unit cell. The unoccupied
conduction and the occupied valence LLs in each sub-group behave similarly. For
the first group, there exist certain important differences between the two
sub-groups, including the LL energy spacings, quantum numbers, spatial
distributions of the LL wavefunctions, and the field-dependent energy spectra.
The LL crossings and anticrossings occur frequently in each sub-group during
the variation of field strengths, which thus leads to the very complex energy
spectra and the seriously distorted wavefunctions. Also, the density of states
(DOS) exhibits rich symmetric peak structures. The predicted results could be
directly examined by experimental measurements. The magnetic quantization is
quite different among the AAB-, AAA-, ABA-, and ABC-stacked configurations.
