The electronic and optical properties of monolayer and bilayer graphene are investigated to verify the effects of interlayer interactions and external magnetic field. Monolayer graphene exhibits linear bands in the low-energy region. Then the interlayer interactions in bilayers change these bands into two pairs of parabolic bands, where the lower pair is slightly overlapped and the occupied states are asymmetric with respect to the unoccupied ones. The characteristics of zero-field electronic structures are directly reflected in the Landau levels. In monolayer and bilayer graphene, these levels can be classified into one and two groups, respectively. With respect to the optical transitions between the Landau levels, bilayer graphene possesses much richer spectral features in comparison with monolayers, such as four kinds of absorption channels and double-peaked absorption lines. The explicit wave functions can further elucidate the frequency-dependent absorption rates and the complex optical selection rules. These numerical calculations would be useful in identifying the optical measurements on graphene layers.
Structure and the Lamb-shift-like quantum splitting of the pseudo-zero-mode Landau levels in bilayer graphene
