Absorption spectra of asymmetric bilayer graphene nanoribbons

The low-frequency optical absorption properties of asymmetric bilayer graphene nanoribbons in an external electric field are investigated by using the gradient approximation. This study shows that the optical absorption spectra exhibit rich prominent peaks structure mainly owing to the one-dimensional subbands. For asymmetric bilayer graphene nanoribbons without the interlayer atomic interactions, there exists an optical selection rule which is caused by the spatial symmetry of the wave functions. Furthermore, such selection rule does not exist with the presence of the interlayer hoppings or an external electric field. In addition, the number, spectral intensity, and energy of the absorption peaks are strongly dependent on the interlayer atomic interactions, the magnitude and direction of the electric field, the relative displacement between the nanoribbons, and the ribbon width. The presented results can be validated by absorption spectroscopy measurements.