Optical absorption of biased bilayer graphene due to electron–phonon coupling and longitudinal magnetic field

Electronic and optical properties of both simple and bernal stacked bilayer graphenes taking into account the effects of interaction between electrons and Einstein phonons have been addressed. Also the magnetic field is applied perpendicular to the plane of bilayer graphene. We study the frequency dependence of absorption rate of electromagnetic wave in bilayer graphene due to magnetic field strength and electron–phonon coupling. Green’s function method has been implemented to obtain electronic properties of the system in the context of Holstein model Hamiltonian. One loop electronic self-energy of the model Hamiltonian has been obtained in order to find interacting electronic Green’s function. Optical absorption rate of electromagnetic wave in bilayer graphene due to electron–phonon coupling can be readily found using interacting Green’s function based on Kubo formula. Our results show turning on electron–phonon coupling leads to reduction of band gap in density of states of bernal stacked bilayer graphene. Also a peak appears in frequency dependence of optical absorption rate of bernal stacked bilayer graphene due to electron–phonon coupling and magnetic field. The Drude wight in absorption rate of electromagnetic wave increases with magnetic field with increase of magnetic field strength for stacking types of bilayer graphene.