Electron–phonon coupling effects on optical absorption of armchair graphene nanoribbon in the presence of magnetic field

Electronic and optical properties of armchair graphene nanoribbon 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 nanoribbon. We study the frequency dependence of absorption rate of electromagnetic wave in armchair graphene nanoribbon 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 armchair graphene nanoribbon due to electron–phonon coupling can be readily found using interacting Green’s function based on Kubo formula. We find numerical results for chemical potential dependence of optical absorption rate in the presence of Holstein phonons. Our results show turning on electron–phonon coupling leads to reduction of band gap in density of states of the armchair nanoribbon. Also a valley is found in frequency dependence of optical absorption rate of armchair nanoribbon due to electron–phonon coupling and magnetic field. Moreover, the chemical potential dependence of optical absorption includes a peak so that the intensity of peak reduces with coupling strength.