Transverse spin susceptibilities of doped armchair graphene nanoribbon due to electron-phonon interaction

Abstract

We present the behaviors of both dynamical and static charge susceptibilities of undoped armchair graphene nanoribbon using the Green's function approach in the context of Holstein model Hamiltonian. Specially, the effects of magnetic field and electron-phonon coupling strength on the plasmon modes of armchair graphene nanoribbon are investigated via calculating correlation function of charge density operators. Random phase approximation has been implemented to find the interacting dynamical charge susceptibility. The electrons in this systems interacts with each other by mediation of dispersionless Holstein phonons. Our results show the increase of electron phonon coupling strength leads to decrease intensity of charge collective mode Also the frequency position of the collective mode tends to higher frequencies with electron phonon coupling. We also show that the frequency positions of plasmon mode of armchair nanoribbon are not affected by increase of magnetic field. Furthermore the number of collective excitation mode increases with ribbon width in the presence of electron-phonon interaction. Finally the temperature dependence of static charge structure factor of armchair graphene nanoribbon is studied. The effects of both magnetic field, ribbon width and electron-phonon interaction on the static structure factor are addressed in details.