Tuning thermodynamics properties of AA stacked bilayer graphene due to lattice vibrations and magnetic field

Electronic and thermodynamic properties of simple stacked bilayer graphene taking into account the effects of interaction between electrons and Einstein phonons have been addressed. Specially we study the temperature dependence of Pauli paramagnetic spin susceptibility and specific heat of the structure. Also the energy dependence of density of states due to effects of electron–phonon coupling strength and bias voltage has been analyzed. The effects of electron–phonon coupling strength and external magnetic field on thermodynamic properties of the system have been studied. 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. The specific heat and spin susceptibility of bilayer graphene in the presence of electron–phonon coupling can be readily found using interacting Green’s function. We find numerical results for temperature dependence of specific heat and spin susceptibility in the presence of Holstein phonons. Our results show increasing electron–phonon coupling leads to enhance zero temperature limit of spin susceptibility of bilayer graphene. Also the height of peak in temperature dependence of specific heat reduces with increase of bias voltage, coupling strength and magnetic field.