Thermodynamic Properties of Gapped Graphene in the Presence of a Transverse Magnetic Field by Considering Holstein Phonons

Using the Holstein model, the thermodynamic properties of gapped graphene in the presence of electron–phonon (e–ph) coupling and a transverse magnetic field are investigated. In particular, we have obtained density of states (DOS), electronic heat capacity (EHC) and magnetic susceptibility (MS) of graphene, for which carbon atoms are substituted by boron and nitride atoms in the presence of Holstein phonons and a transverse magnetic field within the Green’s function approach in order to investigate the dynamic of Dirac fermions. To find the electronic self-energy due to e–ph coupling and the substituted foreign atoms, the self-consistent second order perturbation theory has been implemented. The band gap decreases with magnetic field and e–ph coupling. Also splitting of the quantum states (energy levels) due to the magnetic field is observed as double peaks in DOS (Van Hove singularities). As a remarkable result, EHC and MS are decreased due to the increase of scattering rate between electrons, an applied magnetic field, and e–ph coupling.