Effects of electron-phonon and Rashba spin-orbit coupling on thermodynamic properties of doped graphene under external field

We study the effects of electron-phonon and Rashba spin-orbit coupling on thermodynamic properties of monolayer graphene under external field. We use Green function and Lee–Low–Pines theory to obtain the density of state and the low lying energy level. The effects of electron-phonon coupling, cyclotron frequency, laser frequency, Debye cut-off wavenumber (DCOW) and Rashba spin-orbit coupling (RSOC) on Thermodynamics properties such as internal energy, specific heat, magnetic susceptibility, free energy and entropy are studied. It’s found that there is a competition between gap formation by RSOC through coupling with the substrates and gap suppression due to disorder. thermal energy can be obtained by using high value of DCOW, RSOC and cyclotron frequency. The entropy decreases and reaches its lowest values in particular with h-BN substrate. For high values of Rashba parameter and laser frequency the entropy exhibits saturation. Thus, the presence of the Rashba parameter coupling with external field reduces disorder, improves coherence and stability in graphene.