Cumulated Effects of Magnetic Field, Electron–Phonon and Spin–Orbit Interaction on Thermodynamics Properties of Mono Layer Graphene

We study the electron–phonon and Rashba spin–orbit coupling effects on thermodynamic properties of a monolayer graphene under magnetic field. We propose a diagonalization procedure to solve the Fröhlich-type Hamiltonian based on the Lee–Low–Pines theory. The study reveals that, the cyclotron frequency, Debye cut-off wavenumber (DCOW) and Rashba spin–orbit coupling (RSOC) modulate the thermodynamic properties through Tsallis formalism for different substrates. It is also found that RSOC induce a gap formation while dropping the disorder thus rising up the potential application.