Photoinduced Dynamical Band Gap in Graphene: The Effects of Electron-Phonon and Spin-Orbit Interaction

The combined effects of electron-A(1g) phonon and Rashba spin-orbit couplings on the electronic spectrum of graphene in the presence of Haldane interaction induced by photo-irradiation have been studied. A Frohlich-type Hamiltonian has been proposed to model these interactions, and then a diagonalization procedure based on the Lee-Low-Pines (LLP) theory which includes two successive unitary transformations has been applied. The results show that combined effects arising from the Rashba spin-orbit interaction and electron-A(1g) phonon interaction in the presence of Haldane interaction remove the valley degeneracy of electronic bands, and thus allow one to tune the resulting band gap just by adjusting the associated strengths of the interactions.