Polaron-induced modifications in the linear and nonlinear optical properties of graphene under electric and magnetic fields

Polarons are the primary charge carriers in organic materials. A deep understanding of their properties can open channels for novel optoelectronic applications. By applying electric and magnetic fields, we investigate the influence of polaron interactions on the linear and nonlinear optical properties of a graphene monolayer between a substrate and air. Using the density matrix approach, we derive the linear and nonlinear optical absorption coefficients and the relative refractive index by incorporating the zero-energy level. Our numerical results reveal that the polaron effect and the magnetic field induce shifts in the peak positions of the optical absorption coefficients and refractive index. Moreover, while the presence of electric and magnetic fields significantly alters the amplitude of the absorption coefficients, only the magnetic field affects the refractive index amplitude. Additionally, we find that the magnetic field amplifies the influence of surface optical phonons on the optical properties of graphene. These findings provide deeper insights into the optical behavior of graphene in external fields, which could be relevant for optoelectronic applications.