Study of non-extensive entropy of bound polaron in monolayer graphene

An electron is coupled to the longitudinal acoustic phonon on the surface of the graphene with Coulomb impurity has been considered. The ground state energy of the polaron has been obtained using the variational method. Tsallis entropy variations have been studied with magnetic field, temperature, Coulomb bound parameter and the charge for different substances such as SiC, HfO2, h-BN, and SiO2. It is found that the entropy increases with enhancing temperature and Coulomb bound parameter. But, it decreases with enhancing the charge. The entropy increases with decreasing the non-extensive parameter q for all substances at constant Coulomb bound parameter.