<p>This paper developed a photon propulsion model for the graphene solar-photon sail based on the Auger-like mechanism and investigated its application to the Sun-Earth systems. Firstly, the optical propulsion model of the graphene solar-photon sail was established based on the kinetic energy of photons using classical Maxwell electromagnetism to calculate the number of photons. The effect of the characteristic parameters of the graphene solar-photon sail on the propulsive acceleration and the artificial equilibrium points was analyzed in the Sun-Earth circular restricted three-body problem. Then, the trends of the family of halo orbits around the artificial equilibrium points and their stability were analyzed. Finally, the numerical simulation was conducted to verify the feasibility of the proposed graphene solar-photon sail model and its application.</p>