In this work, we consider a graphene like background in braneworld scenario which is one of the interesting models in particle physics and cosmology. Indeed, this paper is an application of holography in condensed matter physics. We use the geometric form of the potential which helps us to obtain field equations and solve it to obtain the energy spectrum. In that case, we calculate superpotential and energy density of this model. Thermodynamical study of this model suggests that the entropy should be modified due to the large-scale corrections. An important point is the stability of this model in braneworld scenario. We study model stability by two separated methods. We calculate the heat capacity, Gibbs and Helmholtz free energy to analyze thermodynamics stability; then, we consider small perturbations in graphene like metric background to investigate gravitational stability. We nd that the model is completely stable unless in very low temperatures where the graphene structure may break. Hence, we con rm that our braneworld model is thermodynamically stable and also small perturbations yields to an oscillation around the equilibrium point.
