Sahu S.Rout G.C.2025-02-172019http://dx.doi.org/10.1007/s10948-018-4722-8https://idr.iitbbs.ac.in/handle/2008/2346We propose here a tight-binding (TB) model Hamiltonian for monolayer graphene-on-substrate describing the nearest-neighbor-hopping, on-site Coulomb interaction on the sub-lattices and the electron-phonon interaction under the high-frequency limit of phonon vibration. Applying Lang-Firsov canonical transformation, the electron and phonon systems are decoupled in the atomic Hamiltonian, such that the effective Coulomb interaction and effective nearest-neighbor-hopping integral respectively appear as ?= U? 2 t 1 ? and t~1=t1e?t1??0, where U, t 1 , ? and ? 0 are respectively Coulomb energy, nearest-neighbor-hopping integral, electron-phonon (e-ph) coupling and phonon frequency. The effective Coulomb interaction in the Hamiltonian is considered within mean-field approximation. The Hamiltonian is solved by Zubarev�s Green�s function technique. The temperature-dependent electronic entropy and specific heat are calculated from the free energy of graphene system and are computed numerically. The temperature-dependent electronic specific heat exhibits a charge gap peak at room temperature arising due to the effect of Coulomb interaction and electron-phonon interaction. The evolution of these peaks in specific heat is investigated by varying the model parameters of the system. � 2018, Springer Science+Business Media, LLC, part of Springer Nature.enCoulomb potentialElectron-phonon interactionGrapheneSpecific heatArticle