Journal of Superconductivity and Novel Magnetism

, Volume 32, Issue 2, pp 219–228 | Cite as

Theoretical Model Study of Interplay of Coulomb Interaction and Electron-Phonon Interaction in the Thermal Properties of Monolayer Graphene

  • Sivabrata Sahu
  • G. C. RoutEmail author
Original Paper


We 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 \(\tilde {U}=U-2t_{1}\lambda \) and \(\tilde {t}_{1}=t_{1}e^{\frac {-t_{1}\lambda } {\omega _{0}}}\), where U, t1, λ and ω0 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.


Graphene Coulomb potential Electron-phonon interaction Specific heat 


Funding Information

This work is supported by the Centre of Excellence for Novel Energy Materials (CENEMA) under the Ministry of Human Resources Development of India and School of Basic Sciences, Indian Institute of Technology, Bhubaneswar, India.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Centre of Excellence for Novel Energy Material (CENEMA), School of Basic SciencesIndian Institute of Technology BhubaneswarBhubaneswarIndia
  2. 2.Condensed Matter Physics Group, Physics EnclaveBhubaneswarIndia

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