Model Study of Band Gap Opening in Graphene by Electron–Electron and Electron–Phonon Interaction in High Frequency Range
We report here a microscopic model study of band gap opening in graphene by electron–electron interaction and electron–phonon interaction in high frequency limit of phonon vibration. The Hamiltonian represents a tight-binding nearest-neighbor π electron hopping of electrons in graphene plane. The Hamiltonian is further enriched by the substrate effect which enhances the energy of +Δ at A sub-lattice and decreases the energy –Δ at B sub-lattice and there by introducing a gap of 2Δ in the order of few meV energy. The electron–electron repulsive interaction considered here is taken within a mean-field approximation and this introduces a magnetic gap in the graphene. The electrons in the graphene plane interact with the phonons present in the polarized superstrate and thereby introduce electron–phonon interaction which modulates the other interactions. We study here the effect of Coulomb interaction on the band gap induced substrate effect in presence of electron–phonon interactions in high frequency vibration limits. The results are discussed in the text.
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Document Type: Research Article
Publication date: February 1, 2016
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