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Effects of correlations on honeycomb lattice in ionic-Hubbard Model

In a honeycomb lattice the symmetry has been broken by adding an ionic potential and a single-particle gap was generated in the spectrum. We have employed the iterative perturbation theory (IPT) in dynamical mean field approximation method to study the effects of competition between $U$ and $Δ$ on energy gap and renormalized Fermi velocity. We found, the competition between the single-particle gap parameter and the Hubbard potential closed the energy gap and restored the semi-metal phase, then the gap is opened again in Mott insulator phase. For a fixed $Δ$ by increasing $U$, the renormalized Fermi velocity $\tilde{v_F}$ is decreased, but change in $Δ$, for a fixed $U$, has no effects on $\tilde{v_F}$. The difference in filling factor is calculated for various number of $U, ~Δ$. The results of this study can be implicated for gapped graphene e.g. hydrogenated graphene.