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On a lattice model, we study the possibility of existence of gapped brokeninversion symmetry phase (GBISP) of electrons with long-range Coulombinteraction in bilayer graphene using both self-consistent Hartree-Fockapproximation (SCHFA) and the renormalized-ring-diagram approximation (RRDA).RRDA takes into account the charge-density fluctuations beyond the mean field.While GBISP at low temperature and low carrier concentration is predicted bySCHFA, we show here the state can be destroyed by the charge-densityfluctuations. We also present a numerical algorithm for calculating theself-energy of electrons with the singular long-range Coulomb interaction onthe lattice model.

Absence of broken inversion symmetry phase of electrons in bilayer graphene under charge density fluctuations