  We investigate the effect of on-site Coulomb repulsion $U$ on the band gap of
the electrically gated bilayer graphene by employing coherent potential
approximation in the paramagnetic state, based on an ionic two-layer Hubbard
model. We find that, while either the on-site Coulomb repulsion $U$ or the
external perpendicular electric field $E$ alone will favor a gapped state in
the bilayer graphene, competition between them will surprisingly lead to a
suppression of the gap amplitude. Our results can be applied to understand the
discrepancies of gap size reported from optical and transport measurements, as
well as the puzzling features observed in angular resolved photoemission
spectroscopic study.
