  Bilayer graphene (BLG) with a tunable bandgap appears interesting as an
alternative to graphene for practical applications, thus its transport
properties are being actively pursued. Using density functional theory and
perturbation analysis, we investigated, under an external electric field, the
electronic properties of BLGs in various stackings relevant to recently
observed complex structures. We established the first phase diagram summarizing
the stacking-dependent gap openings of BLGs for a given field. We further
identified high-density midgap states, localized on grain boundaries, even
under a strong field, which can considerably reduce overall transport gap.
