  We investigate zero-temperature plasmon modes in a double-layer bilayer
graphene structure under a perpendicular electrostatic bias. The numerical
results demonstrate that there exist two collective modes which are undamped in
the long wavelength limit. The finite potential bias decreases remarkably the
plasmon energy in a wide range of wave-vector and makes plasmon branches become
Landau damped at a higher wave-vector as compared to unbiased case. We find
that the dependence of plasmon dispersions on the system parameters such as the
inter-layer separation and carrier density is similar in two cases with and
without electrostatic bias.
