  We have investigated the Coulomb screening properties and plasmon spectrum in
a bilayer graphene under a perpendicular electric bias. The bias voltage
applied between the two graphene layers opens a gap in the single particle
energy spectrum and modifies the many-body correlations and collective
excitations. The energy gap can soften the plasmon modes and lead to a
crossover of the plasmons from a Landau damped mode to being undamped. Plasmon
modes of long lifetime may be observable in experiments and may have potentials
for device applications.
