  Generating photogalvanic effects in centrosymmetric materials can provide new
opportunities for developing passive photodetectors and energy harvesting
devices. In this work, we investigate the photogalvanic effects in
centrosymmetric two-dimensional materials, AA- and AB-stacked bilayer graphene,
by applying an external gate voltage to break the symmetry. Using a
tight-binding model to describe the electronic states, the injection
coefficients for circular photogalvanic effects and shift conductivities for
linear photogalvanic effects are calculated for both materials with light
wavelengths ranging from THz to visible. We find that gate voltage induced
photogalvanic effects can be very significant for AB-stacked bilayer graphene,
with generating a maximal dc current in the order of mA for a 1 $\mu$m wide
sample illuminated by a light intensity of 0.1 GW/cm$^2$, which is determined
by the optical transition around the band gap and van Hove singularity points.
Although such effects in AA-stacked bilayer graphene are about two orders of
magnitude smaller than those in AB-stacked bilayer graphene, the spectrum is
interestingly limited in a very narrow photon energy window, which is
associated with the interlayer coupling strength. A detailed analysis of the
light polarization dependence is also performed. The gate voltage and chemical
potential can be used to effectively control the photogalvanic effects.
