Gate voltage induced injection and shift currents in AA- and AB-stacked bilayer graphene

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.