Effects of doping and bias voltage on the screening in AAA-stacked trilayer graphene

•We study the screening in AAA-stacked trilayer graphene in undoped, doped and biased regimes.•We show that its static polarization is a combination of that of undoped and doped graphene.•We show that its screening properties can be tuned electrically.•We calculate the power law decay of the screened Coulomb potential from a charged impurity.

We calculate the static polarization of AAA-stacked trilayer graphene (TLG) and study its screening properties within the random phase approximation (RPA) in all undoped, doped and biased regimes. We find that the static polarization of undoped AAA-stacked TLG is a combination of the doped and undoped single-layer graphene static polarization. This leads to an enhancement of the dielectric background constant along a Thomas–Fermi screening with the Thomas–Fermi wave vector which is independent of carrier concentrations and a 1/r31/r3 power law decay for the long-distance behavior of the screened Coulomb potential. We show that effects of a bias voltage can be taken into account by a renormalization of the interlayer hopping energy to a new bias-voltage-dependent value, indicating screening properties of AAA-stacked TLG can be tuned electrically. We also find that screening properties of doped AAA-stacked TLG, when μ   exceeds 2γ, are similar to that of doped SLG only depending on doping. While for μ<2γ, its screening properties are combination of SLG and AA-stacked bilayer graphene screening properties and they are determined by doping and the interlayer hopping energy.