Screening, Kohn anomaly, Friedel oscillation, and RKKY interaction in bilayer graphene.

We calculate the screening function in bilayer graphene (BLG) in both the intrinsic (undoped) and the extrinsic (doped) regimes within the random phase approximation, comparing our results with the corresponding single layer graphene and the regular two-dimensional electron gas. We find that the Kohn anomaly is strongly enhanced in BLG. We also discuss the Friedel oscillation and the RKKY interaction, which are associated with the nonanalytic behavior of the screening function at q=2k(F). We find that the Kohn anomaly, the Friedel oscillation, and the RKKY interaction are all qualitatively different in the BLG compared with the single layer graphene and the two-dimensional electron gas.