Polarizability and screening in chiral multilayer graphene

We calculate the static polarizability of multilayer graphene and study the effect of stacking arrangement, carrier density, and on-site energy difference on graphene screening properties. At low densities, the energy spectrum of multilayer graphene is described by a set of chiral two-dimensional electron systems, and the associated chiral nature determines the screening properties of multilayer graphene, showing very different behavior depending on whether the chirality index is even or odd. As density increases, the energy spectrum follows that of the monolayer graphene and thus the polarizability approaches that of monolayer graphene. The qualitative dependence of graphene polarizability on chirality and layering indicates the possibility of distinct graphene quantum phases as a function of the chirality index.