Dielectric screening and plasmon resonances in bilayer graphene

The plasmon structure of intrinsic and extrinsic bilayer graphene is investigated, in the framework of {\it ab initio} time-dependent density-functional theory~(TDDFT) at the level of the random-phase approximation~(RPA). A two-step scheme is adopted, where the electronic ground-state of a periodically repeated slab of bilayer graphene is first determined with full inclusion of the anisotropic band structure and the inter-layer interaction; a Dyson-like equation is then solved self-consistently in order to calculate the so-called density-response function of the many-electron system. A two-dimensional correction is subsequently applied, in order to eliminate the artificial interaction between the replicas. The energy range below $\sim 30$~eV is explored, focussing on the spectrum of single-particle excitations and plasmon resonances induced by external electrons or photons. The high-energy loss features of the $\pi$ and $\sigma+\pi$ plasmons, particularly their anisotropic dispersions, are predicted and discussed in relation with previous calculations and experiments performed on monolayer and bilayer graphene. At the low-energy end, the energy-loss function is found to be (i) very sensitive to the injected charge carrier density in doped bilayer graphene and (ii) highly anisotropic. Furthermore, various plasmon modes are predicted to exist and are analyzed with reference to the design of novel nanodevices.