Screening and Collective Modes in Disordered Graphene Antidot Lattices

The excitation spectrum and the collective modes of graphene antidot lattices (GALs) are studied in the context of a $pi$-band tight-binding model. The dynamical polarizability and dielectric function are calculated within the random phase approximation. The effect of different kinds of disorder, such as geometric and chemical disorder, are included in our calculations. We highlight the main differences of GALs with respect to single-layer graphene (SLG). Our results show that, in addition to the well-understood bulk plasmon in doped samples, inter-band plasmons appear in GALs. We further show that the static screening properties of undoped and doped GALs are quantitatively different from SLG.

Enhanced Screening in Chemically Functionalized Graphene

Resonant scatterers such as hydrogen adatoms can strongly enhance the low energy density of states in graphene. Here, we study the impact of these impurities on the electronic screening. We find a two-faced behavior: Kubo formula calculations reveal an increased dielectric function $varepsilon$ upon creation of midgap states but no metallic divergence of the static $varepsilon$ at small momentum transfer $qto 0$. This bad metal behavior manifests also in the dynamic polarization function and can be directly measured by means of electron energy loss spectroscopy. A new length scale $l_c$ beyond which screening is suppressed emerges, which we identify with the Anderson localization length.