Classical and Quantum Plasmonics in Graphene Nanodisks: the Role of Edge States

Edge states are ubiquitous for many condensed matter systems with multicomponent wave functions. For example, edge states play a crucial role in transport in zigzag graphene nanoribbons. Here, we report microscopic calculations of quantum plasmonics in doped graphene nanodisks with zigzag edges. We express the nanodisk conductivity $\sigma(\omega)$ as a sum of the conventional bulk conductivity $\sigma_{\scriptscriptstyle\text{B}}(\omega)$, and a novel term $\sigma_{\scriptscriptstyle\text{E}}(\omega)$, corresponding to a coupling between the edge and bulk states. We show that the edge states give rise to a red-shift and broadening of the plasmon resonance, and that they often significantly impact the absorption efficiency. We further develop simplified models, incorporating nonlocal response within a hydrodynamical approach, which allow a semiquantitative description of plasmonics in the ultrasmall size regime. However, the polarization dependence is only given by fully microscopic models. The approach developed here should have many applications in other systems supporting edge states.