Abstract
We derive a material-realistic real-space many-body Hamiltonian for twisted bilayer graphene from first principles, including both single-particle hopping terms for $p_z$ electrons and their long-range Coulomb interaction. By disentangling low- and high-energy subspaces of the electronic dispersion, we are able to utilize state-of-the-art constrained Random Phase Approximation calculations to reliably describe the non-local background screening from the high-energy $s$, $p_x$, and $p_y$ electron states which we find to be independent of the bilayer stacking and thus of the twisting angle. The twist-dependent low-energy screening from $p_z$ states is subsequently added to obtain a full screening model. We use this modeling scheme to study plasmons in electron-doped twisted bilayer graphene supercells. We find that the finite system size yields discretized plasmonic levels, which are controlled by the system size, doping level, and twisting angle. This tunability together with atomic-like charge distributions of some of the excitations renders these plasmonic excitations remarkably similar to the electronic states in electronic quantum dots. To emphasize this analogy in the following we refer to these supercells as \emph{plasmonic quantum dots}. Based on a careful comparison to pristine AB-stacked bilayer graphene plasmons, we show that two kinds of plasmonic excitations arise, which differ in their layer polarization. Depending on this layer polarization the resulting plasmonic quantum dot states are either significantly or barely dependent on the twisting angle. Due to their tunability and their coupling to light, these plasmonic quantum dots form a versatile and promising platform for tailored light-matter interactions.
General continuum model for twisted bilayer graphene and arbitrary smooth deformations
