Quantum dot-like plasmonic modes in twisted bilayer graphene supercells

We derive a material-realistic real-space many-body Hamiltonian for twisted bilayer graphene from first principles, including both single-particle hopping terms $p_z$ electrons and long-range Coulomb interactions. By disentangling low- high-energy subspaces of the electronic dispersion, we are able to utilize state-of-the-art constrained Random Phase Approximation calculations reliably describe non-local background screening $s$, $p_x$, $p_y$ electron states arbitrary twist angles. The twist-dependent low-energy is subsequently added obtain full model. use this approach study plasmonic patterns in electron-doped supercells find, next classical dipole-like modes, also twist-angle-dependent quantum-dot-like excitations with $s$ $p$ symmetries. Based on their inter-layer charge modulations footprints energy loss spectrum, can classify these modes into "bright" "dark" states, which show different dependencies angle.