Electronic excitations in quasi-2D crystals: What theoretical quantities are relevant to experiment?

The ab initio theory of electronic excitations in atomically thin (quasi-two-dimensional (Q2D)) crystals presents extra challenges in comparison to both the bulk and purely 2D cases. We argue that the conventionally used energy-loss function (where 1/ε(q/ω), and are the dielectric function, the momentum, and the energy transfer, respectively) is not, generally speaking, the suitable quantity for the interpretation of the electron-energy loss spectroscopy (EELS) in the Q2D case, and we construct different functions pertinent to the EELS experiments on Q2D crystals. Secondly, we emphasize the importance and develop a convenient procedure of the elimination of the spurious inter-layer interaction inherent to the use of the 3D super-cell method for the calculation of excitations in Q2D crystals. Thirdly, we resolve the existing controversy in the interpretation of the so-called π and excitations in monolayer graphene by demonstrating that both dispersive collective excitations (plasmons) and non-dispersive single-particle (inter-band) transitions fall in the same energy ranges, where they strongly influence each other.