Ab initio quasiparticle bandstructure of ABA and ABC-stacked graphene trilayers

We obtain the quasiparticle band structure of ABA and ABC-stacked graphene trilayers through ab initio density functional theory (DFT) and many-body quasiparticle calculations within the GW approximation. To interpret our results, we fit the DFT and GW $\pi$ bands to a low energy tight-binding model, which is found to reproduce very well the observed features near the K point. The values of the extracted hopping parameters are reported and compared with available theoretical and experimental data. For both stackings, the self energy corrections lead to a renormalization of the Fermi velocity, an effect also observed in previous calculations on monolayer graphene. They also increase the separation between the higher energy bands, which is proportional to the nearest neighbor interlayer hopping parameter $\gamma_1$. Both features are brought to closer agreement with experiment through the self energy corrections. Finally, other effects, such as trigonal warping, electron-hole asymmetry and energy gaps are discussed in terms of the associated parameters.