Electronic states and transitions in twisted bilayer graphene from large-scale first-principles calculations

Using recently developed optimized basis sets for graphene in the Siesta density functional theory (DFT) code, we perform first-principles calculations of twisted bilayer graphene (TBG) consisting of over 10,000 atoms per moiré cell. We perform full atomic relaxation and band structure calculations in DFT and draw comparisons with continuum elastic model calculations. We compute the wavefunctions of the low energy bands and perform a Brillouin zone-wide characterization of the localization of the wavefunctions. By compressing the graphene layers, we show that smaller twist angles can be accessed through applied pressure, and by examining the changes in the symmetry of the wavefunctions upon layer compression, we observe a re-ordering of electronic states in the flat bands at an angle below the magic angle. Such a transition may affect the consequences of electron and hole doping in TBG. Using our first-principles results, we fit minimal tight-binding models and compute on-site and nearest neighbor Coulomb interactions as ingredients for more accurate effective models of correlated behavior in TBG.