Relaxation effects in twisted bilayer graphene: A multiscale approach

We present a multiscale density functional theory (DFT) informed molecular dynamics and tight-binding approach to capture the interdependent atomic and electronic structures of twisted bilayer graphene. We calibrate the flat band magic angle to be at θM=1.08° by rescaling the interlayer tunneling for different atomic structure relaxation models as a way to resolve the indeterminacy of existing atomic and electronic structure models whose predicted magic angles vary widely between 0.9° and 1.3°. The interatomic force fields are built using input from various stacking and interlayer distance-dependent DFT total energies including the exact exchange and random phase approximation (EXX+RPA). We use a Fermi velocity of υF≃106 m/s for graphene that is enhanced by ∼15% over the local density approximation (LDA) values. Based on this atomic and electronic structure model we obtain high-resolution spectral functions comparable with experimental angle-resolved photoemission spectroscopy. Our analysis of the interdependence between the atomic and electronic structures indicates that the intralayer elastic parameters compatible with the DFT-LDA, which are stiffer by ∼30% than widely used reactive empirical bond order force fields, can combine with EXX+RPA interlayer potentials to yield the magic angle at ∼1.08° without further rescaling of the interlayer tunneling.