Relaxation Effects in the Electronic Structure of Twisted Bilayer Graphene: a Multi-Scale Approach*

We introduce a multi-scale approach to obtain accurate atomic and electronic structures for atomically relaxed twisted bilayer graphene. High-level exact exchange and random phase approximation (EXX+RPA) correlation data provides the foundation to parametrize systematically improved force fields for molecular dynamics simulations that allow relaxing twisted layered graphene systems containing millions of atoms making possible a fine sweeping of twist angles. These relaxed atomic positions are used as input for tight-binding band-structure calculations where the distance & angle-dependent interlayer hopping terms are extracted from ab-initio calculations & subsequent representation with Wannier orbitals. We benchmark our results against published force fields and widely used tight-binding models and discuss their impact in the spectrum around the flat band energies. We find that our relaxation scheme yields a magic angle of twisted bilayer graphene consistent with experiments between 1.0^o∼1.1^o using Fermi velocities υ_F≈1.0∼1.1×10⁶ m/s. We present high-resolution spectral function calculations to compare with experimental ARPES.