Relaxation Effects in Twisted Bilayer Graphene: a Multi-Scale Approach*

We present a multi-scale approach to capture the interdependent atomic and electronic structures of suspended and hexagonal boron nitride (hBN) supported twisted bilayer graphene (tBG) by using rescaled two center interlayer hopping terms to calibrate the flat band magic angle to ∼ 1.08^ο, as a way to resolve the indeterminacy of atomic/electronic structure models whose magic angles are bracketed between 0.9^ο −1.3^ο. We use electronic structrure hopping parameters extracted from density functional local density approximation except for an enhanced Fermi velocity of υ_F ≈ 10⁶ m/s and atomic force fields informed by stacking and interlayer distance-dependent density functional theory total energies, including systematically improved exact exchange and random phase approximation (EXX+RPA), to calculate the high-resolution spectral functions that can be compared with experimental angle-resolved photoemission spectra (ARPES).