Relaxation effects in twisted bilayer graphene: A multiscale approach

Abstract

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 ${\ensuremath{\theta}}_{\mathrm{M}}=1.{08}^{\ensuremath{\circ}}$ 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 $0.{9}^{\ensuremath{\circ}}$ and $1.{3}^{\ensuremath{\circ}}$. 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 ($\mathrm{EXX}+\mathrm{RPA}$). We use a Fermi velocity of ${\ensuremath{\upsilon}}_{\mathrm{F}}\ensuremath{\simeq}{10}^{6}$ m/s for graphene that is enhanced by $\ensuremath{\sim}15%$ 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 $\ensuremath{\sim}30%$ than widely used reactive empirical bond order force fields, can combine with $\mathrm{EXX}+\mathrm{RPA}$ interlayer potentials to yield the magic angle at $\ensuremath{\sim}1.{08}^{\ensuremath{\circ}}$ without further rescaling of the interlayer tunneling.