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

TL;DR

This paper develops a multi-scale computational approach combining DFT, molecular dynamics, and tight-binding methods to accurately model atomic and electronic structures of twisted bilayer graphene, resolving the variability in predicted magic angles.

Contribution

It introduces a calibrated multi-scale model that accurately predicts the magic angle at 1.08° by integrating DFT-informed force fields and electronic structure calculations.

Findings

Calibrated the magic angle to 1.08° using rescaled interlayer tunneling.

High-resolution spectral functions match experimental ARPES data.

Atomic and electronic structures are interdependent, influencing the magic angle prediction.

Abstract

We present a multi-scale density functional theory (DFT) informed molecular dynamics and tight-binding (TB) approach to capture the interdependent atomic and electronic structures of twisted bilayer graphene. We calibrate the flat band magic angle to be at $\theta_{\rm M} = 1.08^{\circ}$ 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 $0.9^\circ \sim 1.3^\circ$. 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 (EXX+RPA). We use a Fermi velocity of $\upsilon_{\rm F} \simeq 10^{6}$~m/s for graphene that is enhanced by about $\sim 15\%$ 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 spectra (ARPES). 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 $\sim$30\% than widely used reactive empirical bond order force fields, can combine with EXX+RPA interlayer potentials to yield the magic angle at $\sim 1.08^{\circ}$ without further rescaling of the interlayer tunneling.