# The crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the "magic angle" $\theta\sim 1.08^\circ$

## TL;DR

This paper demonstrates that atomic corrugation significantly influences the flat bands and energy gaps in twisted bilayer graphene at the magic angle, emphasizing the importance of out-of-plane relaxations for accurate modeling.

## Contribution

It combines large-scale first principles calculations with a continuum model to accurately describe flat bands, highlighting the role of atomic corrugation and relaxations.

## Key findings

- Out-of-plane relaxations are essential for accurate flat band width and gap predictions.
- Results align quantitatively with recent experimental data.
- Atomic corrugation critically affects electronic properties at the magic angle.

## Abstract

We combine state-of-the-art large-scale first principles calculations with a low-energy continuum model to describe the nearly flat bands of twisted bilayer graphene at the first magic angle $\theta =1.08^\circ$. We show that the energy width of the flat band manifold, as well as the energy gap separating it from the valence and conduction bands, can be obtained only if the out-of-plane relaxations are fully taken into account. The results agree both qualitatively and quantitatively with recent experimental outcomes.