Effect of bilayer stacking on the atomic and electronic structure of twisted double bilayer graphene

TL;DR

This study investigates how different stacking configurations in twisted double bilayer graphene influence atomic relaxations and electronic flat bands, revealing stacking-dependent electronic properties and potential for tunable moiré phenomena.

Contribution

It provides a comparative analysis of atomic and electronic structures in AB/AB, AA/AA, and AB/AA twisted double bilayer graphene, highlighting stacking-dependent relaxations and flat band behaviors.

Findings

Inner layers show significant relaxations similar to twisted bilayer graphene.

Outer layer relaxations depend on stacking, with AA layers avoiding high-energy configurations.

All configurations exhibit flat bands at small twist angles, with shapes sensitive to stacking.

Abstract

Twisted double bilayer graphene has recently emerged as an interesting moir\'e material that exhibits strong correlation phenomena that are tunable by an applied electric field. Here we study the atomic and electronic properties of three different graphene double bilayers: double bilayers composed of two AB stacked bilayers (AB/AB), double bilayers composed of two AA stacked bilayers (AA/AA) as well as heterosystems composed of one AB and one AA bilayer (AB/AA). The atomic structure is determined using classical force fields. We find that the inner layers of the double bilayer exhibit significant in-plane and out-of-plane relaxations, similar to twisted bilayer graphene. The relaxations of the outer layers depend on the stacking: atoms in AB bilayers follow the relaxations of the inner layers, while atoms in AA bilayers attempt to avoid higher-energy AA stacking. For the relaxed structures, we calculate the electronic band structures using the tight-binding method. All double bilayers exhibit flat bands at small twist angles, but the shape of the bands depends sensitively on the stacking of the outer layers. To gain further insight, we study the evolution of the band structure as the outer layers are rigidly moved away from the inner layers, while preserving their atomic relaxations. This reveals that the hybridization with the outer layers results in an additional flattening of the inner-layer flat band manifold. Our results establish AA/AA and AB/AA twisted double bilayers as interesting moir\'e materials with different flat band physics compared to the widely studied AB/AB system.