First-Principles Study of Lattice Relaxation Effects in Twisted Bilayer Graphene

The structural and electronic properties of twisted bilayer graphene (TBG) with a wide range of twist angles are studied using density-functional-theory calculations with plane-wave and atomic-orbital basis. By properly taking into account the long-range van der Waals dispersion, we provide the patterns for the interlayer separation and the in-plane displacements of TBG. As the twist angle becomes small, the graphene sheet undergoes a gradual transition from a nearly flat to a corrugated layer, with maximal separation in the region dominated by the AA stacking and minimal separation in the AB region. At about 2°, these two extreme values have almost approached the limiting value possessed by the pure AA and pure AB bilayer graphene. In addition to the corrugation, the in-plane displacement exhibits a vortex-like pattern, where the curl of the displacement field is reversed when moving from the AA to the AB region. Overall, atomic relaxation leads to shrinkage of the AA stacking area in favor of the more energetically stable AB/BA stacking domains. Moreover, if one takes as the reference the TBG with a uniform AA interlayer distance, the band structure with out-of-plane relaxation can reduce the band width. In-plane relaxation, on the other hand, can increase the Fermi velocity at the K point. The fully relaxed structure, compared to the non-relaxed one, shows the isolation of the four flat bands near the Fermi level. The strain-induced pseudomagnetic fields are also evaluated.

This work is in collaboration with Chi-Ruei Pan, Martin Callsen, and Wei-En Tseng.