Mirror symmetry breaking and lateral stacking shifts in twisted trilayer graphene

We construct a continuum model of twisted trilayer graphene using ab initio density-functional-theory calculations, and we apply it to address twisted trilayer electronic structure. Our model accounts for moire variation in site energies, hopping between outside layers, and hopping within layers. We focus on the role of a mirror symmetry present in ABA graphene trilayers with a middle layer twist. The mirror symmetry is lost intentionally when a displacement field is applied between layers, and unintentionally when the top layer is shifted laterally relative to the bottom layer. We calculate two band-structure characteristics that are directly relevant to transport measurements, namely the Drude weight and the weak-field Hall conductivity. We relate them via the Hall density to assess the influence of the accidental lateral stacking shifts currently present in all experimental devices on electronic properties. Finally, we comment on the role of the possible importance of accidental lateral stacking shifts for superconductivity in twisted trilayers.

Automated summary

Researchers constructed a continuum model to study twisted trilayer graphene and found that mirror symmetry plays a key role in electronic properties. They calculated characteristics such as the Drude weight and weak-field Hall conductivity, and evaluated the influence of accidental lateral stacking shifts on electronic properties in experimental devices. They also discussed the possible importance of these shifts for superconductivity in twisted trilayers.