Lattice reconstruction behavior across twist-angle pairs in twisted trilayer graphene

Determine how lattice reconstruction behaves in twisted trilayer graphene for twist angle pairs (θ_TM, θ_MB) beyond the few angle pairs that have been investigated to date, by characterizing the structural reconstruction patterns across additional angle combinations.

Background

Twisted trilayer graphene (TTG) with two independent twist angles (θ_TM for top–middle and θ_MB for middle–bottom) can form quasiperiodic moiré structures and a super-long-range moiré-of-moiré (MoM) pattern. Lattice relaxation influences these structures and, in previously studied cases near θ_TM/θ_MB ≈ ±1, can lead to large-area single-moiré structures.

In this work, the authors examine several TTG samples with θ_TM/θ_MB away from ±1 and observe weak supermoiré-scale lattice relaxation and TBG-like reconstruction features. They note that, although their results reveal angle-dependent reconstruction effects, only a few angle pairs have been explored so far, leaving the behavior of lattice reconstruction for other twist angle pairs unresolved.

References

Up to now, the structure reconstruction of the TTG is investigated only in few angle pairs and how it behaves in other angle pairs is still unclear.

— Robust flat bands in twisted trilayer graphene quasicrystals  (2401.09010 - Hao et al., 2024) in Main text, paragraph discussing lattice relaxation differences relative to θ_TM/θ_MB ≈ ±1; immediately before the paragraph beginning “To gain insights into the electronic structure…”