paper

Multi-scale lattice relaxation in general twisted trilayer graphenes

arXiv:2305.13155 · doi:10.1103/PhysRevX.13.041007

Abstract

We present comprehensive theoretical studies on the lattice relaxation and the electronic structures in general non-symemtric twisted trilayer graphenes. By using an effective continuum model, we show that the relaxed lattice structure forms a patchwork of moiré-of-moiré domains, where a moiré pattern given by layer 1 and 2 and another pattern given by layer 2 and 3 become locally commensurate. The atomic configuration inside the domain exhibits a distinct contrast between chiral and alternating stacks, which are determined by the relative signs of the two twist angles. In the chiral case, the electronic band calculation reveals a wide energy window ( 50 meV) with low density of states, featuring sparsely distributed highly one-dimensional electron bands. These one-dimensional states exhibit a sharp localization at the boundaries between super-moiré domains, and they are identified as a topological boundary state between distinct Chern insulators. The alternating trilayer exhibits a coexistence of the flat bands and a monolayer-like Dirac cone, and it is attributed to the formation of moiré-of-moiré domains equivalent to the mirror-symmetric twisted trilayer graphene.

18 pages, 16 figures

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