Multiscale Lattice Relaxation in General Twisted Trilayer Graphenes

We present comprehensive theoretical studies on the lattice relaxation and the electronic structures in general nonsymmetric twisted trilayer graphenes. By using an effective continuum model, we show that the relaxed lattice structure forms a patchwork of moire-of-moire domains, where a moire 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 supermoire 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 monolayerlike Dirac cone, and it is attributed to the formation of moire-of-moire domains equivalent to the mirror-symmetric twisted trilayer graphene.

Automated summary

This study presents comprehensive theoretical studies on the lattice relaxation and electronic structures of general nonsymmetric twisted trilayer graphenes. It reveals that the lattice structure forms patchwork of moire-of-moire domains and exhibits distinct chiral and alternating stacks. The electronic band calculations show the existence of topological boundary states in the chiral case and the coexistence of flat bands and monolayerlike Dirac cones in the alternating trilayer.