Commensurate and incommensurate double moire interference in twisted trilayer graphene

H Meng and Z Zhan and SJ Yuan, PHYSICAL REVIEW B, 107, 035109 (2023).

DOI: 10.1103/PhysRevB.107.035109

Twisted graphene multilayers have been recently demonstrated to share several correlation-driven behaviors with twisted bilayer graphene. In general, the van Hove singularities (VHSs) can be used as a proxy of the tendency for correlated behaviors. In this paper, we adopt an atomistic method by combining the tight-binding method with the semiclassical molecular dynamics to investigate the electronic structures of twisted trilayer graphene (TTG) with two independent twist angles. The two independent twist angles can lead to the interference of the moire patterns forming a variety of commensurate/incommensurate complex supermoire patterns. In particular, the lattice relaxation, twist angle and angle disorder effects on the VHS are discussed. We find that the lattice relaxation significantly influences the position and magnitude of the VHSs. In the supermoire TTG, the moire interference provides constructive or destructive effects depending on the relative twist angle. By modulating the two independent twist angles, novel superstructures, for instance, the Kagome-like lattice, could be constructed via the moire pattern. Moreover, we demonstrate that a slight change in twist angles (angle disorder) provides a significant suppression of the peak of the VHSs. Apart from the moire length, the evolution of the VHSs and the LDOS mapping in real space could be used to identify the twist angles in the complicated TTG. In practice, our work could provide a guide for exploring the flat band behaviors in the supermoire TTG experimentally.

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