Abstract
We study the lattice configuration and electronic structure of a double moiré superlattice, which is composed of a graphene layer encapsulated by two other layers in a way such that the two hexagonal moiré patterns are arranged in a dodecagonal quasicrystalline configuration. We show that there are between 0 and 4 such configurations depending on the lattice mismatch between graphene and the encapsulating layer. We then reveal the resonant interaction, which is distinct from the conventional 2-, 3-, 4-wave mixing of moiré superlattices, that brings together and hybridizes twelve degenerate Bloch states of monolayer graphene. These states do not fully satisfy the dodecagonal quasicrystalline rotational symmetry due to the symmetry of the wave vectors involved. Instead, their wave functions exhibit trigonal quasicrystalline order, which lacks inversion symmetry, at the energies much closer to the charge neutrality point of graphene.
Highlights
We study the lattice configuration and electronic structure of a double moiré superlattice, which is composed of a graphene layer encapsulated by two other layers in a way such that the two hexagonal moiré patterns are arranged in a dodecagonal quasicrystalline configuration
We investigated the lattice configuration and electronic structures of a double moiré superlattice of which two hexagonal moiré patterns are arranged in a dodecagonal quasicrystalline configuration
We first find the condition which gives a 30◦ stack of the two moiré patterns in graphene encapsulated by another layers, and show that there are 0 to 4 such configurations depending on the lattice mismatch between graphene and the encapsulating layer
Summary
We study the lattice configuration and electronic structure of a double moiré superlattice, which is composed of a graphene layer encapsulated by two other layers in a way such that the two hexagonal moiré patterns are arranged in a dodecagonal quasicrystalline configuration. Where G3M,(l) = −G1M,(l) − G2M,(l) , are arranged in 12-fold rotational symmetry (Fig. 4a), just like the reciprocal lattice vectors in quasicrystalline twisted bilayer graphene that give rise to the resonant states (Fig. 1b)[22].
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