Quasicrystalline electronic states in twisted bilayers and the effects of interlayer and sublattice symmetries

Abstract

We study the electronic structure of quasicrystals composed of incommensurate stacks of atomic layers. We consider two systems: a pair of square lattices with a relative twist angle of $\theta =45^{\circ }$ and a pair of hexagonal lattices with a relative twist angle of $\theta =30^{\circ }$, with various interlayer interaction strengths. This constitutes every two-dimensional bilayer quasicrystal system. We investigate the resonant coupling governing the quasicrystalline order in each quasicrystal symmetry, and calculate the quasi-band dispersion. The resonant interaction emerges in bilayer quasicrystals if all the dominant interlayer interactions occur between the atomic orbitals that have the same magnetic quantum number. Thus, not only the quasicrystal composed of the widely studied graphene, but also those composed of transition metal dichalcogenides will exhibit the quasicrystalline states. We find that some quasicrystalline states, which are usually obscured by decoupled monolayer states, are more prominent, i.e., "exposed", in the systems with strong interlayer interaction. We also show that we can switch the states between quasicrystalline configuration and its layer components, by turning on and off the interlayer symmetry.

arXiv comment18 pages, 10 figures

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Cited by in corpus (12)

• Fractal energy gaps and topological invariants in hBN/Graphene/hBN double moiré systems
• Interlayer hybridization in graphene quasicrystal and other bilayer graphene systems
• Quasiperiodic pairing in graphene quasicrystals
• Moir{é} pattern assisted geometric resonant tunneling in disordered twisted bilayer graphene
• Resonant interaction in chiral, Eshelby-twisted van der Waals atomic layers
• Coexistence of 1D and 2D topology and genesis of Dirac cones in the chiral Aubry-André model
• Moiré fractals in twisted graphene layers
• Superconductivity and charge-density-wave in the Holstein model on the Penrose Lattice
• Trigonal Quasicrystalline States in $30^{\circ }$ Rotated Double Moiré Superlattices
• Electronic Observables for Relaxed Bilayer 2D Heterostructures in Momentum Space
• Proximity Effects Between the Graphene Quasicrystal and Magic-Angle Twisted Bilayer Graphene
• Symmetry-directed electronic and optical properties in a two-dimensional square-lattice ZnPc-MOF