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

TL;DR

This paper investigates the electronic structure of bilayer quasicrystals with different lattice symmetries and twist angles, revealing how interlayer interactions and symmetries influence quasicrystalline states and their tunability.

Contribution

It introduces a comprehensive analysis of quasicrystalline states in incommensurate bilayer systems, highlighting the role of interlayer interactions and symmetry in their emergence and control.

Findings

Quasicrystalline states are more prominent with strong interlayer interactions.

Resonant coupling depends on atomic orbitals with the same magnetic quantum number.

States can be switched between quasicrystalline and layer components by symmetry control.

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.