Proximity effects between a graphene quasicrystal and magic-angle twisted bilayer graphene

We present a numerical study of three-layer graphene heterostructures in which the layers are twisted by the magic angle ($\ensuremath{\sim}1.{1}^{\ensuremath{\circ}}$) or by $\ensuremath{\sim}{30}^{\ensuremath{\circ}}$ to form a graphene quasicrystal. The heterostacks are described using realistic structural relaxations and tight-binding Hamiltonians, and their transport properties are computed for both pristine and disordered systems containing up to $\ensuremath{\sim}8$ million atoms. Owing to the weak interlayer coupling, we resolve the hybridization between magic-angle flat bands and quasicrystalline states, which are modified in distinct ways across low- and high-energy windows, revealing a different hybrid electronic regime to explore.