Proximity Effects Between the Graphene Quasicrystal and Magic-Angle Twisted Bilayer Graphene

Abstract

We present a numerical study of three-layer graphene heterostructures in which the layers are twisted by the magic angle ($\sim$1.1$^\circ$) or by $\sim$$30^\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 $\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 new hybrid electronic regime to explore.

Figures (7)

• Figure 1: Schematic of twisted multilayer graphene systems on a flat substrate such as bulk h-BN (top panel), and top view of the atomic structure of the trilayer stack (bottom panel). Patterns reminiscent of the AA (center region) and AB zones of MATBLG and the 12-fold rotational structures of the quasicrystalline approximant are visible.
• Figure 2: Density of states (top panel) and Fermi velocities (bottom panel) of MATBLG (purple solid line) and the two trilayer systems (black solid and dashed lines). The averaged Fermi velocity of the trilayer system is depicted by the red line, considering a trilayer system where the MATBLG and the quasicrystalline layer are decoupled (see main text).
• Figure 3: Layer-projected DOS (bottom left panel) and LDOS of each of the layers for the $31^\circ$+$1.1^\circ$ trilayer hybrid system at charge neutrality ($E=0$). The moiré pattern is visible in the two $1.1^\circ$-rotated layers, while the extra quasicrystalline layer does not display any signal of the flat band.
• Figure 4: Time-dependent diffusion coefficient in the flat band for different disorder strengths, for MATBLG (inset) and the trilayer with the 29.8º approximant (main panel).
• Figure 5: DOS (top panel) and Fermi velocity (bottom panel) in the high-energy quasicrystalline-state regime. The vertical green dotted line marks the energy of the $\alpha$ quasicrystalline peak ($E=-1.95$ eV) Moon2019.