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

TL;DR

This study numerically investigates three-layer graphene heterostructures with twist angles forming a quasicrystal, revealing hybridization between flat bands and quasicrystalline states and identifying a new electronic regime.

Contribution

It introduces a detailed numerical analysis of twisted graphene heterostructures with quasicrystalline order, highlighting hybridization effects and new electronic phenomena.

Findings

Hybridization between flat bands and quasicrystalline states observed.

Distinct modifications of states across energy windows identified.

A new hybrid electronic regime is revealed.

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.