Abstract
Encapsulating graphene in hexagonal Boron Nitride has several advantages: the highest mobilities reported to date are achieved in this way, and precise nanostructuring of graphene becomes feasible through the protective hBN layers. Nevertheless, subtle effects may arise due to the differing lattice constants of graphene and hBN, and due to the twist angle between the graphene and hBN lattices. Here, we use a recently developed model which allows us to perform band structure and magnetotransport calculations of such structures, and show that with a proper account of the moir\'e physics an excellent agreement with experiments can be achieved, even for complicated structures such as disordered graphene, or antidot lattices on a monolayer hBN with a relative twist angle. Calculations of this kind are essential to a quantitative modeling of twistronic devices.
Highlights
Graphene, the first successfully isolated two-dimensional material, has opened a new research area [1,2]
We use a recently developed model which allows us to perform band structure and magnetotransport calculations of such structures, and show that with a proper account of the moiré physics an excellent agreement with experiments can be achieved, even for complicated structures such as disordered graphene, or antidot lattices on a monolayer hexagonal boron nitride (hBN) with a relative twist angle
Our results show that without relaxation the band structure is particle-hole symmetric, in disagreement with experimental data, while the fully relaxed graphene shows, correctly, a particle-hole asymmetry emphasizing the importance of lattice relaxation of graphene and hexagonal boron nitride (G/hBN)
Summary
The first successfully isolated two-dimensional material, has opened a new research area [1,2]. A sizable band gap opening around the Fermi level in a graphene antidot lattice (GAL, a regular arrangement of antidots in a graphene lattice) has been predicted by several theoretical studies [5,6,7,8,9] and was recently realized in an experiment [10]. The twist-angle dependence of the properties of antidot lattices defined on G/hBN heterostructures has not yet been the subject of a systematical experimental or theoretical study. Another system where moiré effects show up dramatically is twisted bilayer graphene, where unconventional superconductivity or correlated insulator behavior may occur at certain twist angles between the monolayers [24,25]. A major theoretical finding is that the secondary Dirac point will disappear once the distance between antidot edges (“the neck width,” denoted by dn; see Appendix F) is smaller than the moiré wave length, a feature seen in experiments [10]
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