Designing Moiré Patterns by Strain

Abstract

Experiments conducted on two-dimensional twisted materials have revealed a plethora of moiré patterns with different forms and shapes. The formation of these patterns is usually attributed to the presence of small strains in the samples, which typically arise during their fabrication. In this work we find that the superlattice structure of such systems actually depends crucially on the interplay between twist and strain. For systems composed of honeycomb lattices, we show that this can lead to the formation of practically any moiré geometry, even if each lattice is only slightly distorted. As a result, we show that under strain the moiré Brillouin zone is not a stretched irregular hexagon, but rather a primitive cell that changes according to the geometry of the strained moiré vectors. We identify the conditions for the formation of hexagonal moiré patterns arising solely due to shear or biaxial strain, thus opening the possibility of engineering moiré patterns solely by strain. Moreover, we study the electronic properties in such moiré patterns and find that the strain tends to suppress the formation of the flat moiré bands, even in the strain-induced hexagonal patterns analogous to those obtained by the twist only. Our work explains the plethora of moiré patterns observed in experiments, and provides a solid theoretical foundation from which one can design moiré patterns by strain.

19 pages, 13 figures. Accepted version

References in corpus (10)

• A tight-binding approach to uniaxial strain in graphene
• STM Spectroscopy of ultra-flat graphene on hexagonal boron nitride
• Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride
• Continuum Model of the Twisted Bilayer
• Symmetry-based approach to electron-phonon interactions in graphene
• Interlayer interaction in general incommensurate atomic layers
• Strain-shear coupling in bilayer MoS2
• Optical absorption of twisted bilayer graphene with interlayer potential asymmetry
• Moire pattern as a magnifying glass for strain and dislocations in van der Waals heterostructures
• Electron-hole asymmetry and band gaps of commensurate double moire patterns in twisted bilayer graphene on hexagonal boron nitride

Cited by in corpus (19)

• Moire magnetism in CrBr3 multilayers emerging from differential strain
• Diagrammatic perturbation approach to moiré bands in twisted bilayer graphene
• Designing Moire Patterns by Shearing
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Strain-dependent one-dimensional confinement channels in twisted bilayer 1T${}^{\prime }$-WTe${}_2$
• Electronic structure and transport in materials with flat bands: 2D materials and quasicrystals
• Band structure and optical response of Kekulé-modulated $\alpha -{\mathcal{T}}_3$ model
• Geometrical properties of strained and twisted moiré heterostructures
• Review of the tight-binding method applicable to the properties of moiré superlattices
• Mean-field Modelling of Moiré Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene
• Twistraintronics in Square Moire Superlattices of Stacked Graphene Layers
• Theory for Lattice Relaxation in Marginal Twist Moirés
• Moiré magnetism in a bilayer Ising model
• Sliding phasons in Moiré Ladders
• Untangling 3D atomic reconstruction in twisted bilayer 2D crystals via dark field transmission electron microscopy
• Moiré-driven equilibrium of perturbations in moiré systems
• Scalable and deterministic construction of moiré superlattice in 2D materials using stressor films
• Second-Order Synaptic Memory using Inherent Plasticity of Moiré Superlattices
• Straintronics and twistronics in bilayer graphene