A topologically-derived dislocation theory for twist and stretch moiré superlattices in bilayer graphene

Abstract

We develop a continuum dislocation description of twist and stretch moire superlattices in 2D material bilayers. The continuum formulation is based on the topological constraints introduced by the periodic dislocation network associated with the moire structure. The approach is based on solving analytically for the structural distortion and displacement fields that satisfy the topological constraints, and which minimize the total energy. The total energy is described by both the strain energy of each individual distorted layer, and a Peierls-Nabarro like interfacial contribution arising from stacking disregistry. The dislocation core emerges naturally within the formalism as a result of the competition between the two contributions. The approach presented here captures the structure and energetics of twist and stretch moire superlattices of dislocations with arbitrary direction and character, without assuming an analytical solution a priori, with no adjustable parameters, while accounting naturally for dislocation-dislocation image interactions. In comparisons to atomistic simulations using classical potentials, the maximum structure deviation is 6%, while the maximum line energy deviation is 0.019 eV/Angstrom. Several applications of our model are shown, including predicting the variation of structure with twist angle, and describing dislocation line tension and junction energies.

References in corpus (17)

• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Moire bands in twisted double-layer graphene
• Tuning superconductivity in twisted bilayer graphene
• Spin-polarized Correlated Insulator and Superconductor in Twisted Double Bilayer Graphene
• Strain Solitons and Topological Defects in Bilayer Graphene
• Lattice relaxation and energy band modulation in twisted bilayer graphenes
• Cascade of electronic transitions in magic-angle twisted bilayer graphene
• Mapping the twist angle and unconventional Landau levels in magic angle graphene
• Origin of band gaps in graphene on hexagonal boron nitride
• Relaxation and Domain Formation in Incommensurate 2D Heterostructures
• Stacking domains and dislocation networks in marginally twisted bilayers of transition metal dichalcogenides
• Nanoserpents: Graphene Nanoribbons Motion on Two-Dimensional Hexagonal Materials
• Structural and electronic transformation in low-angle twisted bilayer graphene
• Networks of ABA and ABC stacked graphene on mica observed by scanning tunneling microscopy
• Structural relaxation and low energy properties of Twisted Bilayer Graphene
• Toward Moiré engineering in 2D materials via dislocation theory
• Origin of the vortex displacement field in twisted bilayer graphene

Cited by in corpus (7)

• Torsional Periodic Lattice Distortions and Diffraction of Twisted 2D Materials
• Origin of frictional scaling law in circular twist layered interfaces: simulations and theory
• Selection rules of twistronic angles in 2D material flakes via dislocation theory
• Dislocations in twistronic heterostructures
• Quantifying superlubricity of bilayer graphene from the mobility of interface dislocations
• Long wavelength interdomain phonons and instability of dislocations in small-angle twisted bilayers
• Low-Energy Electron Microscopy contrast of stacking boundaries: comparing twisted few-layer graphene and strained epitaxial graphene on silicon carbide