Origin of the vortex displacement field in twisted bilayer graphene

Gornostyrev, Yu. N.; Katsnelson, M. I.

doi:10.48550/arxiv.2006.11551

Cited by 1 publication

(2 citation statements)

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“…The method developed here adapts the original formulation of Daw to the case of interlayer dislocations in bilayer graphene. Compared to existing descriptions of interlayer dislocations in bilayer graphene [11,12], desirable features of our approach are (i) that solutions are obtained directly without the need to assume an analytical form, (ii) dislocationdislocation interactions and periodic boundary conditions are naturally accounted for, and…”

Section: Continuum Model For Interlayer Dislocationsmentioning

confidence: 99%

“…Continuum models have predicted that even finer scale modulations of the dislocation and moiré superlattice structure may be present [10,11]. Together, these set the foundation that dislocation descriptions can effectively describe the structure of moiré superlattices, as recently suggested by Gornostyrev and Katsnelson [12]. However, in order to confidently use continuum dislocation descriptions of moiré superlattices, a formal treatment to establish the equivalence of interlayer dislocations and moiré superlattice topology is needed.…”

Section: Introductionmentioning

confidence: 96%

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

Annevelink,

Johnson,

Ertekin

2020

Preprint

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We develop a continuum dislocation description of twist and stretch moiré superlattices in 2D material bilayers. The continuum formulation is based on the topological constraints introduced by the periodic dislocation network associated with the moiré 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 moiré 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/Å. Several applications of our model are shown, including predicting the variation of structure with twist angle, and describing dislocation line tension and junction energies.

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Section: Continuum Model For Interlayer Dislocationsmentioning

confidence: 99%