Structure and energetics of interlayer dislocations in bilayer graphene

Dai, Shuyang; Xiang, Yang; Srolovitz, David J.

doi:10.1103/physrevb.93.085410

Cited by 47 publications

(59 citation statements)

References 33 publications

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“…al. determining the size of the lines and vortices using the Peierls-Nabarro model [41,42] are in very good agreement (within 10%) with our estimate of constant size in the thermodynamic limit. Alden et.…”

Section: Resultssupporting

confidence: 83%

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Structure of twisted and buckled bilayer graphene

Jain¹,

Juričić²,

Barkema³

2016

2D Mater.

116

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Abstract. We study the atomic structure of twisted bilayer graphene, with very small mismatch angles (θ ∼ 0.28 0 ), a topic of intense recent interest. We use simulations, in which we combine a recently presented semi-empirical potential for single-layer graphene, with a new term for out-of-plane deformations, [Jain et al., J. Phys. Chem. C, 119, 2015] and an often-used interlayer potential [Kolmogorov et al., Phys. Rev. B, 71, 2005]. This combination of potentials is computationally cheap but accurate and precise at the same time, allowing us to study very large samples, which is necessary to reach very small mismatch angles in periodic samples. By performing large scale atomistic simulations, we show that the vortices appearing in the Moiré pattern in the twisted bilayer graphene samples converge to a constant size in the thermodynamic limit. Furthermore, the well known sinusoidal behavior of energy no longer persists once the misorientation angle becomes very small (θ < 1 0 ). We also show that there is a significant buckling after the relaxation in the samples, with the buckling height proportional to the system size. These structural properties have direct consequences on the electronic and optical properties of bilayer graphene.

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Section: Resultssupporting

confidence: 83%

“…Recently, out-of-plane ripples in bilayer graphene have been detected and investigated via TEM [37,38] and the combination of dark-field TEM with scanning transmission electron microscopy (STEM) [39]. The buckling effect in bilayer graphene has also been studied using computer simulations [40,41,42].…”

Section: Introductionmentioning

confidence: 99%

Structure of twisted and buckled bilayer graphene

Jain¹,

Juričić²,

Barkema³

2016

2D Mater.

116

View full text Add to dashboard Cite

show abstract

“…These narrow strips are referred to as domain walls [2][3][4][5]7,8 or boundaries between commensurate domains. 1,[15][16][17][18] In previous theoretical works, 1,3,4,15,16,18,19 it was assumed that domain walls do not cross as long as the distance between them is large and can be treated as isolated. It was shown that formation of domain walls becomes energetically favourable above some critical uniaxial elongation of the bottom layer.…”

Section: Introductionmentioning

confidence: 99%

Commensurate-incommensurate phase transition and a network of domain walls in bilayer graphene with a biaxially stretched layer

Lebedeva

Popov

2019

Phys. Rev. B

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The two-chain Frenkel-Kontorova model is applied for an analytical description of the energy and structure of the network of domain walls in bilayer graphene. Using this approach, the commensurate-incommensurate phase transition upon biaxial stretching of one of the graphene layers is considered. We demonstrate that formation of the equilateral triangular network of domain walls becomes energetically favourable above the critical relative biaxial elongation of the bottom layer of 3.0 · 10 −3 . It is shown that the optimal period of the triangular network of domain walls is inversely proportional to the difference between the biaxial elongation of the bottom layer and the critical elongation as long as it is much greater than the width of domain walls. Quantitative estimates of the contribution of a single dislocation node to the system energy and the period of the network of domain walls are obtained. Experimental measurements of the period could help to verify the energy of the fully incommensurate state (such as obtained by relative rotation of the layers) with respect to the commensurate one. arXiv:1906.11190v1 [cond-mat.mes-hall]

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“…The majority of the previous theoretical works on the structure and energetics of domain walls were devoted to isolated domain walls which do not cross. 1,3,4,[28][29][30][31] The approach developed in these papers allowed to predict the commensurate-incommensurate phase transition 32 related to the formation of the first domain wall in two-dimensional bilayer systems with one layer stretched uniaxially and another layer free, such as bilayer graphene, 1,29 bilayer boron nitride 28,29 and graphene-boron nitride heterostructure. 30 Although it is in principle possible to study the structure of triangular domain wall networks by atomistic 22,25 and multiscale 33 simulations, the number of atoms in the supercell grows rapidly with decreasing the angle of relative rotation of the layers.…”

Section: Introductionmentioning

confidence: 99%

Energetics and Structure of Domain Wall Networks in Minimally Twisted Bilayer Graphene under Strain

Lebedeva

Popov

2019

J. Phys. Chem. C

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The parameters of the triangular domain wall network in bilayer graphene with a simultaneously twisted and biaxially stretched bottom layer are studied using the two-chain Frenkel-Kontorova model. It is demonstrated that if the graphene layers are free to rotate, they prefer to stay coaligned upon stretching the bottom layer and the regular triangular network of tensile domain walls is formed upon the commensurate-incommensurate phase transition. If the angle between the layers is fixed, the regular triangular network of shear domain walls is observed at zero elongation of the bottom layer. Upon stretching the bottom layer, however, the domain walls transform into the tensile ones and the size of the commensurate domains decreases. We also show that the parameters of the isosceles triangular domain wall network in twisted bilayer graphene under shear strain can be determined through purely geometrical considerations. Experimental analysis of the orientation of domain walls and period of the triangular network would, on the one hand, contribute to understanding of the interlayer interaction of graphene layers, and, on the other hand, serve for detection of relative strains and rotation between the layers. Vice versa external strains can be used to control the parameters of the triangular domain wall network and, therefore, electronic properties of twisted bilayer graphene. arXiv:2001.10791v1 [cond-mat.mes-hall]

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Structure and energetics of interlayer dislocations in bilayer graphene

Cited by 47 publications

References 33 publications

Structure of twisted and buckled bilayer graphene

Structure of twisted and buckled bilayer graphene

Commensurate-incommensurate phase transition and a network of domain walls in bilayer graphene with a biaxially stretched layer

Energetics and Structure of Domain Wall Networks in Minimally Twisted Bilayer Graphene under Strain

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