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Why twisting angles are diverse in graphene Moiré patterns?
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10.1063/1.4805036
/content/aip/journal/jap/113/19/10.1063/1.4805036
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/19/10.1063/1.4805036
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The interlayer potential energy calculated from the registry-dependent potential with different cut-offs. The -axis () is the total interlayer energy per atom. In this calculation, the radius of the top graphene layer is  = 100 Å. The twisting angle °, i.e., AB-stacking BLG. For a cut-off , the variation in the energy is on the order of 10 meV. Inset displays the cross section of a twisting BLG, where is the radius and is the boundary region.

Image of FIG. 2.
FIG. 2.

The saturation of the energy per atom with increasing radius for different twisting angles θ. (a) °, i.e., AB-stacking BLG. Solid and open dots correspond to cut-off and 50 Å. (b) , i.e., AA-stacking BLG. Theenergy per atom in the AA-stacking BLG is radius independent. (c) , i.e., the first commensurable angle. (d) , i.e., the second commensurable angle.

Image of FIG. 3.
FIG. 3.

The energy per atom versus twisting angle θ. The whole curve is symmetric about due to the mirror symmetry between the two nonequivalent atoms in graphene, so is not shown. Inset shows the interlayer space verses twisting angle θ.

Image of FIG. 4.
FIG. 4.

The energy per atom versus twisting angle around °. For curves from bottom to top, the radius increases from 10 to 100 Å. All curves can be well fitted to , where is the value at °. α is the fitting parameter. Inset shows the radius-dependence of α. α is fitted to .

Image of FIG. 5.
FIG. 5.

The energy per atom versus twisting angle around . For curves from top to bottom, the radius increases from 10 to 100 Å. All curves can be well fitted to , where is the value at . β is the fitting parameter. Inset shows the radius-dependence of β. β is fitted to .

Image of FIG. 6.
FIG. 6.

The registry-dependent potential between a single atom and an infinite large graphene sheet. The single atom is on top of the graphene at a fixed distance  = 3.478 Å. and axes in the figure are the other two coordinates of the single atom. (a) shows six-fold symmetry in the energy, due to the hexagon structure of graphene. (b) shows only one valley of the energy. (c) shows the convergence of the average of the energy over area with increasing grid points. The dashed line (red) depicts the platform value of the energy per atom in Fig. 3 .

Image of FIG. 7.
FIG. 7.

The interlayer potential energy calculated from Lennard-Jones potential with different cut-offs. The -axis () is the energy per atom. In this calculation, the radius of the top layer is 100 Å. The twisting angle . For a cut-off distance of , the variation in the energy is on the order of 10 meV.

Image of FIG. 8.
FIG. 8.

The saturation of the energy per atom with increasing radius for different twisting angles θ. (a) °, i.e., AB-stacking BLG. (b) , i.e., AA-stacking BLG. The energy per atom in the AA-stacking BLG is radius independent. (c) , i.e., the first commensurable angle. (d) . (e) , i.e., the second commensurable angle. (f) .

Image of FIG. 9.
FIG. 9.

The energy per atom versus twisting angle θ. The top inset shows the close-up of the middle region , where curves for large radius of 500 and 1000 Å are indistinguishable. Two bottom insets show the close-up of the boundary regions ° and 60°.

Image of FIG. 10.
FIG. 10.

The energy per atom versus twisting angle around °. For curves from bottom to top, the radius increases as 20, 55, 150, 190, 250, 310, 400, 520, 665, 850, and 1000 Å. All curves can be well fitted to , where is the value at °. α is the fitting parameter. Inset shows the radius-dependence of α. α is fitted to .

Image of FIG. 11.
FIG. 11.

The energy per atom versus twisting angle around . For curves from top to bottom, the radius increases as 20, 55, 150, 190, 250, 310, 400, 520, 665, 850, and 1000 Å. All curves can be well fitted to , where is the value at . β is the fitting parameter. Inset shows the radius-dependence of β. β is fitted to .

Image of FIG. 12.
FIG. 12.

The Lennard-Jones potential between a single atom and an infinite large graphene sheet. The single atom is on top of the graphene at a fixed distance  =  = 3.35 Å. (a) shows six-fold symmetry in the energy, due to the hexagon structure of graphene. (b) shows only one valley of the energy. (c) shows the convergence of the average of the energy over area with increasing grid points. The dashed line (red) depicts the platform value of the energy per atom in Fig. 9 .

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/content/aip/journal/jap/113/19/10.1063/1.4805036
2013-05-16
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Why twisting angles are diverse in graphene Moiré patterns?
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/19/10.1063/1.4805036
10.1063/1.4805036
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