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Configuration of Moiré pattern in BLG. (a) Seven lattice vectors in the graphene related to a single integer i: , , , , , , and . (b) A particular Moiré pattern with twisting angle in the circular graphene of radius 26 Å. Two vectors show the base for the unit cell, i.e., and .
The inter-layer potential energy versus the twisting angle of the Moiré pattern in BLG with various radius (r) and inter-layer space (c). Stars locate the twisting angle observed by experiment in Ref. 25. Open circles correspond to twisting angles from Eq. (1).
The frequency versus twisting angle for two z-direction vibration modes. The upper three curves are for the z-direction breathing mode. The three lower curves are for the z-direction acoustic mode.
The size dependence for the two z-direction vibration modes: (a) z-direction acoustic mode and (b) z-direction breathing mode. The calculation data (solid points) are fitted to analytical functions.
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