Moiré Patterns and Commensurability in Rotated Graphene Bilayers

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This Demonstration shows the appearance of Moiré patterns in hexagonal lattice systems as you rotate a honeycomb layer on top of another identical layer by an angle . The rotation angle
can be freely chosen or, as done in this Demonstration, specified by a couple of integer indices
following [1]. These integers also give the number of atoms and the unit cell basis vectors of the supercell of the bilayer system. Some example systems where Moiré patterns on hexagonal lattices that have been recently experimentally observed are bilayer graphene systems.
Contributed by: Jessica Alfonsi (December 2013)
Open content licensed under CC BY-NC-SA
Snapshots
Details
Snapshot 1: perfect AA stacking () with
Snapshot 2: quasi-perfect AB stacking limit () with large
Snapshot 3: example of an extremely large supercell ( limit) with small
Snapshot 4: example of a commensurate bilayer cell , symmetric with respect to the case in the thumbnail snapshot with
Reference
[1] G. T. de Laissardière, D. Mayou, and L. Magaud, "Localization of Dirac Electrons in Rotated Graphene Bilayers," Nano Letters, 10(3), 2010 pp. 804–808. pubs.acs.org/doi/abs/10.1021/nl902948m.
Permanent Citation