# 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.

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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

"Moiré Patterns and Commensurability in Rotated Graphene Bilayers"

http://demonstrations.wolfram.com/MoirePatternsAndCommensurabilityInRotatedGrapheneBilayers/

Wolfram Demonstrations Project

Published: December 6 2013