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Open AccessArticle

Twisted Graphene Bilayers and Quasicrystals: A Cut and Projection Approach

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Depto. de Nanotecnología, Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, Boulevard Juriquilla 3001, 76230 Querétaro, Mexico
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Depto. de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 Ciudad de México, Mexico
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Depto. de Materia Condensada, Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 Ciudad de México, Mexico
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Author to whom correspondence should be addressed.
Crystals 2019, 9(10), 519; https://doi.org/10.3390/cryst9100519
Received: 1 September 2019 / Revised: 22 September 2019 / Accepted: 23 September 2019 / Published: 10 October 2019
(This article belongs to the Collection Structure and Properties of Quasicrystals)
In this work, a modified version of the cut and projection approach is proposed to describe the structure of graphene bilayers with twist angles. With this method, the rotation between two graphene layers is viewed as a rotation of the projection space and the resulting projected structure is interpreted as the set of points of best fit between the two rotated structures. Additionally, focus is given to the pertinence of the many algebraic and geometric tools used in grain boundaries and in quasicrystals to graphene bilayer system (or any other bilayer system, for that matter) case. View Full-Text
Keywords: graphene bilayers; twist grain boundaries; coincidence site lattices; quasicrystals; cut and projection method graphene bilayers; twist grain boundaries; coincidence site lattices; quasicrystals; cut and projection method
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MDPI and ACS Style

Aragón, J.L.; Naumis, G.G.; Gómez-Rodríguez, A. Twisted Graphene Bilayers and Quasicrystals: A Cut and Projection Approach. Crystals 2019, 9, 519.

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