Twisted Graphene Bilayers and Quasicrystals: A Cut and Projection Approach
José L. Aragón,
Gerardo G. Naumis,
Alfredo Gómez-Rodríguez
Affiliations
José L. Aragón
Depto. de Nanotecnología, Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, Boulevard Juriquilla 3001, 76230 Querétaro, Mexico
Gerardo G. Naumis
Depto. de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 Ciudad de México, Mexico
Alfredo Gómez-Rodríguez
Depto. de Materia Condensada, Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 Ciudad de México, Mexico
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.
