Moiré, Euler and self-similarity – the lattice parameters of twisted hexagonal crystals
What is it about?
If periodic patterns are rotated with respect to each other, a resulting "superpattern" becomes visible. In this article, I calculate the geometric properies of this resulting pattern for the case of hexagonal crystals. This is interesting by itself, but also technologically relevant as it applies for the case of mutually rotated two-dimensional crystals such a s graphene.
Why is it important?
The research on rotated two-dimensional crystals is currently very intense because at certain angles these materials show highly unexpected properties and are interesting candidates for functional devices. This work shows that the properties of the resulting device critically depends on the rotation angle, which is crucial for the understanding of their working, the production process, and their functionality.