TY  - JOUR
AU  - Feuerbacher, Michael
TI  - Moiré, Euler and self-similarity – the lattice parameters of twisted hexagonal crystals
JO  - Acta crystallographica / A
VL  - 77
IS  - 5
SN  - 2053-2733
CY  - Oxford [u.a.]
PB  - Blackwell
M1  - FZJ-2021-03699
SP  - 460 - 471
PY  - 2021
AB  - A real-space approach for the calculation of the moiré lattice parameters for superstructures formed by a set of rotated hexagonal 2D crystals such as graphene or transition-metal dichalcogenides is presented. Apparent moiré lattices continuously form for all rotation angles, and their lattice parameter to a good approximation follows a hyperbolical angle dependence. Moiré crystals, i.e. moiré lattices decorated with a basis, require more crucial assessment of the commensurabilities and lead to discrete solutions and a non-continuous angle dependence of the moiré-crystal lattice parameter. In particular, this lattice parameter critically depends on the rotation angle, and continuous variation of the angle can lead to apparently erratic changes of the lattice parameter. The solutions form a highly complex pattern, which reflects number-theoretical relations between formation parameters of the moiré crystal. The analysis also provides insight into the special case of a 30° rotation of the constituting lattices, for which a dodecagonal quasicrystalline structure forms.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000693011800008
DO  - DOI:10.1107/S2053273321007245
UR  - https://juser.fz-juelich.de/record/897237
ER  -