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@ARTICLE{Feuerbacher:897237,
      author       = {Feuerbacher, Michael},
      title        = {{M}oiré, {E}uler and self-similarity – the lattice
                      parameters of twisted hexagonal crystals},
      journal      = {Acta crystallographica / A},
      volume       = {77},
      number       = {5},
      issn         = {2053-2733},
      address      = {Oxford [u.a.]},
      publisher    = {Blackwell},
      reportid     = {FZJ-2021-03699},
      pages        = {460 - 471},
      year         = {2021},
      abstract     = {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.},
      cin          = {PGI-5},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-5-20110106},
      pnm          = {5353 - Understanding the Structural and Functional Behavior
                      of Solid State Systems (POF4-535)},
      pid          = {G:(DE-HGF)POF4-5353},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000693011800008},
      doi          = {10.1107/S2053273321007245},
      url          = {https://juser.fz-juelich.de/record/897237},
}