Regensburg 2013 – scientific programme

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MM: Fachverband Metall- und Materialphysik

MM 4: Topical Session: Quasicrystals & Complex Metallic Alloys I

MM 4.2: Talk

Monday, March 11, 2013, 10:45–11:00, H25

Geometric Properties of N-fold Symmetric Quasicrystals — •Johannes Roth — ITAP, Universität Stuttgart

Rhombic quasicrystals with n-fold planar symmetry contain configurations with 2n- or n-fold point symmetry. These “flowers” or “stars” are very predominant in fivefold quasicrystals and play an important role for example in the stabilization of colloidal quasicrystals. We have determined the number of stars directly up to n=11. We observe that if n increases, the number of stars decreases more than exponentially. Thus we argue that finite tiling patches with very high n up to 30, which many groups study experimentally, should not be called “quasicrystals” since these patches do not form representative samples of a quasicrystal due to the small sample size.

Laser potentials which are generated by the superposition of harmonic waves exhibit local isomorphism classes much like rhombus tilings. While these classes are well known for tilings, we describe them for n-fold symmetric laser fields using the methods of Mermin et al. and show how many free parameters exist.