Title: Quasicrystals without forbidden symmetries
Speaker: Ron Lifshitz, School of Physics & Astronomy, Tel Aviv University
Abstract:
Quasicrystals with symmetries that can be found in both periodic and aperiodic crystals have remained relatively unexplored over the years. This is despite the fact that they readily appear as the low-symmetry surfaces of standard quasicrystals, in 2-dimensional layered structures like graphene, as well as other experimental systems. Moreover, tiling models of such systems often provide new insight into the physical nature of aperiodic long-range order in situations that are potentially easier to treat. After giving a brief primer on quasiperiodic tilings, I shall describe a number of such models, starting with the rather simple and well-known example of the square Fibonacci tiling, and moving on to more interesting and complex tilings with trigonal and hexagonal point group symmetries. I will show how to generate and then analyze such tilings, employing the same standard methods one uses to study the most common quasicrystals.
Graphics (if there's space for it): The square and hexagonal Fibonacci tilings.
R. Lifshitz, J. Alloys Compd. 342, 186 (2002) and S. Coates et al., Preprint, arXiv:2201.11848.v2 (2022).