Abstract

For soft-matter to form quasicrystals, an important ingredient is to have two characteristic length scales in the interparticle interactions. To be more precise, for stable quasicrystals, periodic modulations of the local density distribution with two particular wave numbers should be favoured, and the ratio of these wave numbers should be close to certain special values. In simple model systems, only these two wave numbers are needed. However, for more realistic models, where in principle all wave numbers can be involved, other wave numbers are also important, specifically those of the second and higher reciprocal lattice vectors. We identify features in the particle pair interaction potentials that can suppress or encourage density modes with wave numbers associated with one of the regular crystalline orderings that compete with quasicrystals, enabling either the enhancement or suppression of quasicrystals in a generic class of systems. Our strategy for finding quasicrystals involves tuning locations of maxima in the dispersion relation, or equivalently in the liquid state partial static structure factors. We also extend our approach to obtain some other quasicrystals, including the bronze mean structure, having a hexagonal symmetry and a new related quasicrystal. I will finish with a discussion of recent related work investigating one-component systems of core-shell particles that for some parameter values exhibit phase diagrams with 20+ different patterned phases.