Anomalous quasicrystals

Despite a strong potential for numerous technical applications, the conditions under which quasicrystals form are still poorly understood. Currently, it is not clear why most two-dimensional quasicrystals are 5- or 10-fold symmetric. We investigate the role of geometrical constraints which can impede the formation of quasicrystals with certain symmetries in a colloidal model system. This is achieved by subjecting a colloidal monolayer to n = 5- and 7-beam quasiperiodic potential landscapes. Our results clearly demonstrate that quasicrystalline order is much easier established for n = 5 compared to n = 7. With increasing laser intensity we observe that the colloids first adopt quasiperiodic order at local areas which then laterally grow until an extended quasicrystalline layer forms. As nucleation sites where quasiperiodicity originates, we identify highly symmetric motifs in the laser pattern. We find that their density strongly varies with n and surprisingly is smallest exactly for those quasicrystalline symmetries which have never been observed in atomic systems. Since such high symmetry motifs also exist in atomic quasicrystals where they act as preferential adsorption sites, this suggests that it is indeed the deficiency of such motifs which accounts for the absence of materials with e.g. 7-fold symmetry.