Quasicrystals are somewhat paradoxical structures which exhibit many amazing properties distinguishing them from ordinary crystals. Although the atoms are not localized at periodic positions, quasicrystals posses perfect long-range order. Until the early 1980s it was unanimously established that ordered matter is always periodic. Accordingly, the rotational symmetry in real space was thought to be limited to n = 2, 3, 4 and 6. However more than a hundred complex metal alloys, for instance the discretely diffracting icosahedral AlPdMn or decagonal AlNiCo, have defied these crystallographic rules and self-organized into quasicrystals. Quasicrystalline structures have been theoretically predicted also in systems with a single type of particles. Nevertheless, experimentally their spontaneous formation has been only observed in binary, ternary or even more complex alloys. Accordingly, their surfaces exhibit a high degree of structural and chemical complexity and show intriguing properties. In order to understand the origin of those characteristics it would be helpful to create artificial quasicrystals in which the structure and the chemical aspects are disentangled. This can be achieved, for e.g., by exposing colloidal monolayers to quasicrystalline light fields. Apart from understanding how quasicrystalline properties can be transferred to such monolayers, this approach might allow fabrication of materials with novel properties.
Although periodic crystals and quasicrystals both exhibit long-range positional order, their atomic configuration is markedly different. In contrast to periodic crystals, which are formed by the repetition of a unit cell, quasicrystals are created by the aperiodic arrangement of atoms. In view of these striking differences regarding their intrinsic order, the experimental observation of phase transitions between quasicrystals and crystals (or their corresponding approximants) upon variations in temperature or pressure, exposure to electron beams or small changes in the sample conditions, is surprising. In particular, it is not obvious what atomic movements are required to allow for such phase transitions.
We experimentally study the phase behavior of a charge-stabilized two-dimensional colloidal monolayer which is subjected to a one-dimensional quasiperiodic substrate potential. Upon increasing the laser intensity, we observe a transition from a periodic to a quasiperiodic state. It proceeds via the formation of an intermediate periodic average structure (PAS) which is related to the quasiperiodic lattice by a bounded 1-1 mapping. Because PAS can transform to crystals and quasicrystals by minute particle displacements, they provide a mechanism to allow for interesting insights into the relationship between periodic and quasiperiodic order.
The surfaces of quasiperiodic materials hold tremendous interest due to their potential for creating new forms of matter with exotic properties. The use of quasicrystalline surfaces as templates for adsorbed monolayers provides the opportunity to transfer typical quasicrystalline properties to a wide range of materials. We demonstrate this approach by exposing a colloidal monolayer to a decagonal laser light field where the substrate strength is continuously adjustable. At intermediate substrate potentials we observe a novel pseudomorphic phase exhibiting likewise crystalline and quasicrystalline order and which can be explained by an Archimedean-like tiling structure. In addition to this surprising new link between such tilings and quasicrystals our experiments allow to investigate in real space how single-element monolayers arrange locally on quasicrystalline surfaces.
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.
Particles which are driven across periodic substrate potentials show a number of intriguing phenomena. Depending on the direction of the applied driving force F, the orientation of the particle's motion can substantially deviate from F but is locked-in to directions determined by the substrate's symmetry. Examples of such kinetically locked-in states range from atom migration on crystalline surfaces, driven charge density waves to flux flow in type-II superconductors. Also, it has been demonstrated that directional locking can be employed for sorting of colloidal particles according to their size, refractive index or chirality. When subjecting a monolayer of colloidal particles to quasiperiodic substrates potentials being created by interfering laser beams, we also observe dynamical ordering with a pronounced colloidal smectic phase. This suggests that dynamical ordering is not restricted to periodic potentials but also occurs under more general conditions.