Soft quasicrystals – Why are they stable?

In the last two years we have witnessed the exciting experimental discovery of soft matter with nontrivial quasiperiodic long-range order – a new form of matter termed a soft quasicrystal. Two groups have independently discovered such order in soft matter: Zeng et al. in a system of dendrimer liquid crystals; and Takano et al. in a system of ABC star-shaped polymers. These newly discovered soft quasicrystals not only provide exciting platforms for the fundamental study of both quasicrystals and of soft matter, but also hold the promise for new applications based on self-assembled nanomaterials with unique physical properties that take advantage of the quasiperiodicity, such as complete and isotropic photonic band-gap materials. Here we provide a concise review of the emerging field of soft quasicrystals, suggesting that the existence of two natural length-scales, along with three-body interactions, may constitute the underlying source of their stability. 1. Background The discovery of quasicrystals by Shechtman more than two decades ago [1] signalled the beginning of a remarkable scientific revolution [2], in which some of the most basic notions of condensed matter physics have undergone a thorough reexamination. Today, the science of quasicrystals, with its growing number of textbooks}, is in its adolescence. Old paradigms are being carefully transformed into new ones [11]; definitions are being changed [12]; space-group theory has been generalized to quasicrystals using two alternative approaches [13–16], and even extended to treat novel long-range order possessing colour [17] or magnetic symmetry [18, 19]; and many fundamental problems – including Bak’s famous question: ‘Where are the atoms? ’ [20] – are gradually finding their solutions. Nevertheless, other questions that are equally important have remained unanswered to this day. Some of these – such as the stabilization of quasicrystals, the role of clusters, and the importance