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In previous approaches to form quasicrystals, multiple competing lengthscales involved in particle size, shape or interaction potential are believedto be necessary. It is unexpected that quasicrystals can be self-assembled bymonodisperse, isotropic particles interacting via a simple potential withoutmultiple length scales. Here we report the surprising finding of theself-assembly of such quasicrystals in two dimensional systems of soft-coredisks interacting via repulsions. We find not only dodecagonal but alsooctagonal quasicrystals, which have not been found yet in soft quasicrystals.In the self-assembly of such unexpected quasicrystals, particles tend to formpentagons, which are essential elements to form the quasicrystalline order. Ourfindings pave an unexpected and simple way to form quasicrystals and pose a newchallenge for theoretical understanding of quasicrystals.

Self-assembling two-dimensional quasicrystals in simple systems of monodisperse soft-core disks