Self-assembly of quasicrystals under cyclic shear

TL;DR

This study demonstrates that cyclic shear can effectively induce the self-assembly of two-dimensional dodecagonal quasicrystals, offering a non-equilibrium pathway to complex ordered structures comparable to thermal systems.

Contribution

It reveals that mechanical cyclic shear can stabilize quasicrystalline order in particle systems, bypassing the need for thermal annealing and mimicking entropic effects.

Findings

Cyclic shear drives random configurations into ordered quasicrystals.

The non-equilibrium phase diagram mirrors thermal equilibrium phases.

Quasicrystals form quickly without complex annealing protocols.

Abstract

We investigate the self-assembly of two-dimensional dodecagonal quasicrystals driven by cyclic shear, effectively replacing thermal fluctuations with plastic rearrangements. Using particles interacting via a smoothed square-shoulder potential, we demonstrate that cyclic shearing drives initially random configurations into ordered quasicrystalline states. The resulting non-equilibrium phase diagram qualitatively mirrors that of thermal equilibrium, exhibiting square, quasicrystalline, and hexagonal phases, as well as phase coexistence. Remarkably, the shear-stabilised quasicrystal appears even where the zero-temperature equilibrium ground state favours square-hexagonal coexistence, suggesting that mechanical driving can stabilise quasicrystalline order in a way analogous to entropic effects in thermal systems. The structural quality of the self-assembled state is maximised near the yielding transition, even though the dynamics are slowest there. Yet, the system still quickly forms monodomain quasicrystals without any complex annealing protocols, unlike at equilibrium, where thermal annealing would be required. Finite-size scaling analysis reveals that global orientational order decays slowly with system size, indicative of quasi-long-range order comparable to equilibrium hexatic phases. Overall, our results establish cyclic shear as an efficient pathway for the self-assembly of complex structures.