A simple mechanism for emergent chirality in achiral hard particle assembly

For centuries, chirality has been appreciated as a key component in understanding how matter orders. While intuitively chiral particles can self-assemble into chiral superstructures, it is often less obvious how achiral particles can do the same. Here we show that there is a potentially general, packing-based mechanism that explains why many simple, two-dimensional achiral particles assemble into chiral materials. Namely, we use simulations of hard, regular polygons to show that the subtle shape modification of corner rounding surprisingly can induce chiral symmetry breaking by deforming the underlying close-packed lattice. The mechanism quantitatively explains recent experimental results reporting chiral symmetry breaking in the hard triangle system. Moreover, it predicts similar symmetry breaking in the rounded hard rectangle system, which we verify through simulations. Because effective corner rounding is easily realized by modulating repulsive interactions in real systems, this simple mechanism suggests tremendous potential for creating dynamically tunable chiral surfaces with a variety of applications.