Continuous chiral distances for two-dimensional lattices.

Abstract

Chirality was traditionally considered a binary property of periodic lattices and crystals. However, the classes of two-dimensional lattices modulo rigid motion form a continuous space, which was recently parametrized by three geographic-style coordinates. The four non-oblique Bravais classes of two-dimensional lattices form low-dimensional singular subspaces in the full continuous space. Now, the deviations of a lattice from its higher symmetry neighbors can be continuously quantified by real-valued distances satisfying metric axioms. This article analyzes these and newer G-chiral distances for millions of two-dimensional lattices that are extracted from thousands of available two-dimensional materials and real crystal structures in the Cambridge Structural Database.