Structural chirality measurements and computation of handedness in periodic solids

TL;DR

This paper compares existing measures of chirality in solids, evaluates their effectiveness, and introduces a new pseudoscalar helicity method to better quantify and distinguish crystal handedness.

Contribution

It proposes a novel helicity-based approach for quantifying crystal handedness, improving upon classical measures in complex solids.

Findings

Helicity effectively distinguishes crystal handedness.

Classical measures have limitations in complex structures.

The new method shows promise in various model systems.

Abstract

We compare the various chirality measures most widely used in the literature to quantify chiral symmetry in extended solids, i.e., the continuous chirality measure, the Hausdorff distance, and the angular momentum. By studying these functions in an algebraically tractable case, we can evaluate their strengths and weaknesses when applied to more complex crystals. Going beyond those classical calculations, we propose a new method to quantify the handedness of a crystal based on a pseudoscalar function, i.e., the helicity. This quantity, borrowed from hydrodynamics, can be computed from the eigenvector carrying the system from the high-symmetry non-chiral phase to the low-symmetry chiral phase. Different model systems like K$_3$NiO$_2$, CsCuCl$_3$ and MgTi$_2$O$_4$ are used as test cases where we show the superior interest of using helicity to quantify chirality together with the handedness distinction.