Structural Chirality and Natural Optical Activity across the $\alpha$-to-$\beta$ Phase Transition in SiO$_2$ and AlPO$_4$ from first-principles

Natural optical activity (NOA), the ability of a material to rotate the plane of polarized light, has traditionally been associated with structural chirality. However, this relationship has often been oversimplified, leading to conceptual misunderstandings, particularly when attempts are made to directly correlate structural handedness with optical rotatory power. In reality, the relationship between chirality and NOA is more nuanced: optical activity can arise in both chiral and achiral crystal structures, and the sign of the rotation cannot necessarily be inferred from the handedness of the space group. % In this work, we conduct a first-principles investigation of natural optical activity in SiO$_2$ and AlPO$_4$ crystals, focusing on their enantiomorphic structural phase transition from high-symmetry hexagonal ($P6_422$ or $P6_222$) to low-symmetry trigonal ($P3_121$ or $P3_221$) space groups. This transition, driven by the condensation of a zone-center $\Gamma_3$ phonon mode, reverses the screw axis type given by the space group symbol while leaving the sign of the optical activity unchanged. By following the evolution of the structure and the optical response along the transition pathway, we clarify the microscopic origin of this behavior. We demonstrate that the sense of optical rotation is determined not by the nominal helicity of the screw axis given in the space group symbol, but by the atomic-scale helicity of the most polarizable atoms of the structure.