A symmetry-based descriptor for structural chirality in two-dimensional periodic crystals

Characterizing structural chirality in two-dimensional (2D) periodic crystals remains nontrivial because existing measures often require additional treatments of periodicity, structural correspondence, or reference configurations. Here, we introduce a signed pseudoscalar descriptor constructed directly from atomic coordinates and local atomic environments. It combines global structural asymmetry with local axiality, retains sensitivity to elemental occupation, and requires neither a predefined achiral reference nor explicit matching to a mirror-image counterpart. Because a particular primitive-cell representation of a globally achiral crystal may yield a finite value, we formulate a practical assessment procedure that considers nonprimitive translations and symmetry-equivalent unit-cell choices, supplemented by layer-group or point-group analysis when a vanishing descriptor is inconclusive. Applications to representative monolayer and bilayer systems illustrate its use in assessing structural chirality, distinguishing opposite-handed configurations through its sign, and tracking field-induced chirality within a fixed structural family. Although its value depends on the selected unit-cell representation and its absolute magnitude should not be compared between structurally unrelated materials, the descriptor provides a practical computational tool for handedness assignment and tracking structural chirality under consistent conventions.