Emergence of chirality from electron spins, physical fields, and material-field composites.

This article focuses on clarifying the concept of chirality in spin-active electronic states and its broader implications across physics and chemistry. It emphasizes the electric toroidal monopole \( G_0 \), a time-reversal (T)-even pseudoscalar, as a rigorous measure of true chirality, distinguishing it from false chirality associated with other multipole bases such as magnetic monopoles \( M_0 \). The work systematically classifies various chiral and achiral spin configurations and physical fields using a symmetry-adapted multipole basis framework, linking electronic chirality to relativistic quantum theory via the Dirac equation. It further explores the emergence of chirality through interconversions among multipole bases and discusses enantiospecific responses in chiral materials, including phenomena like chirality-induced spin selectivity (CISS), magneto-chiral anisotropy (MChA), and natural optical activity (NOA). The paper highlights the potential of chirality as a binary information carrier in spintronics and suggests that understanding multipole interconversions could enable novel applications in chirality-based technologies.