Emergence of chirality by multipole interconversion

Abstract: A clear understanding of chirality in spin-active electronic states is discussed in order to address confusions about chiral effects recently discovered in materials science. Electronic toroidal monopole $G_0$ can serve as a measure of chirality in this categorization, which can be clearly related to the chiral density operator in the Dirac equation. We extend the concepts of chirality not only to those of materials but also to those of physical fields, and to material-field composites. Additionally, we illustrate specific examples from physics and chemistry that demonstrate the process of acquiring chirality through the combination of seemingly achiral degrees of freedom, which we term the emergence of chirality. Interference among multiple chiralities exhibiting phenomena specific to handedness is also discussed.