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

In this work, chirality in spin-active electronic states is explained clearly to address confusion about chiral effects recently discovered in materials science. We stress that the electronic toroidal monopole G0 can serve as a measure of chirality. By using the symmetry classification in terms of four distinct types of multipole bases, we extend the concept of chirality from materials to physical fields and 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 between multiple chiralities exhibiting phenomena specific to handedness is also discussed.