On the definition of chirality and enantioselective fields

TL;DR

This paper defines the order parameter for molecular and crystal chirality as an electric toroidal monopole G_0, enabling the discussion of external fields distinguishing enantiomers and providing insights into chiral phenomena like CISS.

Contribution

It introduces G_0 as the order parameter for chirality, linking symmetry breaking to physical fields and chiral effects, which was previously undefined.

Findings

G_0 serves as the order parameter for chirality.

External fields can distinguish enantiomers via G_0.

Insights into CISS and chiral resolution mechanisms.

Abstract

In solid state physics, any symmetry breaking is known to be associated with emergence of an order parameter. However, the order parameter for molecular and crystal chirality, which is a consequence of parity and mirror symmetry breaking, has not been known since its discovery. In this article, the authors show that the order parameter for chirality can be defined by electric toroidal monopole G_0. By this definition, one becomes able to discuss external filed that can distinguish two different enantiomers only by physical fields. In addition, dynamics and fluctuations of the order parameter G_0 can be discussed, with which one can obtain fruitful insights on a spin filtering effect called CISS (Chirality Induced Spin Selectivity). Emergence of time-reversal-odd dipole M_z by time propagation of G_0 quantities is discussed to explain the enantioselective effect (chiral resolution) at a ferromagnetic surface.