Quantification of electronic asymmetry: chirality and axiality in solids

TL;DR

This paper introduces a new method to quantify chirality and axiality in solids using electron chirality distribution and spin-derived electric polarization, supported by first-principles calculations and observable via circular dichroism spectroscopy.

Contribution

It presents a novel framework for quantifying material chirality and axiality through electron distribution and polarization, enabling exploration of new functional materials.

Findings

Electron chirality distribution characterizes material chirality and axiality.

Spin-derived electric polarization indicates material polarity.

Electron chirality can be observed via circular dichroism in photoemission spectroscopy.

Abstract

Chiral and axial materials offer platforms for intriguing phenomena, such as cross-correlated responses and chirality-induced spin selectivity. However, quantifying the properties of such materials has generally been considered challenging. Here, we demonstrate that the spatial distribution of the electron chirality, represented by $\Psi^\dagger \gamma^5 \Psi$ with the four-component Dirac field $\Psi$, characterizes the chirality and axiality of materials. Furthermore, we reveal that spin-derived electric polarization can serve as an effective indicator of material polarity. We present quantitative evaluations of electron chirality distribution and spin-derived electric polarization based on first-principles calculations. Additionally, we propose that electron chirality can be directly observed via circular dichroism in photoemission spectroscopy, which measures the difference between right- and left-handed circularly polarized light. Electron chirality and spin-derived electric polarization provide a new framework for quantifying chirality, axiality, and polarity in asymmetric materials, paving the way for the exploration of novel functional materials.