Electron chirality and hydrodynamic helicity: Analysis in the atomic limit

TL;DR

This paper investigates electron chirality and hydrodynamic helicity in atomic models, revealing how crystal fields, spin-orbit coupling, and electron interactions influence these measures, with implications for understanding electronic chirality.

Contribution

It introduces a detailed analysis of electron chirality and hydrodynamic helicity in atomic models, clarifying their dependence on various microscopic parameters and symmetry considerations.

Findings

Electron chirality increases with spin-orbit coupling and chiral crystal field strength.

Hydrodynamic helicity remains non-zero without spin-orbit coupling due to electron-electron interactions.

Near quasidegenerate energy levels, electron chirality becomes insensitive to spin-orbit coupling.

Abstract

Electron chirality has been proposed as a microscopic quantity that characterizes electronic handedness, yet its underlying control parameter has not been clearly identified. Furthermore, its applicability is limited to systems with spin-orbit coupling, which motivates the need for alternative measures of chirality. In this work, we explore two complementary measures of chirality: electron chirality and hydrodynamic helicity. By analyzing a minimal atomic model under chiral crystal fields, we clarify how the interplay among crystal fields, spin-orbit coupling, and electron correlation gives rise to non-zero values of chirality measures. Although electron chirality increases with both spin-orbit coupling and chiral crystal field strength, the dependence on these two factors is highly non-trivial. Particularly, when the chiral crystal field is varied continuously and the energy levels approach quasidegenerate points, the electron chirality is insensitive to spin-orbit coupling, resulting in a remarkable enhancement of chirality. In contrast, the hydrodynamic helicity, defined as a two-body pseudoscalar quantity, remains non-zero even without spin-orbit coupling, originating from electron-electron interactions. Perturbative analysis reveals distinct symmetry selection rules governing the two quantities. Our results provide fundamental insight into the origin of chiralities in electronic systems.