Spin current and chirality degrees of freedom inherent in localized electron orbitals

TL;DR

This paper reveals an exotic order parameter in localized electron orbitals linked to spin currents and chirality, offering new insights into quantum states of matter beyond traditional charge, spin, or current descriptions.

Contribution

It introduces the concept of electric toroidal multipoles as an order parameter connected to spin currents and chirality in localized electron orbitals, expanding understanding of quantum states.

Findings

Identification of an exotic order parameter in electron orbitals.

Link between spin currents, chirality, and electric toroidal multipoles.

New perspective on microscopic quantum states of matter.

Abstract

In solid state physics, any phase transition is commonly observed as a change in the microscopic distribution of charge, spin, or current. Here we report the nature of an exotic order parameter inherent in the localized electron orbitals that cannot be primarily captured by these three fundamental quantities. This order parameter is described as the electric toroidal multipoles connecting different total angular momenta under the spin-orbit coupling. The corresponding microscopic physical quantity is the spin current tensor on an atomic scale, which induces spin-derived electric polarization and the chirality of the Dirac equation. We stress that the chirality intrinsic to the elementary particle is the essence of electric toroidal multipoles. These findings link microscopic spin currents and chirality in the Dirac theory to the concept of multipoles and provide a new perspective for quantum states of matter.