Broken Relativistic Symmetry Groups, Toroidal Moments and Superconductivity in Magnetoelectric Crystals

TL;DR

This paper explores how breaking relativistic symmetry in magnetoelectric crystals leads to toroidal moments and phases, with implications for superconductivity, by linking symmetry breaking to magnetic and electric interactions.

Contribution

It introduces a connection between relativistic symmetry breaking, toroidal moments, and superconductivity in magnetoelectric crystals, expanding understanding of their interplay.

Findings

Toroidal moments are linked to symmetry breaking in crystals.

Goldstone bosons associated with toroidal moments are identified.

Possible effects on superconductor behavior in magnetoelectric materials.

Abstract

A connection between creation of toroidal moments and breaking of the relativistic crystalline group associated to a given crystal, is presented in this paper. Indeed, if magnetoelectric effects exist, the interaction between electrons and elementary magnetic cells appears in such a way that the resulting local polarization and magnetization break the local relativistic crystalline symmetry. Therefore, Goldstone bosons, also associated to toroidal moments, are created and, as a consequence, corresponding toroidal phases in crystals. The list of the Shubnikov groups compatible with this kind of phases is given and possible consequences in superconductor theory in magnetoelectric crystals are examined.