Can electrostatic field lift spin degeneracy?

TL;DR

This paper explores whether electrostatic fields alone can lift electron spin degeneracy, proposing a novel mechanism that requires broken inversion and translational symmetry, distinct from traditional magnetic or spin-orbit effects.

Contribution

It introduces a new theoretical perspective on spin degeneracy lifting, emphasizing the role of symmetry breaking and challenging the necessity of spin-orbit coupling.

Findings

Pure electrostatic fields cannot lift spin degeneracy in Bloch states due to translational invariance.

Breaking inversion and translational symmetry may enable electrostatic fields to lift spin degeneracy.

The work suggests a new avenue for spin control in materials without relying on spin-orbit interactions.

Abstract

There are two well known mechanisms which lead to lifting of energy spin degeneracy of single electron systems - magnetic field and spin-orbit coupling. We investigate the possibility for existence of a third mechanism in which electrostatic field can lead to lifting of spin-degeneracy directly without the mediation of spin-orbit coupling. A novel argument is provided for the need of spin-orbit coupling different from the usual relativistic considerations. It is shown that due to preserved translational invariance spin splitting purely by electrostatic field is not possible for Bloch states. A possible lifting of spin degeneracy by electrostatic field characterized by broken inversion and translational invariance is considered.