Exchange energy and generalized polarization in the presence of spin-orbit coupling in two dimensions

TL;DR

This paper develops a generalized framework for exchange energy in two-dimensional electron systems with spin-orbit coupling, revealing that polarization does not always increase exchange energy, which aligns with recent experimental observations.

Contribution

It introduces a new formulation of exchange energy using generalized fractional polarization, highlighting its impact on spin states in 2D systems with spin-orbit interaction.

Findings

Generalized polarization does not necessarily increase exchange energy.

Unpolarized states can be energetically favored due to spin-orbit effects.

Results qualitatively match recent experimental findings.

Abstract

We discuss a general form of the exchange energy for a homogeneous system of interacting electrons in two spatial dimensions which is particularly suited in the presence of a generic spin-orbit interaction. The theory is best formulated in terms of a generalized fractional electronic polarization. Remarkably we find that a net generalized polarization does not necessarily translate into an increase in the magnitude of the exchange energy, a fact that in turn favors unpolarized states. Our results account qualitatively for the findings of recent experimental investigations.