Gauge-Invariant Formulation of Spin-Current-Density Functional Theory

TL;DR

This paper introduces a gauge-invariant approach to spin-current-density functional theory by defining a new variable called invariant vorticity, enabling the construction of exchange-correlation functionals that respect gauge symmetries.

Contribution

It presents a novel formulation of spin-current-density functional theory using invariant vorticity to ensure gauge invariance, addressing a longstanding challenge.

Findings

Constructed a gauge-invariant xc energy functional for 2D electron gas with spin-orbit coupling.

Demonstrated the functional's proportionality to the fourth power of the spin current.

Provided a practical example illustrating the new formulation.

Abstract

Spin-currents and non-abelian gauge potentials in electronic systems can be treated by spin-current-density functional theory, whose main input is the exchange-correlation (xc) energy expressed as a functional of spin-currents. Constructing a functional of spin currents that is invariant under U(1)$\times$SU(2) transformations is a long-standing challenge. We solve the problem by expressing the energy as a functional of a new variable we call "invariant vorticity". As an illustration we construct the xc energy functional for a two-dimensional electron gas with linear spin-orbit coupling and show that it is proportional to the fourth power of the spin current.