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

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

2009-02-02

arxiv.org/abs/0902.0374v2

Phys. Rev. B 81, 125123 (2010)

Physics

Condensed Matter

Materials Science

8 pages, 3 figures, submitted

Scientific paper

10.1103/PhysRevB.81.125123

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.

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