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

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.

8 pages, 3 figures, submitted

References in corpus (4)

• The electronic properties of graphene
• Microscopic approach to current-driven domain wall dynamics
• Equilibrium spin currents: Non-Abelian gauge invariance and color diamagnetism in condensed matter
• Exchange-correlation orbital functionals in current-density-functional theory: Application to a quantum dot in magnetic fields

Cited by in corpus (7)

• Wannier-based calculation of the orbital magnetization in crystals
• Pseudo-potentials based first-principles approach to the magneto-optical Kerr effect: from metals to the inclusion of local fields and excitonic effects
• U(1)$\times$SU(2) Gauge Invariance Made Simple for Density Functional Approximations
• Transverse and longitudinal gradients of the spin magnetization in Spin-Density-Functional Theory
• High density limit of the two-dimensional electron liquid with Rashba spin-orbit coupling
• Two exact properties of the perturbative expansion for the two-dimensional electron liquid with Rashba or Dresselhaus spin-orbit coupling
• Quasiparticle velocities in 2D electron/hole liquids with spin-orbit coupling