Spin-orbit coupling in the spin-current-density-functional theory
Journal of Physics A: Mathematical and General, Volume 36, No. 48, Year 2003
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Starting from the spin-current-density-functional theory for electronic systems, we extend the formulation to include spin-orbit coupling. Particular attention is devoted to the symmetry of the problem. Here we show that the exchange-correlation energy functional is invariant by the U(1)em × SU(2)spin gauge transformations. We give the transformation laws of the paramagnetic current and also the paramagnetic spin current density by the U(1)em × SU(2)spin gauge transformations. For the case where the spin-orbit coupling is taken into account, we generalize the equations of continuity satisfied by the current density and the spin current density, derived by Vignale and Rasolt.