Spin–orbit coupling in the spin-current-density-functional theory

Abstract

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.