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Spin-current density functional theory (SCDFT) is a formally exact frameworkdesigned to handle the treatment of interacting many-electron systems includingspin-orbit coupling at the level of the Pauli equation. In practice, robust andaccurate calculations of the electronic structure of these systems call forfunctional approximations that depend not only on the densities, but also onspin-orbitals. Here we show that the call can be answered by resorting to anextension of the Kohn-Sham formalism, which admits the use of non-localeffective potentials, yet it is firmly rooted in SCDFT. The power of theextended formalism is demonstrated by calculating the spin-orbit-inducedband-splittings of inversion-asymmetric MoSe$_2$ monolayer andinversion-symmetric bulk $\alpha$-MoTe$_2$. We show that quantitative agreementwith experimental data is obtainable via global hybrid approximations bysetting the fraction of Fock exchange at the same level which yields accuratevalues of the band gap. Key to these results is the ability of the method toself-consistently account for the spin currents induced by the spin-orbitinteraction. The widely used method of refining spin-density functional theoryby a second-variational treatment of spin-orbit coupling is unable to match ourSCDFT results.

Generalized Kohn-Sham Approach for the Electronic Band Structure of Spin-Orbit Coupled Materials