Spin current density functional theory of Weyl semimetals

Weyl fermions are massless solutions of the Dirac equation described by two-component (2c) complex spinors. Such elusive objects emerge as quasiparticles in so-called Weyl semi-metals (WSM). We discuss the generalization of the standard one-component density functional theory (DFT) to a 2c approach (the spin-current density functional theory, SCDFT), and its application to the practical quantum-mechanical description of WSMs through a self-consistent treatment of the spin-orbit coupling (SOC) and nonlocal Fock exchange. For hybrid exchange-correlation functionals in the local density approximation or generalized gradient approximation of the SCDFT, we use Levy's constrained search formalism to map specific blocks of the SCDFT potential to specific blocks of the one-electron density matrix, which allows for a straightforward comparison of SCDFT with DFT. We show how a three-dimensional doubly degenerate bulk Dirac node is present in the TaAs WSM in the absence of SOC, lying on the k(x) = 0 mirror plane, which is split into two singly degenerate Weyl nodes off the mirror plane by the SOC. This breaking of the degeneracy and the corresponding splitting of the two Weyl nodes with opposite chirality offers a measurable way to assess different theories. We show how an SCDFT formulation is essential to a correct quantitative description of the electronic features of WSMs.