Absence of intrinsic spin splitting in one-dimensional quantum wires of tetrahedral semiconductors

The energy bands of three-, two-, and one-dimensional (1D) structures are generally split at certain wave-vector values into spin components, a spin splitting (SS) that occurs even without an external magnetic field and reflects the effect of spin-orbit interaction on certain symmetries. We show via atomistic theory that 1D quantum wires made of conventional zinc-blende semiconductors have unexpected zero SS for all electron and hole bands if the wire is oriented along (001) (belonging to D-2d symmetry), and for some of bands if the wire is oriented along (111) (belonging to C-3v symmetry). We find that the predicted absence of a Dresselhaus SS in both (001)-oriented and (111)-oriented 1D wires is immune to perturbations lowering their original D-2d and C-3v structural symmetries, such as alloying of the matrix around the wire or application of an external electric field. Indeed, such perturbations induce only a Rashba SS. We find that the scaling of the SS with the wave vector is dominated by a linear term plus a minor cubic term.