Valley Structure and Giant Spin Splitting in Lead Salts Nanowires

We employ tight-binding method and ${\bf k} \cdot {\bf p}$ theory to analyze valley structure of PbSe nanowires grown along the $[111]$ direction and having unit cells of different point symmetry: $D_{3d}$, $D_3$, and $C_{2h}$. We show that, while all three nanowire symmetries ehxibit large valley splittings of electronic subbands, the $D_3$ wires are of special interest, as they possess a screw axis which results in appreciable spin-dependent splittings of electronic subbands, linear in one-dimensional wave vector.