Shape effect on the valley splitting in lead selenide nanowires

We study the cross-section shape and size effects on the valley splitting in PbSe nanowires within the framework of empirical $s{p}^3{d}^5{s}^{\ast }$ tight-binding method. We consider ideallized prismatic nanowires, grown along [110], with the cross-section shape varying from rectangular (terminated by $\{001\}$ and $\{110\}$ facets) to rhombic (terminated mostly by $\{111\}$ facets). The valley splitting energies have the maximal value (up to hundreds meV) in rectangular nanowires, while in rhombic ones they are almost absent. The shape dependence is shown to be similar for a wide range cross-section sizes and different point symmetries of nanowires.