Valley and spin splittings in PbSe nanowires

Abstract

We use an empirical tight-binding approach to calculate electron and hole states in [111]-grown PbSe nanowires. We show that the valley-orbit and spin-orbit splittings are very sensitive to the atomic arrangement within the nanowire elementary cell and differ for [111] nanowires with microscopic D3d,C2h, and D3 symmetries. For the nanowire diameter below 4 nm the valley-orbit splittings become comparable with the confinement energies and the k·p method is inapplicable. Nanowires with the D3 point symmetry having no inversion center exhibit giant spin splitting E=αkz, linear in one-dimensional wave vector kz, with the constant α up to 1eVÅ.