# Valley and spin splittings in PbSe nanowires

## TL;DR

This study investigates how atomic arrangement and symmetry affect valley and spin splittings in PbSe nanowires, revealing significant effects at small diameters and giant spin splitting in certain symmetries.

## Contribution

It provides a detailed analysis of valley and spin splittings in PbSe nanowires using an empirical tight-binding approach, highlighting the impact of atomic symmetry and size.

## Key findings

- Valley-orbit and spin-orbit splittings are highly sensitive to atomic arrangement.
- Nanowires with D3 symmetry exhibit giant linear spin splitting up to 1 eV·Å.
- For diameters below 4 nm, splittings become comparable to confinement energies.

## 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 $D_{3d}$, $C_{2h}$ and $D_{3}$ symmetries. For the nanowire diameter below 4 nm the valley-orbit splittings become comparable with the confinement energies and the $\boldsymbol{k}\cdot\boldsymbol{p}$ method is inapplicable. Nanowires with the $D_{3}$ point symmetry having no inversion center exhibit giant spin splitting $E = \alpha k_z$, linear in one-dimensional wave vector $k_z$, with the constant $\alpha$ up to 1 eV$\cdot$\AA.