The impacts of the quantum-dot confining potential on the spin-orbit effect

TL;DR

This paper investigates how the confining potential shape in nanowire quantum dots influences the spin-orbit effect, revealing a critical well height that maximizes this interaction and detailing the bound states' properties.

Contribution

It provides exact solutions for energy spectra and wave functions in finite and infinite wells, highlighting the impact of well height on spin-orbit enhancement in quantum dots.

Findings

Existence of at least two bound states regardless of well height.

Position shift of the first excited state's probability density with well height.

Identification of a critical well height for maximal spin-orbit effect.

Abstract

For a nanowire quantum dot with the confining potential modeled by both the infinite and the finite square wells, we obtain exactly the energy spectrum and the wave functions in the strong spin-orbit coupling regime. We find that regardless of how small the well height is, there are at least two bound states in the finite square well: one has the $\sigma^{x}\mathcal{P}=-1$ symmetry and the other has the $\sigma^{x}\mathcal{P}=1$ symmetry. When the well height is slowly tuned from large to small, the position of the maximal probability density of the first excited state moves from the center to $x\ne0$, while the position of the maximal probability density of the ground state is always at the center. A strong enhancement of the spin-orbit effect is demonstrated by tuning the well height. In particular, there exists a critical height $V^{c}_{0}$, at which the spin-orbit effect is enhanced to maximal.