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

Rui Li,Yidong Wu,C S Liu,Zhi-Hai Liu

doi:10.1038/s41598-018-25692-2

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 σx{mathscr{P}} = −1 symmetry and the other has the σx{mathscr{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 ≠ 0, 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}_{0}^{c}, at which the spin-orbit effect is enhanced to maximal.

Highlights

The spin-orbit coupling (SOC), originating from the lacking of space-inversion symmetry in semiconductor materials[1], has played an important role in the studies of topological insulators[2,3], topological superconductors[4,5,6], cold atom physics[7,8,9], spin quantum computings[10,11,12,13,14,15,16], etc
For quantum dot confined in quasi-2D with strong SOC, many theoretical works have devoted to solving the single electron energy spectrum
We only focus on the strong SOC regime, and the quantum-dot confining potential is modeled by both the infinite square well (ISW) [see Fig. 1(a)] and the finite square well (FSW) [see Fig. 1(b)], i.e., VI(x) = ∞0

Summary

Introduction

The spin-orbit coupling (SOC), originating from the lacking of space-inversion symmetry in semiconductor materials[1], has played an important role in the studies of topological insulators[2,3], topological superconductors[4,5,6], cold atom physics[7,8,9], spin quantum computings[10,11,12,13,14,15,16], etc. For quantum dot confined in quasi-2D with strong SOC, many theoretical works have devoted to solving the single electron energy spectrum. We study the strong spin-orbit effect in a quasi-1D quantum dot with the confining potential modeled by both the infinite square well (ISW) and the finite square well (FSW). With respect to both the Z2 symmetry of the model and the energy region, we obtain a serious of transcendental equations, their solutions give rise to the exact energy spectrum of the quantum dot. We find that there exists a critical well height V0c, at which the spin-orbit effect is enhanced to maximal

Methods

Results

Conclusion