Spin-orbit coupling and spin relaxation of hole states in [001]- and [111]-orientedquantum dots of various geometry

TL;DR

This study analyzes how spin-orbit coupling affects hole states and spin relaxation in InAs/GaAs quantum dots with different orientations and geometries, revealing slower relaxation in [111]-oriented dots and strain effects on state coupling.

Contribution

It provides a detailed comparison of spin relaxation and coupling mechanisms in [001]- and [111]-oriented quantum dots using multiband k.p modeling.

Findings

[111]-oriented dots have an order of magnitude slower spin relaxation.

Shear strain significantly influences state coupling.

No s-p shell coupling in [111]-oriented quantum dots.

Abstract

We study the influence of spin-orbit coupling on the hole states in InAs/GaAs quantum dots grown on [001]- and [111]-oriented substrates belonging to symmetry point groups: C2v, C3v and D2d. We investigate the impact of various spin-orbit mechanisms on the strength of coupling between s- and p-shell states, which is a significant spin-flip channel in quantum dots. We calculate spin relaxation rates between the states of lowest Zeeman doublet and show that the [111]-oriented structure offers one order of magnitude slower relaxation compared to the usual [001]-oriented self-assembled QD. The magnetic-field dependence of the hole states is calculated using multiband (up to 14 bands) k.p model. We identify the irreducible representations linked to the states and discuss the selection rules, which govern the avoided-crossing pattern in magnetic-field dependence of the energy levels. We show that dominant contribution to the coupling between some of these states comes from the shear strain. On the other hand, we demonstrate no coupling between s- and p-shell states in the [111]-oriented structure.