# Confinement sensitivity in quantum dot singlet-triplet relaxation

## TL;DR

This paper investigates how the shape of a quantum dot influences spin relaxation rates, focusing on phonon interactions and spin-orbit effects in two-electron GaAs systems under magnetic fields.

## Contribution

It compares different confining potentials and analyzes the role of spin-orbit interactions and magnetic field orientation on relaxation rates in quantum dots.

## Key findings

- Elliptical and cylindrical potentials show different relaxation behaviors.
- Spin hot-spots significantly affect relaxation rates.
- Cubic Dresselhaus effect influences phonon-induced transitions.

## Abstract

Spin-orbit mediated phonon relaxation in a two-dimensional quantum dot is investigated using different confining potentials. Elliptical harmonic oscillator and cylindrical well results are compared to each other in the case of a two-electron GaAs quantum dot subjected to a tilted magnetic field. The lowest energy set of two-body singlet and triplet states are calculated including spin-orbit and magnetic effects. These are used to calculate the phonon induced transition rate from the excited triplet to the ground state singlet for magnetic fields up to where the states cross. The roll of the cubic Dresselhaus effect and the positioning of "spin hot-spots" are discussed and relaxation rates for a few different systems are exhibited.