Spin relaxation at the singlet-triplet crossing in a quantum dot

TL;DR

This paper investigates how spin relaxation occurs at the singlet-triplet crossing in a two-electron quantum dot, highlighting the roles of spin-orbit coupling, Coulomb interaction, and phonons, and providing theoretical rates consistent with experiments.

Contribution

It offers a detailed analysis of singlet-triplet spin relaxation mechanisms, including the effects of Coulomb interaction and spin-orbit coupling, with calculations matching experimental observations.

Findings

Spin relaxation rates vary strongly with singlet-triplet splitting.

Coulomb interaction influences relaxation channels differently depending on its strength.

Relaxation rates are proportional to the square of the Zeeman energy.

Abstract

We study spin relaxation in a two-electron quantum dot in the vicinity of the singlet-triplet crossing. The spin relaxation occurs due to a combined effect of the spin-orbit, Zeeman, and electron-phonon interactions. The singlet-triplet relaxation rates exhibit strong variations as a function of the singlet-triplet splitting. We show that the Coulomb interaction between the electrons has two competing effects on the singlet-triplet spin relaxation. One effect is to enhance the relative strength of spin-orbit coupling in the quantum dot, resulting in larger spin-orbit splittings and thus in a stronger coupling of spin to charge. The other effect is to make the charge density profiles of the singlet and triplet look similar to each other, thus diminishing the ability of charge environments to discriminate between singlet and triplet states. We thus find essentially different channels of singlet-triplet relaxation for the case of strong and weak Coulomb interaction. Finally, for the linear in momentum Dresselhaus and Rashba spin-orbit interactions, we calculate the singlet-triplet relaxation rates to leading order in the spin-orbit interaction, and find that they are proportional to the second power of the Zeeman energy, in agreement with recent experiments on triplet-to-singlet relaxation in quantum dots.