Spin relaxation in a Si quantum dot due to spin-valley mixing

TL;DR

This paper investigates how spin relaxation in silicon quantum dots is affected by spin-valley mixing and electrical noise, revealing a dominant relaxation channel at the hot spot and implications for low-field qubit coherence.

Contribution

It demonstrates that spin-valley mixing significantly contributes to spin relaxation in Si quantum dots, especially under electrical noise, and identifies the conditions where this effect is maximized.

Findings

Spin relaxation peaks at the hot spot where Zeeman and valley splittings match.

Electrical noise via spin-valley mixing can dominate relaxation at low magnetic fields.

The results align with recent experimental observations of relaxation behavior.

Abstract

We study the relaxation of an electron spin qubit in a Si quantum dot due to electrical noise. In particular, we clarify how the presence of conduction-band valleys influences spin relaxation. In single-valley semiconductor quantum dots, spin relaxation is through the mixing of spin and envelope orbital states via spin-orbit interaction. In Si, the relaxation could also be through the mixing of spin and valley states. We find that the additional spin relaxation channel, via spin-valley mixing and electrical noise, is indeed important for an electron spin in a Si quantum dot. By considering both spin-valley and intravalley spin-orbit mixings and Johnson noise in a Si device, we find that the spin relaxation rate peaks at the hot spot, where the Zeeman splitting matches the valley splitting. Furthermore, because of a weaker field dependence, the spin relaxation rate due to Johnson noise could dominate over phonon noise at low magnetic fields, which fits well with recent experiments.