Electron spin decoherence in isotope-enriched silicon

TL;DR

This paper investigates the factors limiting electron spin coherence times in isotope-enriched silicon, highlighting the significant role of residual electron spins from impurities, and uses advanced modeling to match experimental data.

Contribution

It introduces a cluster expansion method to analyze spin decoherence, emphasizing the impact of background electron spins from residual impurities in silicon.

Findings

Background electron spins significantly limit $T_2$ in isotope-enriched silicon.

Model results agree with experimental spin echo data.

Residual phosphorus impurities are identified as a key decoherence source.

Abstract

Silicon is promising for spin-based quantum computation because nuclear spins, a source of magnetic noise, may be eliminated through isotopic enrichment. Long spin decoherence times, $T_2$, have been measured in isotope-enriched silicon but come far short of the $T_2 = 2 T_1$ limit. The effect of nuclear spins on $T_2$ is well established. However, the effect of background electron spins from ever present residual phosphorus impurities in silicon can also produce significant decoherence. We study spin decoherence decay as a function of donor concentration, $^{29}$Si concentration, and temperature using cluster expansion techniques specifically adapted to the problem of a sparse dipolarly coupled electron spin bath. Our results agree with the existing experimental spin echo data in Si:P and establish the importance of background dopants as the ultimate decoherence mechanism in isotope-enriched silicon.