Theory of nuclear induced spectral diffusion: Spin decoherence of phosphorus donors in Si and GaAs quantum dots

Abstract

We propose a model for spectral diffusion of localized spins in semiconductors due to the dipolar fluctuations of lattice nuclear spins. Each nuclear spin flip-flop is assumed to be independent, the rate for this process being calculated by a method of moments. Our calculated spin decoherence time $T_M=0.64$ ms for donor electron spins in Si:P is a factor of two longer than spin echo decay measurements. For ${}^{31}$P nuclear spins we show that spectral diffusion is well into the motional narrowing regime. The calculation for GaAs quantum dots gives $T_M=10-50$ $\mu$s depending on the quantum dot size. Our theory indicates that nuclear induced spectral diffusion should not be a serious problem in developing spin-based semiconductor quantum computer architectures.

15 pages, 9 figures. Accepted for publication in Phys. Rev. B

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