Decoherence induced by anisotropic hyperfine interaction in Si spin qubits

We study Si:P donor electron spin decoherence due to anisotropic hyperfine (AHF) interaction with the surrounding nuclear spin bath. In particular, we clarify the electron spin echo envelope modulation (ESEEM) in the Si:P system and the resonancelike contributions from nuclear spins in various shells away from the P atoms. We suggest an approach to minimize AHF-induced decoherence by avoiding the resonances and orienting an applied magnetic field along directions that can periodically eliminate contributions from the dominant nearest neighbor atoms. Our remarkable agreement with experiment demonstrates nearly complete understanding of electron spin decoherence in Si:P when combining ESEEM, spectral diffusion, instantaneous diffusion, and spin-lattice relaxation.