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Tunneling is a fundamental quantum process with no classical equivalent,which can compete with Coulomb interactions to give rise to complex phenomena.Phosphorus dopants in silicon can be placed with atomic precision to addressthe different regimes arising from this competition. However, they exploitwavefunctions relying on crystal band symmetries, which tunneling interactionsare inherently sensitive to. Here we directly image lattice-aperiodic valleyinterference between coupled atoms in silicon using scanning tunnelingmicroscopy. Our atomistic analysis unveils the role of envelope anisotropy,valley interference and dopant placement on the Heisenberg spin exchangeinteraction. We find that the exchange can become immune to valley interferenceby engineering in-plane dopant placement along specific crystallographicdirections. A vacuum-like behaviour is recovered, where the exchange ismaximised to the overlap between the donor orbitals, and pair-to-pairvariations limited to a factor of less than 10 considering the accuracy indopant positioning. This robustness remains over a large range of distances,from the strongly Coulomb interacting regime relevant for high-fidelity quantumcomputation to strongly coupled donor arrays of interest for quantum simulationin silicon.

Valley interference and spin exchange at the atomic scale in silicon