Valley interference and spin exchange at the atomic scale in silicon

TL;DR

This paper uses scanning tunneling microscopy to image valley interference effects between phosphorus dopants in silicon and demonstrates how precise dopant placement can make spin exchange interactions more robust against valley interference, advancing quantum computing and simulation.

Contribution

It reveals how in-plane dopant placement along specific crystallographic directions can mitigate valley interference effects on spin exchange in silicon.

Findings

Valley interference affects spin exchange interactions.

Engineering dopant placement enhances robustness of exchange.

Exchange interactions remain stable over a range of distances.

Abstract

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 address the different regimes arising from this competition. However, they exploit wavefunctions relying on crystal band symmetries, which tunneling interactions are inherently sensitive to. Here we directly image lattice-aperiodic valley interference between coupled atoms in silicon using scanning tunneling microscopy. Our atomistic analysis unveils the role of envelope anisotropy, valley interference and dopant placement on the Heisenberg spin exchange interaction. We find that the exchange can become immune to valley interference by engineering in-plane dopant placement along specific crystallographic directions. A vacuum-like behaviour is recovered, where the exchange is maximised to the overlap between the donor orbitals, and pair-to-pair variations limited to a factor of less than 10 considering the accuracy in dopant positioning. This robustness remains over a large range of distances, from the strongly Coulomb interacting regime relevant for high-fidelity quantum computation to strongly coupled donor arrays of interest for quantum simulation in silicon.