Valley interference and spin exchange at the atomic scale in silicon

B Voisin,S Rogge,R Rahman,L C L Hollenberg,M Y Simmons,A Tankasala,J Salfi,M Usman,J Bocquel

doi:10.1038/s41467-020-19835-1

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.

Highlights

Tunneling is a fundamental quantum process with no classical equivalent, which can compete with Coulomb interactions to give rise to complex phenomena
Resolved transport is performed at 4 K between a heavily doped reservoir and the tip of a scanning tunnelling microscope (STM)
We found that the exchange interaction along the [110] direction is dominated by the jzz term and is insensitive to in-plane valley interference Δφx and Δφy

Summary

Introduction

Tunneling is a fundamental quantum process with no classical equivalent, which can compete with Coulomb interactions to give rise to complex phenomena. 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. 2D donor arrays (see Fig. 1a) can be fabricated using scanning tunnelling lithography, where the atoms can be placed anywhere in a single atomic plane These atomically precise devices can be engineered to achieve both the Heisenberg limit or the non-perturbative tunnelling interactions regime at short inter-dopant distances, with ratios U/t possibly lower than 10

Objectives

Methods

Results

Conclusion