Shallow donor wavefunctions and donor-pair exchange in silicon: Ab initio theory and floating-phase Heitler-London approach

TL;DR

This paper investigates shallow donor wavefunctions in silicon using ab initio methods and introduces a floating-phase Heitler-London approach to better understand exchange interactions relevant for quantum computing.

Contribution

It develops a floating-phase Heitler-London model that confirms and extends previous understanding of exchange oscillations in silicon donors, incorporating ab initio data.

Findings

Inter-valley interference causes oscillatory exchange coupling.

The plane-wave parts of Bloch functions dominate exchange oscillations.

The floating-phase HL approach generalizes the analysis of oscillatory behavior.

Abstract

Electronic and nuclear spins of shallow donors in Silicon are attractive candidates for qubits in quantum computer proposals. Shallow donor exchange gates are frequently invoked to preform two-qubit operations in such proposals. We study shallow donor electron properties in Si within the Kohn-Luttinger envelope function approach, incorporating the full Bloch states of the six band edges of Si conduction band, obtained from {\it ab initio} calculations within the density-functional and pseudopotential frameworks. Inter-valley interference between the conduction-band-edge states of Si leads to oscillatory behavior in the charge distribution of one-electron bound states and in the exchange coupling in two-electron states. The behavior in the donor electron charge distribution is strongly influenced by interference from the plane-wave and periodic parts of the Bloch functions. For two donors, oscillations in the exchange coupling calculated within the Heitler-London (HL) approach are due to the plane-wave parts of the Bloch functions alone, which are pinned to the impurity sites. The robustness of this result is assessed by relaxing the phase pinning to the donor sites. We introduce a more general theoretical scheme, the floating-phase HL, from which the previously reported donor exchange oscillatory behavior is qualitatively and quantitatively confirmed. The floating-phase formalism provides a ``handle'' on how to theoretically anticipate the occurrence of oscillatory behavior in electronic properties associated with electron bound states in more general confining potentials, such as in quantum dots.