First-principles calculations of hyperfine interaction, binding energy, and quadrupole coupling for shallow donors in silicon

Michael W Swift,Chris G Van De Walle,Hartwin Peelaers,John J L Morton,Sai Mu

doi:10.1038/s41524-020-00448-7

Abstract

Spin qubits based on shallow donors in silicon are a promising quantum information technology with enormous potential scalability due to the existence of robust silicon-processing infrastructure. However, the most accurate theories of donor electronic structure lack predictive power because of their reliance on empirical fitting parameters, while predictive ab initio methods have so far been lacking in accuracy due to size of the donor wavefunction compared to typical simulation cells. We show that density functional theory with hybrid and traditional functionals working in tandem can bridge this gap. Our first-principles approach allows remarkable accuracy in binding energies (67 meV for bismuth and 54 meV for arsenic) without the use of empirical fitting. We also obtain reasonable hyperfine parameters (1263 MHz for Bi and 133 MHz for As) and superhyperfine parameters. We demonstrate the importance of a predictive model by showing that hydrostatic strain has much larger effect on the hyperfine structure than predicted by effective mass theory, and by elucidating the underlying mechanisms through symmetry analysis of the shallow donor charge density.

Highlights

The advent of quantum computers capable of completing tasks beyond the capabilities of the most powerful classical supercomputers represents a new era in computation[1]
Our results clearly show that the isotropic hyperfine parameter depends linearly on the hydrostatic component of strain with a coefficient that significantly differs from that predicted by effective mass theory, highlighting the importance of valleyorbit coupling and central-cell corrections
This allows us to study the evolution of the hyperfine parameter and quadrupole coupling of shallow donors as a function of strain without the use of empirical fitting parameters

Summary

INTRODUCTION

The advent of quantum computers capable of completing tasks beyond the capabilities of the most powerful classical supercomputers represents a new era in computation[1]. The extrapolated value is 93.6 MHz, compared to an experimental value of 198.3 MHz17 This underestimation of the hyperfine parameter is again due to a lack of localization in the PBE wavefunction, and can be improved using HSE in a similar way as for the binding energies. The calculation of the hyperfine parameter as a function of hydrostatic strain [Fig. 4a for n = 6, N = 1728] was repeated at different supercell sizes and subjected to similar scaling analysis as binding energies (Fig. 1) and hyperfine parameters (Fig. 2) Our results clearly show that the isotropic hyperfine parameter depends linearly on the hydrostatic component of strain with a coefficient that significantly differs from that predicted by effective mass theory, highlighting the importance of valleyorbit coupling and central-cell corrections. The “Kohn–Luttinger oscillations” evident in the shf parameters (Fig. 3) may be seen in the shape of the visualized spin density, which differs significantly from the effective-mass-theory prediction

DISCUSSION

Findings

METHODS