Hubbard model description of silicon spin qubits: charge stability diagram and tunnel coupling in Si double quantum dots

TL;DR

This paper uses a Hubbard model approach to accurately describe charge stability and tunnel coupling in silicon double quantum dots, aligning well with experimental data and simplifying complex multi-electron systems.

Contribution

It introduces a Hubbard model-based method for modeling silicon quantum dots, reducing complex multi-electron systems to an effective two-electron model for better tractability.

Findings

Excellent agreement between theory and experiment.

Effective two-electron model captures key physics.

Comparison of confinement potentials shows robustness.

Abstract

We apply the recently introduced Hubbard model approach to quantitatively describe the experimental charge stability diagram and tunnel coupling of silicon double quantum dot systems. The results calculated from both the generalized Hubbard model and the microscopic theory are compared with existing experimental data, and excellent agreement between theory and experiment is found. The central approximation of our theory is a reduction of the full multi-electron multi-band system to an effective two-electron model, which is numerically tractable. In the microscopic theory we utilize the Hund-Mulliken approximation to the electron wave functions and compare the results calculated with two different forms of confinement potentials (biquadratic and Gaussian). We discuss the implications of our work for future studies.