Theory of charge stability diagrams in coupled quantum dot qubits

TL;DR

This paper develops a detailed numerical model for charge stability diagrams in coupled quantum dot qubits, improving accuracy over classical models and revealing effects of electron interactions and device geometry.

Contribution

It introduces a multi-electron configuration interaction approach combined with an atomic orbital model to accurately predict charge stability diagrams in quantum dots.

Findings

Charge states are predicted more accurately than classical models.

Tunnel couplings are significantly enhanced for multi-electron dots.

Barrier gate strength and dot pitch influence charge stability features.

Abstract

We predict large regions of the charge stability diagram using a multi-band and multi-electron configuration interaction model of a double quantum dot system. We account for many-body interactions within each quantum dot using full configuration interaction and solve for single-particle density operators. This allows charge states to be predicted more accurately than the extensively used classical capacitance model or the single-band Hubbard model. The resulting single-particle mixed states then serve as inputs into an atomic orbital picture that allows for the explicit calculation of the underlying Hubbard model parameters by performing the appropriate integrals. This numerical approach allows for arbitrary choices of electrostatic potential and gate geometry. A common assumption when calculating charge stability diagrams from the Hubbard model is that the charge stability diagrams are periodic, but we find that the tunnel couplings for valence electrons in dots with $N=3$ electrons are significantly enhanced when compared to single-electron dots. This difference is apparent in the charge stability diagram for higher occupancy Coulomb diamonds. We also quantitatively explore how the barrier gate strength and dot pitch impact this behavior. Our work should help improve the future realistic modeling of semiconductor-dot-based quantum circuits.