On the validity of microscopic calculations of double-quantum-dot spin qubits based on Fock-Darwin states

TL;DR

This paper critically evaluates the accuracy of common microscopic models for double-quantum-dot spin qubits, revealing significant underestimations of the exchange interaction due to limitations of Fock-Darwin states, especially in higher dimensions.

Contribution

It demonstrates that typical Fock-Darwin-based calculations underestimate the exchange interaction, highlighting the need to reassess these models for better accuracy in quantum dot qubit analysis.

Findings

Fock-Darwin states underestimate exchange interactions.

Heitler-London and Hund-Mulliken approximations have limitations.

Underestimation worsens in higher dimensions.

Abstract

We consider two typical approximations that are used in the microscopic calculations of double-quantum dot spin qubits, namely, the Heitler-London (HL) and the Hund-Mulliken (HM) approximations, which use linear combinations of Fock-Darwin states to approximate the two-electron states under the double-well confinement potential. We compared these results to a case in which the solution to a one-dimensional Schr\"odinger equation was exactly known and found that typical microscopic calculations based on Fock-Darwin states substantially underestimate the value of the exchange interaction, which is the key parameter that controls the quantum dot spin qubits. This underestimation originates from the lack of tunneling of Fock-Darwin states, which is accurate only in the case with a single potential well. Our results suggest that the accuracies of the current two-dimensional molecular-orbit-theoretical calculations based on Fock-Darwin states should be revisited since underestimation could only deteriorate in dimensions that are higher than one.