Spin-orbit coupling and anisotropic exchange in two-electron double quantum dots

TL;DR

This paper investigates how spin-orbit interactions affect the energy spectrum of two-electron quantum dots, validating an effective Hamiltonian model with numerical results and highlighting its practical reliability.

Contribution

It demonstrates the quantitative reliability of the anisotropic exchange Hamiltonian in double quantum dots and confirms the validity of the Heitler-London approximation in weak coupling regimes.

Findings

The model remains valid even at maximal interdot coupling due to symmetry.

Heitler-London approximation accurately predicts anisotropic exchange in weak coupling.

Discrepancies are mainly due to the cubic Dresselhaus term.

Abstract

The influence of the spin-orbit interactions on the energy spectrum of two-electron laterally coupled quantum dots is investigated. The effective Hamiltonian for a spin qubit pair proposed in F. Baruffa et al., Phys. Rev. Lett. 104, 126401 (2010) is confronted with exact numerical results in single and double quantum dots in zero and finite magnetic field. The anisotropic exchange Hamiltonian is found quantitatively reliable in double dots in general. There are two findings of particular practical importance: i) The model stays valid even for maximal possible interdot coupling (a single dot), due to the absence of a coupling to the nearest excited level, a fact following from the dot symmetry. ii) In a weak coupling regime, the Heitler-London approximation gives quantitatively correct anisotropic exchange parameters even in a finite magnetic field, although this method is known to fail for the isotropic exchange. The small discrepancy between the analytical model (which employes the linear Dresselhaus and Bychkov-Rashba spin-orbit terms) and the numerical data for GaAs quantum dots is found to be mostly due to the cubic Dresselhaus term.