Spin-orbit coupling and the singlet-triplet transition in lateral double quantum dots

We study the electronic level structure in lateral double quantum dots containing one and two electrons. The calculations consider the role of spin-orbit coupling arising from structure inversion asymmetry (Rashba) and bulk inversion asymmetry (Dresselhaus), as well as the competition with diamagnetic and Zeeman effects. Utilizing a finite element approach and full diagonalization of the Hamiltonian, we explore the spatial spin textures and their progression with magnetic field. The competition of different energy scales gives rise to interesting level anticrossings and associated spin mixtures which result in weaker effective Zeeman splitting (smaller effective g factors). The singlet-triplet transition of interest for qubit operations is shown to be strongly affected in narrow band-gap materials, which should have important consequences in phonon-assisted relaxation rates.