g -factor of electrons in gate-defined quantum dots in a strong in-plane magnetic field

Abstract

We analyze orbital effects of an in-plane magnetic field on the spin structure of states of a gated quantum dot based in a two-dimensional electron gas. Starting with a k·p Hamiltonian, we perturbatively calculate these effects for the conduction band of GaAs, up to the third power of the magnetic field. We quantify several corrections to the g-tensor and reveal their relative importance. We find that for typical parameters, the Rashba spin-orbit term and the isotropic term, H43 ∝ P 2 B · σ, give the largest contributions in magnitude. The in-plane anisotropy of the g-factor is, on the other hand, dominated by the Dresselhaus spin-orbit term. At zero magnetic field, the total correction to the g-factor is typically 5-10% of its bulk value. In strong in-plane magnetic fields, the corrections are modified appreciably. arXiv:1808.03963v2 [cond-mat.mes-hall] 4 Dec 2018 3 We stick here to the triangular heterostructure confinement in Eq. (4) and do not discuss in the main text, for the sake of brevity, other confinement types considered in Ref. 22. We give results for a symmetric confinement in App. D. 4 The corrections resulting from such terms are expected to be much smaller than the terms denoted gz (see below), which are of similar origin and which are subdominant.

The germanium quantum information route

“…For systems such as Ge/SiGe heterostructures and Ge HWs, in which the hole confinement in one direction clearly exceeds that in the other directions, the DRSOI is less pronounced on account of a large HH-LH splitting 10,50 . However, it is known from studying conduction-band electrons in lateral quantum dots [76][77][78] that many spin-orbit interaction terms exist which can be of high relevance. For holes in quasi-2D systems, great efforts in both theory and experiment have led to detailed insights and knowledge about the spin-orbit interaction 10,29,37,40,42,[79][80][81][82][83][84][85][86][87][88][89][90] .…”

Orbital effects of a strong in-plane magnetic field on a gate-defined quantum dot

“…If these phases are of relevance, 23 For the symmetric confinements given in Eqs. (14) and (15), this would be the choice z 0 = 0. We also note that such gauge removal is not possible for H 1 itself, where z is still an operator.…”

3D Map of a Quantum Dot’s Potential

“…(4) for each orbital state (separately for the green and purple data) assuming a direction-independent Zeeman energy. Since the g factor anisotropy is small [40], this is a very good approximation. The fit givesδ x ¼−8°AE4°,δ y ¼ 62°AE 4°, and λ z ¼ 6.1 AE 0.3 nm (E z ¼ 30.7 AE 3 meV) [34].…”