Spin-orbit coupling and spin relaxation of hole states in [001]- and [111]-oriented quantum dots of various geometry

Abstract

We study the influence of spin-orbit coupling on the hole states in InAs/GaAs quantum dots grown on [001]-and [111]-oriented substrates belonging to symmetry point groups: C2v, C3v and D 2d . We investigate the impact of various spin-orbit mechanisms on the strength of coupling between s-and p-shell states, which is a significant spin-flip channel in quantum dots. We calculate spin relaxation rates between the states of lowest Zeeman doublet and show that the [111]-oriented structure offers one order of magnitude slower relaxation compared to the usual [001]-oriented self-assembled QD. The magnetic-field dependence of the hole states is calculated using multiband (up to 14 bands) k·p model. We identify the irreducible representations linked to the states and discuss the selection rules, which govern the avoided-crossing pattern in magnetic-field dependence of the energy levels. We show that dominant contribution to the coupling between some of these states comes from the shear strain. On the other hand, we demonstrate no coupling between s-and p-shell states in the [111]-oriented structure. arXiv:1809.09062v3 [cond-mat.mes-hall]

Hole spin-flip transitions in a self-assembled quantum dot

“…These results are consistent with Ref. 49, where d v shearstrain terms were shown as one of the most important contributions determining the hole s-p coupling. The contribution from the Dresselhaus bulk inversion asymmetry (BIA) spin-orbit coupling is relatively small for the structure A and it interferes destructively with the background.…”

“…The hole phonon-assisted spin-flip relaxation rates can be accounted for using wave functions obtained from the effective model with empirical parameters fitted to the k • p simulation data. We use heavy-hole Gaussian wave functions and a simple hole Hamiltonian based on the Fock-Darwin model, supplemented by additional terms accounting for the spin-orbit interaction 49 .…”

“…Since, the fitting procedure gives only the absolute values of parameters, the relative phases of terms in H eff are assumed. We also neglected terms |0 −1| ⊗ |⇓ ⇑| + H.c. and |0 1| ⊗ |⇑ ⇓| + H.c. since they are not represented by any avoided crossing in target magnetic-field energy dependence 49 . The parameters describing wave function spacial extension (l p , l z ) are extracted from probability density maps at B = 0.…”

“…The processes of hole spin-flip transition in a QD due to the mechanisms described above were widely studied 7,14,[18][19][20][21][22][23][24][25] . It has been shown that phonon coupling via piezoelectric field (PZ) is more important at small and moderate Zeeman splittings, while deformation potential (DP) coupling becomes dominate for larger splittings.…”

“…It is known, however, that strain provides channels of spin mixing 26 which can significantly affect the spin relaxation 19 . In fact, recent results show an important contribution to the spin relaxation rates coming from the structural shear strain in a self-assembled QD 25 .…”