Spin–orbit-induced hole spin relaxation in InAs and GaAs quantum dots

Abstract

We study the effect of valence band spin-orbit interactions (SOI) on the acoustic phonon-assisted spin relaxation of holes confined in quantum dots (QDs). Heavy hole-light hole (hh-lh) mixing and all the spin-orbit terms arising from zinc-blende bulk inversion asymmetry (BIA) are considered on equal footing in a fully three-dimensional Hamiltonian. We show that hh-lh mixing and BIA have comparable contributions to the hole spin relaxation in self-assembled QDs, but BIA becomes dominant in gated QDs. Simultaneously accounting for both mechanisms is necessary for quantitatively correct results in quasi-two-dimensional QDs. The dependence of the hole spin relaxation on the QD geometry and spin splitting energy is drastically different from that of electrons, with a non-monotonic behavior which results from the interplay between SOI terms. Our results reconcile contradictory predictions of previous theoretical works and are consistent with experiments. For a qualitative understanding of the geometry dependence of 1/T h 1 , we rewrite the hole states, equation (14), as | h m = J z c m J z |φ m J z |3/2, J z , where |φ m J z = r c m J z ,r |r is the envelope function associated with the periodic Bloch function |3/2, J z . If we restrict to the diagonal components of H h-ph , the matrix element determining the relaxation rate becomes

Spin blockade in hole quantum dots: Tuning exchange electrically and probing Zeeman interactions

“…The period of the anisotropic leakage is critically dependent on the relative magnitude of Zeeman interaction terms linear and cubic in the magnetic field. The current and singlet-triplet exchange splitting can be effectively adjusted by an appropriate choice of field direction, providing a simple control variable for quantum information processing and a way of tailoring magnetic interactions in hole spin qubits.Spin-based quantum information processing platforms relying on hole quantum dots (QDs) have recently attracted considerable attention [1][2][3][4][5][6][7][8][9][10][11], since they permit long spin coherence and electrically driven spin resonance thanks to the strong hole spinorbit (SO) interaction [12][13][14][15][16][17][18][19][20]. Owing to their effective spin J = 3 2 , spin dynamics in hole systems often exhibits physics not found in electron systems [21][22][23][24][25][26].…”

Hole spin relaxation in InAs/GaAs quantum dot molecules

“…The complete expressions and derivation of the piezoelectric potential and the deformation potential operators for the three phonon branches is presented in [31]. The transition rate between the initial hole state |Ψ h i and the final hole state |Ψ h f is estimated using the Fermi golden rule…”

“…[28] Several works have theoretically addressed the hole spin relaxation in single QDs taking into account different SOI mechanisms and have showed that one or another prevail depending on the QD traits. [20,29,30,31,32] By comparison, the spin relaxation of holes in DQDs is still poorly understood. This is inspite of their promising prospects for the development of quantum information architectures.…”

“…The hole states are simulated using three-dimensional (3D) Hamiltonians including not only quadratic-in-k LH-HH coupling present in the Luttinger-Kohn Hamiltonian, but also cubic Dresselhaus SOI, which was found to be potentially important in single InAs QDs. [31] Calculations are carried out for varying strength of an electric field applied along the DQD stacking direction. This makes possible to study the transition from atomic-like states confined in one of the constituent QDs to fully molecular-like states, which are obtained when the field brings the hole levels in the upper and lower dots into resonance.…”

Large hole spin anticrossings in InAs/GaAs double quantum dots

“…12 and 15, which is confirmed here using exact numerical solutions of the three-dimensional system. [27][28][29] To understand the different magnitude of the gaps, note that D s 2 takes place at F $ 0, while D s 1 does so at F ( 0 (see the example in Fig. 1(b)).…”