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(Color online) Phonon induced spin-flip rate due to spin-orbit admixture mechanism as a function of QDs radius in symmetric QDs (a = b = 1). We choose B = 1 T. Also, inset plot shows the g-factor vs. QDs radius. The level crossing point occurs at ℓ 0 = 73 nm. The material constants for GaAs QDs have been chosen from Refs. 4 and 19 as follows: g 0 = −0.44, m = 0.067, γR = 4.4 Å2, γD = 26 eVÅ3, eh 14 = 2.34 × 10−5 erg/cm, sl = 5.14 × 105 cm/s, st = 3.03 × 105 cm/s, and ρ = 5.3176 g/cm3. At E = 7 × 105 V/cm shown by dashed-dotted lines, the admixture mechanism due to spin-orbit coupling on the spin-flip rate is quite different because the electron spin states change their sign in these regime (see inset plot).
(Color online) Phonon induced spin-flip rate due to spin-orbit admixture mechanism as a function of QDs radius in asymmetric QDs (solid and dotted lines). As a reference, we also plotted spin-flip rate vs. QDs radius for symmetric QDs (dashed and dashed dotted lines). We choose the potentials characterized by a = 0.5 & b = 2 for asymmetric QDs and a = b = 1 for symmetric QDs. Also we choose B = 1 T. As we see, spin-flip rate increases approximately by one half order of magnitude in asymmetric QDs.
(Color online) (a) The anisotropic effect on the g-factor vs. QDs radius at the potentials characterized by a = b = 1 (solid line) for isotropic QDs and a = 0.5, b = 2 (dashed-dotted line) for anisotropic QDs. We choose E = 105 V/cm and B = 1 T. Anisotropic potential gives the suppression of the g-factor towards bulk crystal and hence reduces the level crossing point to lower QDs radius. Accidental degeneracy appears in the range of 70−80 nm QDs radius which gives the cusp like structure in the spin-flip rate (see Refs. 17, 18, and 25). (b) The interplay between Rashba and Dresselhaus spin-orbit couplings on the g-factor vs. the electric field in QDs induces the anisotropic effect due to the suppression of the g-factor towards bulk crystal. Here, we choose ℓ 0 = 20 nm, B = 1 T, and a = b = 1.
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