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^{1,a)}, Roderick V. N. Melnik

^{1,2}and Luis L. Bonilla

^{2}

^{2}NeT Laboratory, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada

### Abstract

We study the anisotropic orbital effect in the electric field tunability of the phonon induced spin-flip rate in quantum dots(QDs). Our study shows that anisotropic gate potential enhances the spin-flip rate and reduces the level crossing point to a lower QDs radius due to the suppression of the Landé g-factor towards bulk crystal. In the range of 10^{4}−10^{6 }V/cm, the electric field tunability of the phonon induced spin-flip rate can be manipulated through strong Dresselhaus spin-orbit coupling. These results might assist the development of a spin based solid state quantum computer by manipulating spin-flip rate through spin-orbit coupling in a regime where the g-factor changes its sign.

This work has been supported by NSERC and CRC programs (Canada) and by MICINN Grants No. FIS2008- 04921-C02-01 and FIS2011-28838-C02-01 (Spain).

### Key Topics

- Quantum dots
- 49.0
- Phonons
- 19.0
- Spin orbit interactions
- 19.0
- G factor
- 15.0
- Anisotropy
- 14.0

## Figures

(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, *γ _{R} * = 4.4 Å

^{2},

*γ*= 26 eVÅ

_{D}^{3},

*eh*

_{14}= 2.34 × 10

^{−5 }erg/cm,

*s*= 5.14 × 10

_{l}^{5 }cm/s,

*s*= 3.03 × 10

_{t}^{5 }cm/s, and

*ρ*= 5.3176 g/cm

^{3}. At

*E*= 7 × 10

^{5 }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 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, *γ _{R} * = 4.4 Å

^{2},

*γ*= 26 eVÅ

_{D}^{3},

*eh*

_{14}= 2.34 × 10

^{−5 }erg/cm,

*s*= 5.14 × 10

_{l}^{5 }cm/s,

*s*= 3.03 × 10

_{t}^{5 }cm/s, and

*ρ*= 5.3176 g/cm

^{3}. At

*E*= 7 × 10

^{5 }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) 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* = 10^{5 }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.

(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* = 10^{5 }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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