Anisotropy of Spin Splitting and Spin Relaxation in Lateral Quantum Dots

Falko, Vladimir; Altshuler, B. L.; Tsyplyatyev, O.

doi:10.1103/physrevlett.95.076603

Cited by 40 publications

(51 citation statements)

References 26 publications

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“…To maximize the relaxation time of electron spin qubits, one needs then to choose an energy separation between the spin states such that the corresponding phonon wavelength is different from the dot size. To complete our study of spin relaxation, it will be interesting to rotate the sample with respect to the magnetic field since the spin-orbit coupling strength depends on the angle between the crystallographic axis and the magnetic field [10,11,26]. …”

Section: Prl 98 126601 (2007) P H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 99%

Experimental Signature of Phonon-Mediated Spin Relaxation in a Two-Electron Quantum Dot

et al. 2007

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We observe an experimental signature of the role of phonons in spin relaxation between triplet and singlet states in a two-electron quantum dot. Using both the external magnetic field and the electrostatic confinement potential, we change the singlet-triplet energy splitting from 1.3 meV to zero and observe that the spin relaxation time depends nonmonotonously on the energy splitting. A simple theoretical model is derived to capture the underlying physical mechanism. The present experiment confirms that spin-flip energy is dissipated in the phonon bath. DOI: 10.1103/PhysRevLett.98.126601 PACS numbers: 72.25.Rb, 63.20.ÿe, 71.70.Ej, 73.21.La Relaxation properties of a quantum system are strongly affected by the reservoir where energy is dissipated [1]. Understanding which reservoir dominates dissipation can thus point at strategies for minimizing relaxation, and thereby improving coherent control of quantum systems. In this context, relaxation of electron spins embedded in nanostructures is of particular relevance, both for spintronic and spin-based quantum information processing devices [2]. For free electrons in a two dimensional electron gas (2DEG), spin relaxation times T 1 up to a few ns have been observed [3]. Here energy is easily given to the motion. In quantum dots, the discrete orbital energy level spectrum imposes other energy transfer mechanisms. Experiments showed that electron spins in quantum dots relax only after about one s [4] near zero magnetic field, by direct flip-flops with the surrounding nuclear spins. Away from zero magnetic field, even longer spin relaxation times, 100 s-100 ms, were observed [4 -9]. Here, direct spin exchange with nuclei is suppressed and the phonon bath is expected to become the dominant reservoir in which spin-flip energy can be dissipated.Direct spin relaxation by phonons is negligible [10], but phonons do couple to electron orbitals, and, through the spin-orbit interaction, can still couple to electron spins indirectly. Spin energy can thus be dissipated in the phonon bath [10 -12]. Energy conservation requires that the phonon energy corresponds to the energy separation between the excited and the ground spin state. Changing the energy separation affects the efficiency of electron spin relaxation in two ways. First, since the phonon density of states increases with energy, the relaxation rate is expected to increase with energy as well. Furthermore, the electronphonon interaction is highly dependent on the phonon wavelength in comparison to the dot size [13,14]. Specifically, we expect a suppression of relaxation for very large and for very small phonon wavelengths. The resulting maximum in the relaxation rate has never been observed so far [4 -9], but would provide insight in the role of the electron-phonon interaction in spin relaxation, as well as an understanding of the limitations on T 1 .Here, we study the spin relaxation time from triplet to singlet states for different energy separations in a single quantum dot containing two electrons. Singlet and triple...

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Section: Prl 98 126601 (2007) P H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 99%

Experimental Signature of Phonon-Mediated Spin Relaxation in a Two-Electron Quantum Dot

et al. 2007

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“…[4][5][6] On the other hand, at higher fields ͑Teslas͒ the relaxation is due to phonon-induced spin-flip transitions. [7][8][9][10][11][12][13][14][15][16][17][18][19] These are allowed due to the presence of spin-orbit coupling. Variants of the phonon-induced spin relaxation has been proposed, such as ripple coupling, 20,21 important in very small quantum dots ͑10 nm͒, or fluctuations in spin-orbit parameters, important when underlying heterostructure inhomogeneities 22 are present.…”

Section: Introductionmentioning

confidence: 99%

Orbital and spin relaxation in single and coupled quantum dots

Stano

Fabian

2006

Phys. Rev. B

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Phonon-induced orbital and spin relaxation rates of single electron states in lateral single and double quantum dots are obtained numerically for realistic materials parameters. The rates are calculated as a function of magnetic field and interdot coupling, at various field and quantum dot orientations. It is found that orbital relaxation is due to deformation potential phonons at low magnetic fields, while piezoelectric phonons dominate the relaxation at high fields. Spin relaxation, which is dominated by piezoelectric phonons, in single quantum dots is highly anisotropic due to the interplay of the Bychkov-Rashba and Dresselhaus spin-orbit couplings. Orbital relaxation in double dots varies strongly with the interdot coupling due to the cyclotron effects on the tunneling energy. Spin relaxation in double dots has an additional anisotropy due to anisotropic spin hot spots which otherwise cause giant enhancement of the rate at useful magnetic fields and interdot couplings. Conditions for the absence of the spin hot spots in in-plane magnetic fields ͑easy passages͒ and perpendicular magnetic fields ͑weak passages͒ are formulated analytically for different growth directions of the underlying heterostructure. It is shown that easy passages disappear ͑spin hot spots reappear͒ if the double dot system loses symmetry by an xy-like perturbation.

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“…DOI: 10.1103/PhysRevLett.96.186602 PACS numbers: 72.25.Rb, 03.67.Lx, 71.70.Ej, 73.21.La Understanding spin relaxation in coupled quantum dots is important for setting the efficiency of spin-based applications of information processing, such as spin quantum computing [1] or controlled generation of spin entanglement [2]. Phonon-induced spin relaxation has already been studied theoretically in single dots for electrons [3][4][5][6][7][8][9][10][11][12], holes [13], and excitons [14], and in one-dimensional coupled dots [15]. Recently, spin relaxation of electrons in single dots has been measured [16].…”

mentioning

confidence: 99%

Theory of Phonon-Induced Spin Relaxation in Laterally Coupled Quantum Dots

2006

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Phonon-induced spin relaxation in coupled lateral quantum dots in the presence of spin-orbit coupling is calculated. The calculation for single dots is consistent with experiment. Spin relaxation in double dots at useful interdot couplings is dominated by spin-hot spots that are strongly anisotropic. Spin-hot spots are ineffective for a diagonal crystallographic orientation of the dots with a transverse in-plane field. This geometry is proposed for spin-based quantum information processing. DOI: 10.1103/PhysRevLett.96.186602 PACS numbers: 72.25.Rb, 03.67.Lx, 71.70.Ej, 73.21.La Understanding spin relaxation in coupled quantum dots is important for setting the efficiency of spin-based applications of information processing, such as spin quantum computing [1] or controlled generation of spin entanglement [2]. Phonon-induced spin relaxation has already been studied theoretically in single dots for electrons [3][4][5][6][7][8][9][10][11][12], holes [13], and excitons [14], and in one-dimensional coupled dots [15]. Recently, spin relaxation of electrons in single dots has been measured [16].Here we present a realistic calculation of phononinduced spin relaxation in single and coupled lateral quantum dots formed over a depleted two-dimensional electron gas in GaAs grown along 001 , the most typical growth direction. We show that our calculation is consistent with the single-dot experiment [16]. We predict the following: (i) Spin relaxation in coupled dots is strongly anisotropic with respect to the orientation of both an in-plane magnetic field (due to the interplay of the Bychkov-Rashba and Dresselhaus spin-orbit terms) and the dots's axis. The anisotropy is limited by the in-plane inversion symmetry only. (ii) The spin relaxation rate varies strongly with the interdot coupling, having a giant enhancement at a significant range of useful tunneling amplitudes due to spin-hot spots (anticrossings caused by spin-orbit coupling [9,[17][18][19]). This variation, which is over several (4 to 5) orders of magnitude, should be included in any realistic modeling of spin coherence phenomena in coupled quantum dots with controlled temporal evolution of the coupling. (iii) Fortunately, the effects of (ii) are absent at specific configurations. The most robust (with respect to materials parameters) such a configuration is with dots oriented along 110 (or 1 10 ) with the in-plane magnetic field along 1 10 ( 110 ). We propose to use this configuration for spinbased quantum information experiments.Our single-electron Hamiltonian is H T V H SO H Z . Here T is the operator of the kinetic energy with the magnetic field B introduced by minimum coupling, and V is the double-dot confinement potential,The plane radius vector is r x; y , where x 100 and y 010 are the crystallographic axes, while d defines the distance (as well as tunneling energy at B 0) and the orientation of the dots; the angle between d andx is denoted below as . The conduction electron mass is m and the single-dot (d 0) confining energy is @! 0 . The spin-orbit coupli...

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Anisotropy of Spin Splitting and Spin Relaxation in Lateral Quantum Dots

Cited by 40 publications

References 26 publications

Experimental Signature of Phonon-Mediated Spin Relaxation in a Two-Electron Quantum Dot

Experimental Signature of Phonon-Mediated Spin Relaxation in a Two-Electron Quantum Dot

Orbital and spin relaxation in single and coupled quantum dots

Theory of Phonon-Induced Spin Relaxation in Laterally Coupled Quantum Dots

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