We investigate the spin relaxation induced by acoustic phonons in the presence of spin-orbit interactions in single electron Si/SiGe lateral coupled quantum dots. The relaxation rates are computed numerically in single and double quantum dots, in in-plane and perpendicular magnetic fields. The deformation potential of acoustic phonons is taken into account for both transverse and longitudinal polarizations and their contributions to the total relaxation rate are discussed with respect to the dilatation and shear potential constants. We find that in single dots the spin relaxation rate scales approximately with the seventh power of the magnetic field, in line with a recent experiment. In double dots the relaxation rate is much more sensitive to the dot spectrum structure, as it is often dominated by a spin hot spot. The anisotropy of the spin-orbit interactions gives rise to easy passages, special directions of the magnetic field for which the relaxation is strongly suppressed. Quantitatively, the spin relaxation rates in Si are typically 2 orders of magnitude smaller than in GaAs due to the absence of the piezoelectric phonon potential and generally weaker spinorbit interactions.

A global quantitative picture of the phonon-induced two-electron spin relaxation in GaAs double quantum dots is presented using highly accurate numerics. Wide regimes of interdot coupling, magnetic field magnitude and orientation, and detuning are explored in the presence of a nuclear bath. Most important, the giant magnetic anisotropy of the singlet-triplet relaxation can be controlled by detuning switching the principal anisotropy axes: a protected state becomes unprotected upon detuning and vice versa. It is also established that nuclear spins can dominate spin relaxation for unpolarized triplets even at high magnetic fields, contrary to common belief. DOI: 10.1103/PhysRevLett.108.246602 PACS numbers: 72.25.Rb, 03.67.Lx, 71.70.Ej, 73.21.La Electron spins in quantum dots [1] are among perspective candidates for a controllable quantum coherent system in spintronics [2,3]. Spin qubits in GaAs quantum dots, the current state of the art [4,5], are coupled to two main environment baths: nuclear spins and phonons [6]. The nuclei dominate decoherence, which is on microsecond time scales. But only phonons are an efficient energy sink for the relaxation of the energy-resolved spin states, leading to spin lifetimes as long as seconds [7].The extraordinary low relaxation is boosted by orders of magnitude at spectral crossings, unless special conditions-such geometries we call easy passages-are met [8,9]. Spectral crossings seem inevitable in the manipulation based on the Pauli spin blockade [1,10], the current choice in spin qubit experiments [11]. On the other hand, a fast spin relaxation channel may be desired, e.g., in the dynamical nuclear polarization [12][13][14].The single-electron spin relaxation is well understood [15,16]: it proceeds through acoustic phonons, in proportion to their density of states, which increases with the transferred energy. The matrix element of the phonon electric field between spin opposite states is nonzero due to spin-orbit coupling or nuclear spins. At anticrossings, the matrix element is enhanced by orders of magnitude, even though the anticrossing gap is minute ($ eV). The relaxation rate can be either enhanced or suppressed, depending on whether the energy or the matrix element effects dominate.The two electron relaxation rates were measured in single [17][18][19] and in double [20][21][22] dots. Theoretical works so far mostly focused on single dots [23,24], or vertical double dots [25,26], in which the symmetry of the confinement potential lowers the numerical demands. A slightly deformed dot was considered in Refs. [27,28], and a lateral coupled double dot in silicon in Ref. [29]. What is key for spin-qubit manipulation and most relevant for ongoing experiments, is the case of weakly coupled and biased coupled dots. In addition, the relative roles of the spin-orbit and hyperfine interactions in the spin relaxation in GaAs quantum dots have not yet been established.The analysis of the two-electron double dot relaxation is challenging because many parameters need to be consider...

Highly accurate numerical results of phonon-induced two-electron spin relaxation in silicon double quantum dots are presented. The relaxation, enabled by spin-orbit coupling and the nuclei of 29 Si (natural or purified abundance), is investigated for experimentally relevant parameters, the interdot coupling, the magnetic field magnitude and orientation, and the detuning. We calculate relaxation rates for zero and finite temperatures (100 mK), concluding that our findings for zero temperature remain qualitatively valid also for 100 mK. We confirm the same anisotropic switch of the axis of prolonged spin lifetime with varying detuning as recently predicted in GaAs. Conditions for possibly hyperfine-dominated relaxation are much more stringent in Si than in GaAs. For experimentally relevant regimes, the spin-orbit coupling, although weak, is the dominant contribution, yielding anisotropic relaxation rates of at least two orders of magnitude lower than in GaAs.

We consider electrostatically coupled quantum dots in topological insulators, otherwise confined and gapped by a magnetic texture. By numerically solving the (2 + 1) Dirac equation for the wave packet dynamics, we extract the energy spectrum of the coupled dots as a function of bias-controlled coupling and an external perpendicular magnetic field. We show that the tunneling energy can be controlled to a large extent by the electrostatic barrier potential. Particularly interesting is the coupling via Klein tunneling through a resonant valence state of the barrier. The effective three-level system nicely maps to a model Hamiltonian, from which we extract the Klein coupling between the confined conduction and valence dots levels. For large enough magnetic fields Klein tunneling can be completely blocked due to the enhanced localization of the degenerate Landau levels formed in the quantum dots. In topological insulators (TIs), according to the bulkboundary correspondence principle [1,2], topologically protected surface states are formed, which are robust against timereversal (TR) elastic perturbations. In the long-wavelength limit the two-dimensional (2D) electron states at the surfaces of three-dimensional (3D) TIs can be described as massless Dirac electrons with the peculiar property that the spin is locked to the momentum, thereby forming a helical electron gas. Charge and spin properties become strongly intertwined, opening new opportunities for spintronic [3,4] applications [5][6][7][8][9][10].To build functional nanostructures, such as quantum dots (QDs) or quantum point contacts, additional confinement of the Dirac electrons is needed. However, conventional electrostatic confinement in a massless Dirac system is ineffective due to Klein (interband) tunneling. In graphene this problem could be overcome by either mechanically cutting or etching QD islands out of graphene flakes [11][12][13] or by inducing a gap by an underlying substrate, which breaks the pseudospin symmetry [14,15]. Another promising idea to overcome the restrictions given by Klein tunneling is to use graphene strips or nanoribbons. An electrostatic confinement in such a system has been proposed in Ref. [16] by employing the transversal electron motion. Moreover, an effective spin exchange coupling of two gate-defined quantum dots becomes possible in a graphene nanoribbon by indirectly coupling the dots via the tunneling to a common continuum of delocalized states [17].In TIs a mass gap can be created by breaking the TR symmetry at the surface by applying a magnetic field. This could be achieved by proximity to a magnetic material [18,19], or by coating the surface randomly with magnetic impurities [20][21][22]. By modifying the magnetic texture of the deposited magnetic film, a spatially inhomogeneous mass term is induced, opening the possibility to define quantum dot (QD) regions [23], or waveguides formed along the magnetic domain wall regions [24]. Another interesting, possibly more feasible way of defining confinement regions, is to ind...

Spin relaxation of a single electron in a weakly coupled double quantum dot is calculated numerically. The phonon‐assisted spin flip is allowed by the presence of the linear and cubic spin–orbit couplings and nuclear spins. The rate is calculated as a function of the interdot coupling, the magnetic field strength and orientation, and the dot bias. In an in‐plane magnetic field, the rate is strongly anisotropic with respect to the magnetic field orientation, due to the anisotropy of the spin–orbit interactions. The nuclear spin influence is negligible. In an out‐of‐plane field, the nuclear spins play a more important role due selection rules imposed on the spin–orbit couplings. Our theory shows a very good agreement with data measured by Srinivasa et al. [Phys. Rev. Lett. 110, 196803 (2013)], allowing us to extract information on the linear spin–orbit interactions strengths in that experiment. We estimate that they correspond to spin–orbit lengths of about 5–15 μm.