Theory of Spin Relaxation in Two-Electron Lateral Coupled Quantum Dots

Abstract

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...

Theory of spin relaxation in two-electron laterally coupled Si/SiGe quantum dots

“…Thus, the anisotropy of the spin-orbit field manifests itself in all the relaxation rates we calculated, yielding the electrically controlled directional switch of the easy passage 70 (a particular orientation of the magnetic field for which the relaxation as a function of some parameter is significantly lower than for other orientations), previously found in GaAs. 69 A temperature of 0.1 K does not change our findings in any qualitative way.…”

“…1 in Ref. 69). In a comparable GaAs double dot, the singlet and triplet anticrossings gaps are small compared to the single-dot exchange coupling.…”

“…This work is an extension to the findings in Ref. 69 for GaAs, and we highlight the differences between these two materials. We fix the double-dot orientation with respect to the crystallographic axes to that which is used most often in experiments.…”

“…The hyperfine-induced rates of purified silicon are further suppressed by about two orders of magnitude compared to those in natural silicon. Although the anomalous regime of nuclei dominating the relaxation, which we identified in GaAs, 69 exists also in Si, here the different material parameters make it much harder to observe in practice. We therefore conclude that, concerning the relaxation, the nuclear field is negligible.…”

“…(5), was introduced in Ref. 69. In this work, the two-electron basis for the configuration-interaction method consists of 1156 Slater determinants, generated by 34 single-electron orbital states.…”