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arXiv:1104.4817 · Journal of Applied Physics

Singlet-triplet relaxation in SiGe/Si/SiGe double quantum dots

L. Wang, M. W. Wu

Published Aug 15, 2011• 14 citations
arXivHTMLPDF

Abstract

We study the singlet-triplet relaxation due to the spin-orbit coupling assisted by the electron-phonon scattering in two-electron SiGe/Si/SiGe double quantum dots in the presence of an external magnetic field in either Faraday or Voigt configuration. By explicitly including the electron-electron Coulomb interaction and the valley splitting induced by the interface scattering, we employ the exact-diagonalization method to obtain the energy spectra and the eigenstates. Then, we calculate the relaxation rates with the Fermi golden rule. We find that the transition rates can be effectively tuned by varying the external magnetic field and the interdot distance. Especially in the vicinity of the anticrossing point, the transition rates show intriguing features. We also investigate the electric-field dependence of the transition rates and find that the transition rates are almost independent of the electric field. This is of great importance in the spin manipulation, since the lifetime remains almost the same during the change of the qubit configuration from (1,1) to (2,0) by the electric field.

DOI
10.1063/1.3625240

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We study the singlet-triplet relaxation due to the spin-orbit coupling assisted by the electron-phonon scattering in two-electron SiGe/Si/SiGe double quantum dots in the presence of an external magnetic field in either Faraday or Voigt configuration. By explicitly including the electron-electron Coulomb interaction and the valley splitting induced by the interface scattering, we employ the exact-diagonalization method to obtain the energy spectra and the eigenstates. Then, we calculate the relaxation rates with the Fermi golden rule. We find that the transition rates can be effectively tuned by varying the external magnetic field and the interdot distance. Especially in the vicinity of the anticrossing point, the transition rates show intriguing features. We also investigate the electric-field dependence of the transition rates and find that the transition rates are almost independent of the electric field. This is of great importance in the spin manipulation, since the lifetime remains almost the same during the change of the qubit configuration from (1,1) to (2,0) by the electric field.
We study theoretically the phonon-induced relaxation and decoherence of spin states of two electrons in a lateral double quantum dot in a SiGe/Si/SiGe heterostructure. We consider two types of singlet-triplet spin qubits and calculate their relaxation and decoherence times, in particular as a function of level hybridization, temperature, magnetic field, spin orbit interaction, and detuning between the quantum dots, using Bloch-Redfield theory. We show that the magnetic field gradient, which is usually applied to operate the spin qubit, may reduce the relaxation time by more than an order of magnitude. Using this insight, we identify an optimal regime where the magnetic field gradient does not affect the relaxation time significantly, and we propose regimes of longest decay times. We take into account the effects of one-phonon and two-phonon processes and suggest how our theory can be tested experimentally. The spin lifetimes we find here for Si-based quantum dots are significantly longer than the ones reported for their GaAs counterparts.
We study theoretically phonon-induced spin dynamics of two electrons confined in a self-assembled double quantum dot. We calculate the transition rates and time evolution of occupations for the spin-triplet and spin-singlet states. We characterize the relative importance of various relaxation channels, including two-phonon processes, as a function of the electric and magnetic fields. The simulations are based on a model combining the eight-band [Formula: see text] method and configuration-interaction approach. We show that the electron g-factor mismatch between the Zeeman doublets localized on different dots opens a relatively fast triplet-singlet phonon-assisted relaxation channel. We also demonstrate, that the relaxation near the triplet-singlet anticrossing is slowed down up to several orders of magnitude due to vanishing of some relaxation channels.
Charge separation from the (4,0)(4,0)(4,0) to the (3,1)(3,1)(3,1) state in a Si/SiGe double quantum dot is commonly used for initialization of spin qubits and Pauli-spin-blockade readout. It was used in recent experiments involving creation of the (3,1)(3,1)(3,1) singlet, and subsequent shuttling of one of the electrons. We present a theoretical description of the process of charge separation and singlet-triplet mixing, arriving at expressions for the singlet return probability that take into account experimentally observed finite probabilities of the creation of singlets with various patterns of valley occupations. In our analysis we focus on magnetic fields for which the electron spin Zeeman splitting is close to the valley splitting in one of the dots, when the spin-valley coupling causes a strong renormalization of the frequency of oscillations of singlet return probability. The latter effect has been recently used to perform valley splitting mapping by shuttling of one quantum dot to various locations with respect to the other. We give a detailed description of singlet-triplet dynamics near these spin-valley resonances and compare the results of calculations with measurements on double quantum dots in two distinct Si/SiGe heterostructures. Comparison of theory with experiments in which the presence of a few valley occupation patterns is visible, gives insight into the valley dependence of ggg-factors in these structures, providing support for a recently proposed theoretical model of this dependence. We also discuss how dephasing of singlet return probability oscillations near the spin-valley resonances is affected by valley splitting fluctuations caused by electric field noise.
While bulk silicon has long been understood to exhibit relatively weak spin-orbit coupling (SOC), confinement of electrons to quantum dots (QDs) at a silicon heterointerface results in significantly larger SOC. This is a concern for electron spin qubit performance, as intravalley and intervalley SOC can significantly perturb the operation of electron spin qubits. While these interactions can be harnessed to drive coherent rotations in a singlet-triplet qubit, coupling to low-lying excited valley states can lead to undesirable spin relaxation when valley splitting is on resonance with the Zeeman energy. In this work, we measure the angular dependence of the interfacial spin-orbit interaction as a function of the direction and magnitude of an applied external magnetic field in SiMOS and Si/SiGe heterostructures, two common material platforms for silicon spin qubits. We construct a physical model that accurately infers intra- and inter-valley SOC physics from fits to the data, allowing for a direct comparison between these two material systems. For the devices measured we find that, while the ggg-factor differences are comparable, the SiMOS QDs exhibit an order of magnitude larger spin-valley coupling than for Si/SiGe. Moreover, we find that the angular dependence of the spin-valley coupling is similar for both devices, with similar magnetic field orientations minimizing the spin-valley coupling. Our work points towards operational schemes for optimizing spin-valley coupling to avoid or exploit this mechanism for qubit operation.
We report a successful measurement of the magnetic field-induced spin singlet-triplet transition in silicon-based coupled dot systems. Our specific experimental scheme incorporates a lateral gate-controlled Coulomb-blockaded structure in Si to meet the proposed scheme of Loss and DiVincenzo [1], and a non-equilibrium single-electron tunneling technique to probe the fine energy splitting between the spin singlet and triplet, which varies as a function of applying magnetic fields and interdot coupling constant. Our results, exhibiting the singlet-triplet crossing at a magnetic field for various interdot coupling constants, are in agreement with the theoretical predictions, and give the first experimental demonstration of the possible spin swapping occurring in the coupled double dot systems with magnetic field. *Electronic address: jungchoi@chungbuk.ac.kr [1] D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998).
Direct phonon spin-lattice relaxation of an electron qubit bound by a donor impurity or quantum dot in SiGe heterostructures is investigated. The aim is to evaluate the importance of decoherence from this mechanism in several important solid-state quantum computer designs operating at low temperatures. We calculate the relaxation rate 1/T1{1/T}_{1}1/T1​ as a function of [100] uniaxial strain, temperature, magnetic field, and silicon/germanium content for Si:P bound electrons and quantum dots. The quantum dot potential is much smoother, leading to smaller splittings of the valley degeneracies. We have estimated these splittings in order to obtain upper bounds for the relaxation rate. In general, we find that the relaxation rate is strongly decreased by uniaxial compressive strain in a SiGe-Si-SiGe quantum well, making this strain an important positive design feature. Ge in high concentrations (particularly over 85%) increases the rate, making Si-rich materials preferable. We conclude that SiGe bound electron qubits must meet certain conditions to minimize decoherence but that spin-phonon relaxation does not rule out the solid-state implementation of error-tolerant quantum computing.