Finally, very long T 1-times far exceeding 1 s are predicted at such low fields, posing a formidable challenge on the long-term stability and control of a semiconductor nanostructure. To check for the direction dependence of relaxation, suitable piezo rotator control over the applied field direction is required, but this has only relatively recently become available. For a spin doublet, only energy selective spin-readout is available, thus requiring rather low electron temperatures below 100 mK to keep the Zeeman splitting well above the thermal broadening. Note that the phonon-assisted inelastic transition is fundamentally different from the elastic electron-nuclear spin flip-flop, which is strongly suppressed due to the pronounced mismatch of the electron and nuclear Zeeman energy for fields above a few mT 16.Įven though the HF-assisted mechanism of spin relaxation was predicted early on 15, experimental observation has remained elusive so far for a number of reasons: rather low fields below 1 T are required to reach the HF limit. These two hallmark features together-isotropic behavior and B 3 scaling-constitute a unique fingerprint of the HF relaxation mechanism. The HF mechanism, on the other hand, is isotropic 15, even for a dot shape which breaks circular symmetry. We estimate that in natural silicon the crossover would happen at magnetic fields roughly hundred times smaller.īeyond field scaling, the SOI with competing Rashba and Dresselhaus terms results in a strong dependence of spin relaxation on the direction of the applied magnetic field in the plane of the two-dimensional (2D) gas-the spin relaxation anisotropy 12– 14. For the parameters of typical surface gate defined GaAs dots, the crossover is predicted at around 1–2 T. Putting these pieces together, the SOI, with W ∝ B 5, will dominate at high fields, and HF, with W ∝ B 3, at low fields. While the HF interaction induces a B-independent moment, the time reversal symmetry of the SOI results, through the Van-Vleck cancellation, in an additional magnetic field proportionality, d 2 ∝ B 2. Their essential difference here is the time-reversal symmetry of the spin–orbit interaction (SOI), which also implies T 2 = 2 T 1 12 there is no such relation for the HF effects. In GaAs, the two most relevant ones are the spin–orbit and hyperfine (HF) interactions. Since the initial and final states are opposite in spin, a non-zero dipole element can only arise due to some spin-dependent interaction. For typical Zeeman energies, piezoelectric phonons dominate. Considering, for simplicity, long-wavelength three-dimensional bulk phonons, one gets the spin relaxation rate W ≡ T 1 - 1 ∝ B 3 d 2 for piezoelectric and W ∝ B 5 d 2 for deformation potential phonons, where d is the dipole moment matrix element between the initial and final state of the transition. The former proceeds by emission of a phonon. To understand this process in a GaAs quantum dot spin qubit, one needs to consider that it involves the dissipation of both energy and angular momentum, i.e., spin. This further motivates investigations of mechanisms and fundamental limits of the spin relaxation in quantum dots. The requirement for a sizable splitting, necessary for many of the protocols to initialize, measure, or manipulate spin qubits 5– 8, then imposes limitations on T 1, which in turn might influence these protocols in a profound way 9– 11. For spin qubits, the energy splitting is due to the Zeeman term of an applied magnetic field B. The suppression of this process in a confined system compared to the bulk 1 makes quantum dot spin qubits a serious candidate for a quantum technology platform 2– 4. In qubits based on electronic spins, it corresponds to the relaxation of spin-a longstanding topic of research in semiconductors. The decay of the energy stored in the qubit defines the relaxation time T 1.
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