# Spin-Singlet–Spin-Triplet Transitions in Quantum Dots

**ABSTRACT** We calculate the rate of the spin-singlet–spin-triplet (ST) relaxation in the two-electron droplet in a magnetic field. Far from the ST crossing point the rate turns out to be rather significant. In connection with the source-drain transport experiments, we consider this result is an explanation of the observed disappearance of the singlet (upper) level at magnetic fields, which are stronger than the ST crossing value.

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**ABSTRACT:**We describe time-dependent single-electron transport through quantum dots in the Coulomb blockade regime. Coherent dynamics of a single charge qubit in a double quantum dot is discussed with full one-qubit manipulation. Strength of decoherence is controlled with the applied voltage, but uncontrolled decoherence arises from electron–phonon coupling and background fluctuations. Then energy-relaxation dynamics is discussed for orbital and spin degree of freedom in a quantum dot. The electron–phonon interaction and spin–orbit coupling can be investigated as the dissipation problem. Finally, charge detection measurement is presented for statistical analysis of single-electron tunnelling transitions and for a sensitive qubit read-out device.Reports on Progress in Physics 02/2006; 69(3):759. DOI:10.1088/0034-4885/69/3/R05 · 15.63 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We study spin relaxation in a two-electron quantum dot in the vicinity of the singlet-triplet crossing. The spin relaxation occurs due to a combined effect of the spin-orbit, Zeeman, and electron-phonon interactions. The singlet-triplet relaxation rates exhibit strong variations as a function of the singlet-triplet splitting. We show that the Coulomb interaction between the electrons has two competing effects on the singlet-triplet spin relaxation. One effect is to enhance the relative strength of spin-orbit coupling in the quantum dot, resulting in larger spin-orbit splittings and thus in a stronger coupling of spin to charge. The other effect is to make the charge density profiles of the singlet and triplet look similar to each other, thus diminishing the ability of charge environments to discriminate between singlet and triplet states. We thus find essentially different channels of singlet-triplet relaxation for the case of strong and weak Coulomb interaction. Finally, for the linear in momentum Dresselhaus and Rashba spin-orbit interactions, we calculate the singlet-triplet relaxation rates to leading order in the spin-orbit interaction, and find that they are proportional to the second power of the Zeeman energy, in agreement with recent experiments on triplet-to-singlet relaxation in quantum dots. Comment: 29 pages, 14 figures, 1 tablePhysical Review B 03/2007; 77(4). DOI:10.1103/PhysRevB.77.045328 · 3.66 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We investigate the singlet-triplet relaxation process of a two electron silicon quantum dot. In the absence of a perpendicular magnetic field, we find that spin-orbit coupling is not the main source of singlet-triplet relaxation. Relaxation in this regime occurs mainly via virtual states and is due to nuclear hyperfine coupling. In the presence of an external magnetic field perpendicular to the plane of the dot, the spin-orbit coupling is important and virtual states are not required. We find that there can be strong anisotropy for different field directions: parallel magnetic field can increase substantially the relaxation time due to Zeeman splitting, but when the magnetic field is applied perpendicular to the plane, the enhancement of the spin-orbit effect shortens the relaxation time. We find the relaxation to be orders of magnitude longer than for GaAs quantum dots, due to weaker hyperfine and spin-orbit effects. Comment: 5 pages, 3 figuresPhysical Review B 01/2008; 77(11). DOI:10.1103/PhysRevB.77.115438 · 3.66 Impact Factor