Spin Relaxation in a Quantum Dot due to Nyquist Noise

We calculate electron and nuclear spin relaxation rates in a quantum dot due to the combined action of Nyquist noise and electron-nuclei hyperfine or spin-orbit interactions. The relaxation rate is linear in the resistance of the gate circuit and, in the case of spin-orbit interaction, it depends essentially on the orientations of both the static magnetic field and the fluctuating electric field, as well as on the ratio between Rashba and Dresselhaus interaction constants. We provide numerical estimates of the relaxation rate for typical system parameters, compare our results with other, previously discussed mechanisms, and show that the Nyquist mechanism can have an appreciable effect for experimentally relevant systems.Comment: v2: New discussion of arbitrary gate setups (1 new figure), more Comments on experiments; 6 pages, 4 figure

Electron-nuclei spin relaxation through phonon-assisted hyperfine interaction in a quantum dot

We investigate the inelastic spin-flip rate for electrons in a quantum dot due to their contact hyperfine interaction with lattice nuclei. In contrast to other works, we obtain a spin-phonon coupling term from this interaction by taking directly into account the motion of nuclei in the vibrating lattice. In the calculation of the transition rate the interference of first and second orders of perturbation theory turns out to be essential. It leads to a suppression of relaxation at long phonon wavelengths, when the confining potential moves together with the nuclei embedded in the lattice. At higher frequencies (or for a fixed confining potential), the zero-temperature rate is proportional to the frequency of the emitted phonon. We address both the transition between Zeeman sublevels of a single electron ground state as well as the triplet-singlet transition, and we provide numerical estimates for realistic system parameters. The mechanism turns out to be less efficient than electron-nuclei spin relaxation involving piezoelectric electron-phonon coupling in a GaAs quantum dot.Comment: 8 pages, 1 figur

Measurement, control, and decay of quantum-dot spins

In this review we discuss a recent proposal to perform partial Bell-state (parity) measurements on two-electron spin states for electrons confined to quantum dots. The realization of this proposal would allow for a physical implementation of measurement-based quantum computing. In addition, we consider the primary sources of energy relaxation and decoherence which provide the ultimate limit to all proposals for quantum information processing using electron spins in quantum dots. We give an account of the Hamiltonians used for the most important interactions (spin-orbit and hyperfine) and survey some of the recent work done to understand dynamics, control, and decoherence under the action of these Hamiltonians. We conclude the review with a table of important decay times found in experiment, and relate these time scales to the potential viability of measurement-based quantum computing.Comment: v1: 15 pages, 1 figure, review article to be published in a special issue of physica status solidi (b); v2: added/updated citation list, decay times in Table 1, made other minor correction

Recipes for spin-based quantum computing

Technological growth in the electronics industry has historically been measured by the number of transistors that can be crammed onto a single microchip. Unfortunately, all good things must come to an end; spectacular growth in the number of transistors on a chip requires spectacular reduction of the transistor size. For electrons in semiconductors, the laws of quantum mechanics take over at the nanometre scale, and the conventional wisdom for progress (transistor cramming) must be abandoned. This realization has stimulated extensive research on ways to exploit the spin (in addition to the orbital) degree of freedom of the electron, giving birth to the field of spintronics. Perhaps the most ambitious goal of spintronics is to realize complete control over the quantum mechanical nature of the relevant spins. This prospect has motivated a race to design and build a spintronic device capable of complete control over its quantum mechanical state, and ultimately, performing computations: a quantum computer. In this tutorial we summarize past and very recent developments which point the way to spin-based quantum computing in the solid-state. After introducing a set of basic requirements for any quantum computer proposal, we offer a brief summary of some of the many theoretical proposals for solid-state quantum computers. We then focus on the Loss-DiVincenzo proposal for quantum computing with the spins of electrons confined to quantum dots. There are many obstacles to building such a quantum device. We address these, and survey recent theoretical, and then experimental progress in the field. To conclude the tutorial, we list some as-yet unrealized experiments, which would be crucial for the development of a quantum-dot quantum computer.Comment: 45 pages, 12 figures (low-res in preprint, high-res in journal) tutorial review for Nanotechnology; v2: references added and updated, final version to appear in journa

Spin dynamics in semiconductors

This article reviews the current status of spin dynamics in semiconductors which has achieved a lot of progress in the past years due to the fast growing field of semiconductor spintronics. The primary focus is the theoretical and experimental developments of spin relaxation and dephasing in both spin precession in time domain and spin diffusion and transport in spacial domain. A fully microscopic many-body investigation on spin dynamics based on the kinetic spin Bloch equation approach is reviewed comprehensively.Comment: a review article with 193 pages and 1103 references. To be published in Physics Reports

Semiconductor Spintronics

Spintronics refers commonly to phenomena in which the spin of electrons in a solid state environment plays the determining role. In a more narrow sense spintronics is an emerging research field of electronics: spintronics devices are based on a spin control of electronics, or on an electrical and optical control of spin or magnetism. This review presents selected themes of semiconductor spintronics, introducing important concepts in spin transport, spin injection, Silsbee-Johnson spin-charge coupling, and spindependent tunneling, as well as spin relaxation and spin dynamics. The most fundamental spin-dependent nteraction in nonmagnetic semiconductors is spin-orbit coupling. Depending on the crystal symmetries of the material, as well as on the structural properties of semiconductor based heterostructures, the spin-orbit coupling takes on different functional forms, giving a nice playground of effective spin-orbit Hamiltonians. The effective Hamiltonians for the most relevant classes of materials and heterostructures are derived here from realistic electronic band structure descriptions. Most semiconductor device systems are still theoretical concepts, waiting for experimental demonstrations. A review of selected proposed, and a few demonstrated devices is presented, with detailed description of two important classes: magnetic resonant tunnel structures and bipolar magnetic diodes and transistors. In most cases the presentation is of tutorial style, introducing the essential theoretical formalism at an accessible level, with case-study-like illustrations of actual experimental results, as well as with brief reviews of relevant recent achievements in the field.Comment: tutorial review; 342 pages, 132 figure