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We develop a theory of extrinsic spin currents in semiconductors, resulting from spin-orbit coupling at charged scatterers, which leads to skew scattering and side jump contributions to the spin Hall conductance. Applying the theory to bulk n-GaAs, without any free parameters, we find spin currents that are in reasonable agreement with recent experiments by Kato et al. [Science 306, 1910].

Spin Hall effects are a collection of phenomena, resulting from spin-orbit coupling, in which an electrical current flowing through a sample can lead to spin transport in a perpendicular direction and spin accumulation at lateral boundaries. These effects, which do not require an applied magnetic field, can originate in a variety of intrinsic and extrinsic spin-orbit coupling mechanisms and depend on geometry, dimension, impurity scattering, and carrier density of the system-making the analysis of these effects a diverse field of research. In this article, we give an overview of the theoretical background of the spin Hall effects and summarize some of the most important results. First, we explain effective spin-orbit Hamiltonians, how they arise from band structure, and how they can be understood from symmetry considerations; including intrinsic coupling due to bulk inversion or structure asymmetry or due to strain, and extrinsic coupling due to impurities. This leads to different mechanisms of spin transport: spin precession, skew scattering, and side jump. Then we present the kinetic (Boltzmann) equations, which describe the spin-dependent distribution function of charge carriers, and the diffusion equation for spin polarization density. Next, we define the notion of spin currents and discuss their relation to spin polarization. Finally, we explain the electrically induced spin effects; namely, spin polarization and currents in bulk and near boundaries (the focus of most current theoretical research efforts), and spin injection, as well as effects in mesoscopic systems and in edge states.

We consider a quantum dot attached to leads in the Coulomb blockade regime that has a spin 1 / 2 ground state. We show that, by applying an ESR field to the dot spin, the stationary current in the sequential tunneling regime exhibits a new resonance peak whose linewidth is determined by the single spin decoherence time T2. The Rabi oscillations of the dot spin are shown to induce coherent current oscillations from which T2 can be deduced in the time domain. We describe a spin inverter which can be used to pump current through a double dot via spin flips generated by ESR.

An arbitrarily small concentration of impurities can affect the spin Hall conductivity in a twodimensional semiconductor system. We develop a Boltzmann-like equation that can be used for impurity scattering with arbitrary angular dependence, and for arbitrary angular dependence of the spin-orbit field b(k) around the Fermi surface. For a model applicable to a 2D hole system in GaAs, if the impurity scattering is not isotropic, we find that the spin Hall conductivity depends on the derivative of b with respect to the energy and on deviations from a parabolic band structure, as well as on the angular dependence of the scattering. In principle, the resulting spin Hall conductivity can be larger or smaller than the "intrinsic value", and can have opposite sign. In the limit of small angle scattering, in a model appropriate for small hole concentrations, where the band is parabolic and b ∝ k 3 , the spin Hall conductivity has opposite sign from the intrinsic value, and has larger magnitude. Our analysis assumes that the spin-orbit splitting b and the transport scattering rate τ −1 are both small compared to the Fermi energy, but the method is valid for for arbitrary value of bτ .PACS numbers: 73.50.Bk

We analyze the frequency-dependent noise of a current through a quantum dot which is coupled to Fermi leads and which is in the Coulomb blockade regime. We show that the asymmetric shot noise, as a function of detection frequency, shows steps and becomes super-Poissonian. This provides experimental access to the quantum fluctuations of the current. We present an exact calculation of the noise for a single dot level and a perturbative evaluation of the noise in Born approximation (sequential tunneling regime but without Markov approximation) for the general case of many levels with charging interaction.

We report measurements of the cross correlation between temporal current fluctuations in two capacitively coupled quantum dots in the Coulomb blockade regime. The sign of the cross-spectral density is found to be tunable by gate voltage and source-drain bias. We find good agreement with the data by including an interdot Coulomb interaction in a sequential-tunneling model.

We propose a protocol and physical implementation for partial Bell-state measurements of Fermionic qubits, allowing for deterministic quantum computing in solid-state systems without the need for two-qubit gates. Our scheme consists of two spin qubits in a double quantum dot where the two dots have different Zeeman splittings and resonant tunneling between the dots is only allowed when the spins are antiparallel. This converts spin parity into charge information by means of a projective measurement and can be implemented with established technologies. This measurement-based qubit scheme greatly simplifies the experimental realization of scalable quantum computers in electronic nanostructures.