Abstract:
The anomalous Hall effect of heavy holes in semiconductor quantum wells is studied in the intrinsic transport regime, where the Berry curvature governs the Hall current properties. Based on the first--order perturbation of wave function the expression of the Hall conductivity the same as that from the semiclassical equation of motion of the Bloch particles is derived. The dependence of Hall conductivity on the system parameters is shown. The amplitude of Hall conductivity is found to be balanced by a competition between the Zeeman splitting and the spin--orbit splitting.

Abstract:
Based on a proper definition of the spin current, we investigate the spin-Hall effect of heavy holes in narrow quantum wells in the presence of Rashba spin-orbit coupling by using a spin-density matrix approach. In contrast to previous results obtained on the basis of the conventional definition of the spin current, we arrive at the conclusion that an electric-field-induced steady-state spin-Hall current does not exist in both, pure and disordered infinite samples. Only an ac field can induce a spin-Hall effect in such systems.

Abstract:
The notion of zitterbewegung is a long-standing prediction of relativistic quantum mechanics. Here we extend earlier theoretical studies on this phenomenon for the case of III-V zinc-blende semiconductors which exhibit particularly strong spin-orbit coupling. This property makes nanostructures made of these materials very favorable systems for possible experimental observations of zitterbewegung. Our investigations include electrons in n-doped quantum wells under the influence of both Rashba and Dresselhaus spin-orbit interaction, and also the two-dimensional hole gas. Moreover, we give a detailed anaysis of electron zitterbewegung in quantum wires which appear to be particularly suited for experimentally observing this effect.

Abstract:
We investigate the ballistic motion of electrons and holes in III-V semiconductor quantum wells with spin-orbit coupling and a homogeneous in-plane electric field. As a result of a non-perturbative treatment of both of these influences, particle wave packets undergo a pronounced side jump perpendicular to the field direction. For wave packets of sufficient width the amplitude of this motion can be estimated analytically and increases with decreasing field strength. We discuss the scaling behavior of the effect and some if its experimental implications

Abstract:
Spin-orbit (SO) interactions give a spin-dependent correction r_so to the position operator, referred to as the anomalous position operator. We study the contributions of r_so to the spin-Hall effect (SHE) in quasi two-dimensional (2D) semiconductor quantum wells with strong band structure SO interactions that cause spin precession. The skew scattering and side-jump scattering terms in the SHE vanish, but we identify two additional terms in the SHE, due to r_so, which have not been considered in the literature so far. One term reflects the modification of the spin precession due to the action of the external electric field (the field drives the current in the quantum well), which produces, via r_so, an effective magnetic field perpendicular to the plane of the quantum well. The other term reflects a similar modification of the spin precession due to the action of the electric field created by random impurities, and appears in a careful formulation of the Born approximation. We refer to these two effects collectively as anomalous spin precession and we note that they contribute to the SHE to the first order in the SO coupling constant even though they formally appear to be of second order. In electron systems with weak momentum scattering, the contribution of the anomalous spin precession due to the external electric field equals 1/2 the usual side-jump SHE, while the additional impurity-dependent contribution depends on the form of the band structure SO coupling. For band structure SO linear in wave vector the two additional contributions cancel. For band structure SO cubic in wave vector only the contribution due to external electric field is present, and can be detected through its density dependence. In 2D hole systems both anomalous spin precession contributions vanish identically.

Abstract:
We have proposed a method to separate Rashba and Dresselhaus spin splittings in semiconductor quantum wells by using the intrinsic Hall effect. It is shown that the interference between Rashba and Dresselhaus terms can deflect the electrons in opposite transverse directions with a change of sign in the macroscopic Hall current, thus providing an alternative way to determine the different contributions to the spin--orbit coupling.

Abstract:
We have developed a theory of the longitudinal $g$ factor of light holes in semiconductor quantum wells. It is shown that the absolute value of the light-hole $g$-factor can strongly exceed its value in the bulk and, moreover, the dependence of the Zeeman splitting on magnetic field becomes non-linear in relatively low fields. These effects are determined by the proximity of the ground light-hole subband, $lh1$, to the first excited heavy-hole subband, $hh2$, in GaAs/AlGaAs-type structures. The particular calculations are performed in the framework of Luttinger Hamiltonian taking into account both the magnetic field-induced mixing of $lh1$ and $hh2$ states and the mixing of these states at heterointerfaces, the latter caused by chemical bonds anisotropy. A theory of magneto-induced reflection and transmission of light through the quantum wells for the light-hole-to-electron absorption edge is also presented.

Abstract:
We have calculated band-edge energies for most combinations of zincblende AlN, GaN, InN, GaP, GaAs, InP, InAs, GaSb and InSb in which one material is strained to the other. Calculations were done for three different geometries, quantum wells, wires, and dots, and mean effective masses were computed in order to estimate confinement energies. For quantum wells, we have also calculated band-edges for ternary alloys. Energy gaps, including confinement, may be easily and accurately estimated using band energies and a simple effective mass approximation, yielding excellent agreement with experimental results. By calculating all material combinations we have identified novel and interesting material combinations, such as artificial donors, that have not been experimentally realized. The calculations were perfomed using strain-dependent k-dot-p theory and provide a comprehensive overview of band structures for strained heterostructures.

Abstract:
Spins of charge carriers, paramagnetic centers, and nuclei in semiconductor structures are known to be oriented if circular-polarized light is shined upon the structure. This is due to transfer of angular momentum from photons to various excitations in the semiconductor. What would happen if the structure is anisotropic, so that the angular momentum is not conserved? Experiments performed on diluted-magnetic II-VI quantum wells (such as CdMnTe/CdMgTe) show that at some conditions the effect of light upon the spin state of the semiconductor structure can be greatly amplified. Exchange field of photoexcited heavy holes initiates a coherent evolution of a great number of localized spins of Mn-ions. In the simplest case, it is just a precession in an effective field, but generally the spin dynamics is more intricate. It shows up, for instance, in long sequences of spin-flip peaks in Raman spectra, in enhanced magnetic-polaron effect, and in modulation of optical response within the picosecond time scale.

Abstract:
We review recent theoretical results for hole spins influenced by spin-orbit coupling and Coulomb interaction in two-dimensional quantum wells as well as the decoherence of single hole spins in quantum dots due to hyperfine interaction with surrounding nuclear spins. After reviewing the different forms of spin-orbit coupling that are relevant for electrons and heavy holes in III-V semiconductor quantum wells, we illustrate the combined effect of spin-orbit coupling and Coulomb interactions for hole systems on spin-dependent quasiparticle group velocities. We further analyze spin-echo decay for a single hole spin in a nuclear-spin bath, demonstrating that this decoherence source can be controlled in these systems by entering a motional-averaging regime. Throughout this review, we emphasize physical effects that are unique to hole spins (rather than electrons) in nanoscale systems.