Abstract:
We investigate mesoscopic fluctuations in the spin polarization generated by a static electric field and by Rashba spin-orbit interaction in a disordered 2D electron gas. In a diagrammatic approach we find that the out-of-plane polarization -- while being zero for self-averaging systems -- exhibits large sample-to-sample fluctuations which are shown to be well within experimental reach. We evaluate the disorder-averaged variance of the susceptibility and find its dependence on magnetic field, spin-orbit interaction, dephasing, and chemical potential difference.

Abstract:
We study macroscopic quantum coherence (MQC) in small ferrimagnets. Through semi-classical calculations we show that even a small uncompensated moment has a drastic effect on MQC. In particular, there is a rapid crossover to a regime where the MQC tunnel splitting is equal to that obtained for a ferromagnet, even though the system is still an antiferromagnet for all other aspects. We calculate this tunnel splitting via instanton methods and compare it with numerical evaluations. As an application we re-examine the experimental evidence for MQC in ferritin and show that even though the uncompensated moment of ferritin is small it greatly modifies the MQC behavior. We also discuss the implications of our results for MQC in molecular magnets.

Abstract:
We show that in the few-excitation regime the classical and quantum time-evolution of the inhomogeneous Dicke model for N two-level systems coupled to a single boson mode agree for N>>1. In the presence of a single excitation only, the leading term in an 1/N-expansion of the classical equations of motion reproduces the result of the Schroedinger equation. For a small number of excitations, the numerical solutions of the classical and quantum problems become equal for N sufficiently large. By solving the Schroedinger equation exactly for two excitations and a particular inhomogeneity we obtain 1/N-corrections which lead to a significant difference between the classical and quantum solutions at a new time scale which we identify as an Ehrenferst time, given by tau_E=sqrt{N}, where sqrt{} is an effective coupling strength between the two-level systems and the boson.

Abstract:
We present a semi-automated computer-assisted method to generate and calculate diagrams in the disorder averaging approach to disordered 2D conductors with intrinsic spin-orbit interaction (SOI). As an application, we calculate the effect of the SOI on the charge conductivity for disordered 2D systems and rings in the presence of Rashba and Dresselhaus SOI. In an infinite-size 2D system, anisotropic corrections to the conductivity tensor arise due to phase-coherence and the interplay of Rashba and Dresselhaus SOI. The effect is more pronounced in the quasi-onedimensional case, where the conductivity becomes anisotropic already in the presence of only one type of SOI. The anisotropy further increases if the time-reversal symmetry of the Hamiltonian is broken.

Abstract:
Motivated by recent experiments on low-dimensional quantum magnets in applied magnetic fields, we present a theoretical analysis of their properties based on the nonlinear sigma model. The spin stiffness and a 1/N expansion are used to map the regimes of spin-gap behavior, predominantly linear magnetization, and spin saturation. A two-parameter renormalization-group study gives the characteristic properties over the entire parameter range. The model is relevant to many systems exhibiting Haldane physics, and is applied here to the two-chain spin ladder compound CuHpCl.

Abstract:
We investigate spin transport of heavy holes in III-V semiconductor quantum wells in the presence of spin-orbit coupling of the Rashba type due to structure-inversion asymmetry. Similarly to the case of electrons, the longitudinal spin conductivity vanishes, whereas the off-diagonal elements of the spin-conductivity tensor are finite giving rise to an intrinsic spin-Hall effect. For a clean system we find a closed expression for the spin-Hall conductivity depending on the length scale of the Rashba coupling and the hole density. In this limit the spin-Hall conductivity is enhanced compared to its value for electron systems, and it vanishes with increasing strength of the impurity scattering. As an aside, we also derive explicit expressions for the Fermi momenta and the densities of holes in the different dispersion branches as a function of the spin-orbit coupling parameter and the total hole density. These results are of relevance for the interpretation of possible Shubnikov-de Haas measurements detecting the Rashba spin splitting.

Abstract:
Electrons in a two-dimensional semiconducting heterostructure interact with nuclear spins via the hyperfine interaction. Using a a Kondo lattice formulation of the electron-nuclear spin interaction, we show that the nuclear spin system within an interacting two-dimensional electron gas undergoes a ferromagnetic phase transition at finite temperatures. We find that electron-electron interactions and non-Fermi liquid behavior substantially enhance the nuclear spin Curie temperature into the $mK$ range with decreasing electron density.

Abstract:
We study the spin polarization and its associated spin-Hall current due to EDSR in disordered two-dimensional electron systems. We show that the disorder induced damping of the resonant spin polarization can be strongly reduced by an optimal field configuration that exploits the interference between Rashba and Dresselhaus spin-orbit interaction. This leads to a striking enhancement of the spin susceptibility while the spin-Hall current vanishes at the same time. We give an interpretation of the spin current in geometrical terms which are associated with the trajectories the polarization describes in spin space.

Abstract:
We show that the conductivity tensor of a disordered two-dimensional electron gas becomes anisotropic in the presence of both Rashba and Dresselhaus spin-orbit interactions (SOI). This anisotropy is a mesoscopic effect and vanishes with vanishing charge dephasing time. Using a diagrammatic approach including zero, one, and two-loop diagrams, we show that a consistent calculation needs to go beyond a Boltzmann equation approach. In the absence of charge dephasing and for zero frequency, a finite anisotropy \sigma_{xy} e^2/lhpf arises even for infinitesimal SOI.

Abstract:
Using a Luttinger liquid description, the correlation function exponents of various response functions are calculated. Their striking sensitivity to the non perturbative Wentzel-Bardeen singularity is discussed. For the Hubbard model coupled to phonons, the equivalent of a phase diagram is established. By increasing the filling factor towards half filling, the Wentzel-Bardeen singularity is rapidly approached. This suppresses antiferromagnetic fluctuations and drives the system in a metallic phase, and ultimately in the triplet superconducting regime.