Role of orbital dynamics in spin relaxation and weak antilocalization in quantum dots

Universal spatial correlations in random spinor fields

We identify universal spatial fluctuations in systems with nontrivial spin dynamics. To this end we calculate by exact numerical diagonalization a variety of experimentally relevant correlations between spinor amplitudes, spin polarizations, and spin currents, both in the bulk and near the boundary of a confined two-dimensional clean electron gas in the presence of spin-orbit interaction. We support our claim of universality with the excellent agreement between the numerical results and system-independent spatial correlations of a random field defined on both the spatial and spin degrees of freedom. A rigorous identity relating our universal predictions with response functions provides a direct physical interpretation of our results in the framework of linear response theory.

Universality in chaotic quantum transport: the concordance between random-matrix and semiclassical theories

Electronic transport through chaotic quantum dots exhibits universal, system-independent properties, consistent with random-matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the classical scattering trajectories. Correlations between such trajectories can be organized diagrammatically and have been shown to yield universal answers for some observables. Here, we develop the general combinatorial treatment of the semiclassical diagrams, through a connection to factorizations of permutations. We show agreement between the semiclassical and random matrix approaches to the moments of the transmission eigenvalues. The result is valid for all moments to all orders of the expansion in inverse channel number for all three main symmetry classes (with and without time-reversal symmetry and spin-orbit interaction) and extends to nonlinear statistics. This finally explains the applicability of random-matrix theory to chaotic quantum transport in terms of the underlying dynamics as well as providing semiclassical access to the probability density of the transmission eigenvalues.

Geometric correlations and breakdown of mesoscopic universality in spin transport

We construct a unified semiclassical theory of charge and spin transport in chaotic ballistic and disordered diffusive mesoscopic systems with spin-orbit interaction. Neglecting dynamic effects of spin-orbit interaction, we reproduce the random matrix theory results that the spin conductance fluctuates universally around zero average. Incorporating these effects into the theory, we show that geometric correlations generate finite average spin conductances, but that they do not affect the charge conductance to leading order. The theory, which is confirmed by numerical transport calculations, allows us to investigate the entire range from the weak to the previously unexplored strong spin-orbit regime, where the spin rotation time is shorter than the momentum relaxation time.

Long-time saturation of the Loschmidt echo in quantum chaotic billiards

The Loschmidt echo (LE) (or fidelity) quantifies the sensitivity of the time evolution of a quantum system with respect to a perturbation of the Hamiltonian. In a typical chaotic system the LE has been previously argued to exhibit a long-time saturation at a value inversely proportional to the effective size of the Hilbert space of the system. However, until now no quantitative results have been known and, in particular, no explicit expression for the proportionality constant has been proposed. In this paper we perform a quantitative analysis of the phenomenon of the LE saturation and provide the analytical expression for its long-time saturation value for a semiclassical particle in a two-dimensional chaotic billiard. We further perform extensive (fully quantum mechanical) numerical calculations of the LE saturation value and find the numerical results to support the semiclassical theory.

Semiclassical theory for decay and fragmentation processes in chaotic quantum systems

We consider quantum decay and photofragmentation processes in open chaotic systems in the semiclassical limit. We devise a semiclassical approach which allows us to consistently calculate quantum corrections to the classical decay to high order in an expansion in the inverse Heisenberg time. We present results for systems with and without time-reversal symmetry, as well as for the symplectic case, and extend recent results to nonlocalized initial states. We further analyze related photodissociation and photoionization phenomena and semiclassically compute cross-section correlations, including their Ehrenfest-time dependence.

All-electrical detection of the relative strength of Rashba and Dresselhaus spin-orbit interaction in quantum wires

We propose a method to determine the relative strength of Rashba and Dresselhaus spin-orbit interaction from transport measurements without the need of fitting parameters. To this end, we make use of the conductance anisotropy in narrow quantum wires with respect to the directions of an in-plane magnetic field, the quantum wire, and the crystal orientation. We support our proposal by numerical calculations of the conductance of quantum wires based on the Landauer formalism which show the applicability of the method to a wide range of parameters.

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. While metal spintronics has already found its niche in the computer industry—giant magnetoresistance systems are used as hard disk read heads—semiconductor spintronics is yet to demonstrate its full potential. This review presents selected themes of semiconductor spintronics, introducing important concepts in spin transport, spin injection, Silsbee-Johnson spin-charge coupling, and spin-dependent tunneling, as well as spin relaxation and spin dynamics. The most fundamental spin-dependent interaction 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 view of the importance of ferromagnetic semiconductor materials, a brief discussion of diluted magnetic semiconductors is included. 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.

Cubic Dresselhaus spin-orbit coupling in 2D electron quantum dots

We study effects of the oft-neglected cubic Dresselhaus spin-orbit coupling (i.e., directly proportional p3) in GaAs/AlGaAs quantum dots. Using a semiclassical billiard model, we estimate the magnitude of the spin-orbit induced avoided crossings in a closed quantum dot in a Zeeman field. Using previous analyses based on random matrix theory, we calculate corresponding effects on the conductance through an open quantum dot. Combining our results with an experiment on an 8 microm2 quantum dot [D. M. Zumbühl, Phys. Rev. B 72, 081305 (2005)10.1103/PhysRevB.72.081305] suggests that (1) the GaAs Dresselhaus coupling constant gamma is approximately 9 eV A3, significantly less than the commonly cited value of 27.5 eV A3, and (2) the majority of the spin-flip effects can come from the cubic Dresselhaus term.

Periodic-orbit theory of universality in quantum chaos

We argue semiclassically, on the basis of Gutzwiller's periodic-orbit theory, that full classical chaos is paralleled by quantum energy spectra with universal spectral statistics, in agreement with random-matrix theory. For dynamics from all three Wigner-Dyson symmetry classes, we calculate the small-time spectral form factor K(tau) as power series in the time tau. Each term tau(n) of that series is provided by specific families of pairs of periodic orbits. The contributing pairs are classified in terms of close self-encounters in phase space. The frequency of occurrence of self-encounters is calculated by invoking ergodicity. Combinatorial rules for building pairs involve nontrivial properties of permutations. We show our series to be equivalent to perturbative implementations of the nonlinear sigma models for the Wigner-Dyson ensembles of random matrices and for disordered systems; our families of orbit pairs have a one-to-one relationship with Feynman diagrams known from the sigma model.

Nonequilibrium spin Hall accumulation in ballistic semiconductor nanostructures

We demonstrate that the flow of a longitudinal unpolarized current through a ballistic two-dimensional electron gas with Rashba spin-orbit coupling will induce a nonequilibrium spin accumulation which has opposite signs for the two lateral edges and is, therefore, the principal observable signature of the spin Hall effect in two-probe semiconductor nanostructures. The magnitude of its out-of-plane component is gradually diminished by static disorder, while it can be enhanced by an in-plane transverse magnetic field. Moreover, our prediction of the longitudinal component of the spin Hall accumulation, which is insensitive to the reversal of the bias voltage, offers direct evidence to differentiate experimentally between the extrinsic, intrinsic, and mesoscopic spin Hall mechanisms.