Spin-polarized Quantum Transport in Mesoscopic Conductors: Computational Concepts and Physical Phenomena

Mesoscopic conductors are electronic systems of sizes in between nano- and micrometers, and often of reduced dimensionality. In the phase-coherent regime at low temperatures, the conductance of these devices is governed by quantum interference effects, such as the Aharonov-Bohm effect and conductance fluctuations as prominent examples. While first measurements of quantum charge transport date back to the 1980s, spin phenomena in mesoscopic transport have moved only recently into the focus of attention, as one branch of the field of spintronics. The interplay between quantum coherence with confinement-, disorder- or interaction-effects gives rise to a variety of unexpected spin phenomena in mesoscopic conductors and allows moreover to control and engineer the spin of the charge carriers: spin interference is often the basis for spin-valves, -filters, -switches or -pumps. Their underlying mechanisms may gain relevance on the way to possible future semiconductor-based spin devices. A quantitative theoretical understanding of spin-dependent mesoscopic transport calls for developing efficient and flexible numerical algorithms, including matrix-reordering techniques within Green function approaches, which we will explain, review and employ.Comment: To appear in the Encyclopedia of Complexity and System Scienc

Coherent spin ratchets: A spin-orbit based quantum ratchet mechanism for spin-polarized currents in ballistic conductors

We demonstrate that the combined effect of a spatially periodic potential, lateral confinement and spin-orbit interaction gives rise to a quantum ratchet mechanism for spin-polarized currents in two-dimensional coherent conductors. Upon adiabatic ac-driving, in the absence of a static bias, the system generates a directed spin current while the total charge current is zero. We analyze the underlying mechanism by employing symmetry properties of the scattering matrix and numerically verify the effect for different setups of ballistic conductors. The spin current direction can be changed upon tuning the Fermi energy or the strength of the Rashba spin-orbit coupling.Comment: 5 pages and 4 Figure

Spin-Orbit Based Coherent Spin Ratchets

The concept of ratchets, driven asymmetric periodic structures giving rise to directed particle flow, has recently been generalized to a quantum ratchet mechanism for spin currents mediated through spin-orbit interaction. Here we consider such systems in the coherent mesoscopic regime and generalize the proposal of a minimal spin ratchet model based on a non-interacting clean quantum wire with two transverse channels by including disorder and by self-consistently treating the charge redistribution in the nonlinear (adiabatic) ac-driving regime. Our Keldysh-Green function based quantum transport simulations show that the spin ratchet mechanism is robust and prevails for disordered, though non-diffusive, mesoscopic structures. Extending the two-channel to the multi-channel case does not increase the net ratchet spin current efficiency but, remarkably, yields a dc spin transmission increasing linearly with channel number.Comment: 23 pages, 7 figures; to be published in Chemical Physic

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.Comment: 4 pages, 4 figure

Resonant tunneling-based spin ratchets

We outline a generic ratchet mechanism for creating directed spin-polarized currents in ac-driven double well or double dot structures by employing resonant spin transfer through the system engineered by local external magnetic fields. We show its applicability to semiconductor nanostructures by considering coherent transport through two coupled lateral quantum dots, where the energy levels of the two dots exhibit opposite Zeeman spin splitting. We perform numerical quantum mechanical calculations for the I-V characteristics of this system in the nonlinear regime, which requires a self-consistent treatment of the charge redistribution due to the applied finite bias. We show that this setting enables nonzero averaged net spin currents in the absence of net charge transport.Comment: 5 pages, 4 figure

Magnetic-field dependence of transport in normal and Andreev billiards: a classical interpretation to the averaged quantum behavior

We perform a comparative study of the quantum and classical transport probabilities of low-energy quasiparticles ballistically traversing normal and Andreev two-dimensional open cavities with a Sinai-billiard shape. We focus on the dependence of the transport on the strength of an applied magnetic field $B$. With increasing field strength the classical dynamics changes from mixed to regular phase space. Averaging out the quantum fluctuations, we find an excellent agreement between the quantum and classical transport coefficients in the complete range of field strengths. This allows an overall description of the non-monotonic behavior of the average magnetoconductance in terms of the corresponding classical trajectories, thus, establishing a basic tool useful in the design and analysis of experiments.Comment: 11 pages, 12 figures; minor revisions including updated inset of Fig. 4(b) and references; version as accepted for publication to Phys. Rev.

Anisotropic universal conductance fluctuations in disordered quantum wires with Rashba and Dresselhaus spin-orbit interaction and applied in-plane magnetic field

We investigate the transport properties of narrow quantum wires realized in disordered two-dimensional electron gases in the presence of k-linear Rashba and Dresselhaus spin-orbit interaction (SOI), and an applied in-plane magnetic field. Building on previous work [Scheid, et al., PRL 101, 266401 (2008)], we find that in addition to the conductance, the universal conductance fluctuations also feature anisotropy with respect to the magnetic field direction. This anisotropy can be explained solely from the symmetries exhibited by the Hamiltonian as well as the relative strengths of the Rashba and Dresselhaus spin orbit interaction and thus can be utilized to detect this ratio from purely electrical measurements.Comment: 10 pages, 4 figures, 1 tabl

Spin Accumulation in Diffusive Conductors with Rashba and Dresselhaus Spin-Orbit Interaction

We calculate the electrically induced spin accumulation in diffusive systems due to both Rashba (with strength $\alpha)$ and Dresselhaus (with strength $\beta)$ spin-orbit interaction. Using a diffusion equation approach we find that magnetoelectric effects disappear and that there is thus no spin accumulation when both interactions have the same strength, $\alpha=\pm \beta$. In thermodynamically large systems, the finite spin accumulation predicted by Chaplik, Entin and Magarill, [Physica E {\bf 13}, 744 (2002)] and by Trushin and Schliemann [Phys. Rev. B {\bf 75}, 155323 (2007)] is recovered an infinitesimally small distance away from the singular point $\alpha=\pm \beta$. We show however that the singularity is broadened and that the suppression of spin accumulation becomes physically relevant (i) in finite-sized systems of size $L$, (ii) in the presence of a cubic Dresselhaus interaction of strength $\gamma$, or (iii) for finite frequency measurements. We obtain the parametric range over which the magnetoelectric effect is suppressed in these three instances as (i) $|\alpha|-|\beta| \lesssim 1/mL$, (ii)$|\alpha|-|\beta| \lesssim \gamma p_{\rm F}^2$, and (iii) |\alpha|-|\beta| \lesssiM \sqrt{\omega/m p_{\rm F}\ell} with $\ell$ the elastic mean free path and $p_{\rm F}$ the Fermi momentum. We attribute the absence of spin accumulation close to $\alpha=\pm \beta$ to the underlying U (1) symmetry. We illustrate and confirm our predictions numerically

A reliable cw Lyman-α\alpha laser source for future cooling of antihydrogen

We demonstrate a reliable continuous-wave (cw) laser source at the 1\,$S$--2\,$P$ transition in (anti)hydrogen at 121.56\,nm (Lyman-$\alpha$) based on four-wave sum-frequency mixing in mercury. A two-photon resonance in the four-wave mixing scheme is essential for a powerful cw Lyman-$\alpha$ source and is well investigated.Comment: 8 pages, 3 figures, Proceedings of LEAP 201