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 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:
One of the hallmarks of spintronics is the control of magnetic moments by electric fields enabled by strong spin-orbit interaction (SOI) in semiconductors. A powerful way of manipulating spins in such structures is electric dipole induced spin resonance (EDSR), where the radio-frequency fields driving the spins are electric, and not magnetic like in standard paramagnetic resonance. Here, we present a theoretical study of EDSR for a two-dimensional electron gas in the presence of disorder where random impurities not only determine the electric resistance but also the spin dynamics via SOI. Considering a specific geometry with the electric and magnetic fields parallel and in-plane, we show that the magnetization develops an out-of-plane component at resonance which survives the presence of disorder. We also discuss the spin Hall current generated by EDSR. These results are derived in a diagrammatic approach with the dominant effects coming from the spin vertex correction, and the optimal parameter regime for observation is identified.

Abstract:
We study Andreev reflection at an interface between a half metal and a superconductor with spin-orbit interaction. While the absence of minority carriers in the half metal makes singlet Andreev reflection impossible, the spin-orbit interaction gives rise to triplet Andreev reflection, i.e., the reflection of a majority electron into a majority hole or vice versa. As an application of our calculation, we consider a thin half metal film or wire laterally attached to a superconducting contact. If the half metal is disorder free, an excitation gap is opened that is proportional to the spin-orbit interaction strength in the superconductor. For electrons with energy below this gap a lateral half-metal--superconductor contact becomes a perfect triplet Andreev reflector. We show that the system supports localized Majorana end states in this limit.

Abstract:
We derive boundary conditions for the electrically induced spin accumulation in a finite, disordered 2D semiconductor channel. While for DC electric fields these boundary conditions select spatially constant spin profiles equivalent to a vanishing spin-Hall effect, we show that an in-plane ac electric field results in a non-zero ac spin-Hall effect, i.e., it generates a spatially non-uniform out-of-plane polarization even for linear intrinsic spin-orbit interactions. Analyzing different geometries in [001] and [110]-grown quantum wells, we find that although this out-of-plane polarization is typically confined to within a few spin-orbit lengths from the channel edges, it is also possible to generate spatially oscillating spin profiles which extend over the whole channel. The latter is due to the excitation of a driven spin-helix mode in the transverse direction of the channel. We show that while finite frequencies suppress this mode, it can be amplified by a magnetic field tuned to resonance with the frequency of the electric field. In this case, finite size effects at equal strengths of Rashba- and Dresselhaus SOI lead to an enhancement of the magnitude of this helix mode. We comment on the relation between spin currents and boundary conditions.

Abstract:
Zeeman fields can drive semiconductor quantum wires with strong spin-orbit coupling and in proximity to s-wave superconductors into a topological phase which supports end Majorana fermions and offers an attractive platform for realizing topological quantum information processing. Here, we investigate how potential disorder affects the topological phase by a combination of analytical and numerical approaches. Most prominently, we find that the robustness of the topological phase against disorder depends sensitively and non-monotonously on the Zeeman field applied to the wire.

Abstract:
One-dimensional topological superconductors harbor Majorana bound states at their ends. For superconducting wires of finite length L, these Majorana states combine into fermionic excitations with an energy $\epsilon_0$ that is exponentially small in L. Weak disorder leaves the energy splitting exponentially small, but affects its typical value and causes large sample-to-sample fluctuations. We show that the probability distribution of $\epsilon_0$ is log normal in the limit of large L, whereas the distribution of the lowest-lying bulk energy level $\epsilon_1$ has an algebraic tail at small $\epsilon_1$. Our findings have implications for the speed at which a topological quantum computer can be operated.

Abstract:
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.

Abstract:
We investigate Josephson currents in mesoscopic rings with a weak link which are in or near a topological superconducting phase. As a paradigmatic example, we consider the Kitaev model of a spinless p-wave superconductor in one dimension, emphasizing how this model emerges from more realistic settings based on semiconductor nanowires. We show that the flux periodicity of the Josephson current provides signatures of the topological phase transition and the emergence of Majorana fermions situated on both sides of the weak link even when fermion parity is not a good quantum number. In large rings, the Majorana fermions hybridize only across the weak link. In this case, the Josephson current is h/e periodic in the flux threading the loop when fermion parity is a good quantum number but reverts to the more conventional h/2e periodicity in the presence of fermion-parity changing relaxation processes. In mesoscopic rings, the Majorana fermions also hybridize through their overlap in the interior of the superconducting ring. We find that in the topological superconducting phase, this gives rise to an h/e-periodic contribution even when fermion parity is not conserved and that this contribution exhibits a peak near the topological phase transition. This signature of the topological phase transition is robust to the effects of disorder. As a byproduct, we find that close to the topological phase transition, disorder drives the system deeper into the topological phase. This is in stark contrast to the known behavior far from the phase transition, where disorder tends to suppress the topological phase.

Abstract:
The influence of low to moderate frequency environments on Macroscopic Quantum Tunneling (MQT) in superconducting circuits is studied within the Im-F approach to evaluate tunneling rates. Particular attention is paid to two model environments, namely, a pure sluggish bath and a sluggish bath with additional 1/f-noise. General findings are applied to Zener flip tunneling, a MQT phenomenon recently predicted and observed in a superconducting circuit implementing a quantum bit.