Distinguishing Majorana bound states from localized Andreev bound states by interferometry

Experimental evidence for Majorana bound states (MBSs) is so far mainly based on the robustness of a zero-bias conductance peak. However, similar features can also arise due to Andreev bound states (ABSs) localized at the end of an island. We show that these two scenarios can be distinguished by an interferometry experiment based on embedding a Coulomb-blockaded island into an Aharonov-Bohm ring. For two ABSs, when the ground state is nearly degenerate, cotunneling can change the state of the island and interference is suppressed. By contrast, for two MBSs the ground state is nondegenerate and cotunneling has to preserve the island state, which leads to $h / e$-periodic conductance oscillations with magnetic flux. Such interference setups can be realized with semiconducting nanowires or two-dimensional electron gases with proximity-induced superconductivity and may also be a useful spectroscopic tool for parity-flip mechanisms

Coupling and braiding Majorana bound states in networks defined in proximitized two-dimensional electron gases

Two-dimensional electron gases with strong spin-orbit coupling covered by a superconducting layer offer a flexible and potentially scalable platform for Majorana networks. We predict Majorana bound states (MBSs) to appear for experimentally achievable parameters and realistic gate potentials in two designs: either underneath a narrow stripe of a superconducting layer (S-stripes) or where a narrow stripe has been removed from a uniform layer (N-stripes). The coupling of the MBSs can be tuned for both types in a wide range (10 $\mu$eV) using gates placed adjacent to the stripes. For both types, we numerically compute the local density of states for two parallel Majorana-stripe ends as well as Majorana trijunctions formed in a tuning-fork geometry. The MBS coupling between parallel Majorana stripes can be suppressed below 1 neV for potential barriers in the meV range for separations of about 200 nm. We further show that the MBS couplings in a trijunction can be gate-controlled in a range similar to the intra-stripe coupling while maintaining a sizable gap to the excited states (tens of $\mu$eV). Altogether, this suggests that braiding can carried out on a time scale of 10-100 ns

Spin quadrupoletronics: moving spin anisotropy around

We show that spin anisotropy can be transferred to an isotropic system by transport of spin quadrupole moment. We derive the quadrupole moment current and continuity equation and study a high-spin valve structure consisting of two ferromagnets coupled to a quantum dot probing an impurity spin. The quadrupole back-action on their coupled spin results in spin torques and anisotropic spin relaxation which do not follow from standard spin current considerations. We demonstrate the detection of the impurity spin by charge transport and its manipulation by electric fields.Comment: v2 updated arXiv reference [6

Transport of spin-anisotropy without spin currents

We revisit the transport of spin-degrees of freedom across an electrically and thermally biased tunnel junction between two ferromagnets with non-collinear magnetizations. Besides the well-known charge and spin currents we show that a non-zero spin-quadrupole current flows between the ferromagnets. This tensor-valued current describes the non-equilibrium transport of spin-anisotropy relating to both local and non-local multi-particle spin correlations of the circuit. This quadratic spin-anisotropy, quantified in terms of the spin-quadrupole moment, is fundamentally a two-electron quantity. In spin-valves with an embedded quantum dot such currents have been shown to result in a quadrupole accumulation that affects the measurable quantum dot spin and charge dynamics. The spin-valve model studied here allows fundamental questions about spin-quadrupole storage and transport to be worked out in detail, while ignoring the detection by a quantum dot. This physical understanding of this particular device is of importance for more complex devices where spin-quadrupole transport can be detected. We demonstrate that, as far as storage and transport are concerned, the spin anisotropy is only partly determined by the spin polarization. In fact, for a thermally biased spin-valve the charge- and spin-current may vanish, while a pure exchange spin-quadrupole current remains, which appears as a fundamental consequence of Pauli's principle. We extend the real-time diagrammatic approach to efficiently calculate the average of multi-particle spin-observables, in particular the spin-quadrupole current. Although the paper addresses only leading order and spin-conserving tunneling we formulate the technique for arbitrary order in an arbitrary, spin-dependent tunnel coupling in a way that lends itself to extension to quantum-dot spin-valve structures

Time scales for Majorana manipulation using Coulomb blockade in gate-controlled superconducting nanowires

We numerically compute the low-energy spectrum of a gate-controlled superconducting topological nanowire segmented into two islands, each Josephson-coupled to a bulk superconductor. This device may host two pairs of Majorana bound states and could provide a platform for testing Majorana fusion rules. We analyze the crossover between (i) a charge-dominated regime utilizable for initialization and readout of Majorana bound states, (ii) a single-island regime for dominating inter-island Majorana coupling, (iii) a Josephson-plasmon regime for large coupling to the bulk superconductors, and (iv) a regime of four Majorana bound states allowing for topologically protected Majorana manipulations. From the energy spectrum, we derive conservative estimates for the time scales of a fusion-rule testing protocol proposed recently [arXiv:1511.05153]. We also analyze the steps needed for basic Majorana braiding operations in branched nanowire structures

Perampanel inhibition of AMPA receptor currents in cultured hippocampal neurons.

Perampanel is an aryl substituted 2-pyridone AMPA receptor antagonist that was recently approved as a treatment for epilepsy. The drug potently inhibits AMPA receptor responses but the mode of block has not been characterized. Here the action of perampanel on AMPA receptors was investigated by whole-cell voltage-clamp recording in cultured rat hippocampal neurons. Perampanel caused a slow (τ∼1 s at 3 µM), concentration-dependent inhibition of AMPA receptor currents evoked by AMPA and kainate. The rates of block and unblock of AMPA receptor currents were 1.5×105 M-1 s-1 and 0.58 s-1, respectively. Perampanel did not affect NMDA receptor currents. The extent of block of non-desensitizing kainate-evoked currents (IC50, 0.56 µM) was similar at all kainate concentrations (3-100 µM), demonstrating a noncompetitive blocking action. Parampanel did not alter the trajectory of AMPA evoked currents indicating that it does not influence AMPA receptor desensitization. Perampanel is a selective negative allosteric AMPA receptor antagonist of high-affinity and slow blocking kinetics

Four-Majorana qubit with charge readout: dynamics and decoherence

We present a theoretical analysis of a Majorana-based qubit consisting of two topological superconducting islands connected via a Josephson junction. The qubit is operated by electrostatic gates which control the coupling of two of the four Majorana zero modes. At the end of the operation, readout is performed in the charge basis. Even though the operations are not topologically protected, the proposed experiment can potentially shed light on the coherence of the parity degree of freedom in Majorana devices and serve as a first step towards topological Majorana qubits. We discuss in detail the charge-stability diagram and its use for characterizing the parameters of the devices, including the overlap of the Majorana edge states. We describe the multi-level spectral properties of the system and present a detailed study of its controlled coherent oscillations, as well as decoherence resulting from coupling to a non-Markovian environment. In particular, we study a gate-controlled protocol where conversion between Coulomb-blockade and transmon regimes generates coherent oscillations of the qubit state due to the overlap of Majorana modes. We show that, in addition to fluctuations of the Majorana coupling, considerable measurement errors may be accumulated during the conversion intervals when electrostatic fluctuations in the superconducting islands are present. These results are also relevant for several proposed implementations of topological qubits which rely on readout based on charge detection

Distance Constraint Satisfaction Problems

We study the complexity of constraint satisfaction problems for templates $\Gamma$ that are first-order definable in $(\Bbb Z; succ)$, the integers with the successor relation. Assuming a widely believed conjecture from finite domain constraint satisfaction (we require the tractability conjecture by Bulatov, Jeavons and Krokhin in the special case of transitive finite templates), we provide a full classification for the case that Gamma is locally finite (i.e., the Gaifman graph of $\Gamma$ has finite degree). We show that one of the following is true: The structure Gamma is homomorphically equivalent to a structure with a d-modular maximum or minimum polymorphism and $\mathrm{CSP}(\Gamma)$ can be solved in polynomial time, or $\Gamma$ is homomorphically equivalent to a finite transitive structure, or $\mathrm{CSP}(\Gamma)$ is NP-complete.Comment: 35 pages, 2 figure

Synoptische, diagnostische und numerische Untersuchungen der Intensitätsänderungen von tropischen Wirbelstürmen und Monsuntiefs

The intensity changes of an Australian monsoon depression and typhoons Flo (1990) and Ed (1990) are investigated using operational analyses, diagnostic studies, and numerical model calculations. The analyses are based on gridded data from the Australian Bureau of Meteorology’s (BMRC’s) Tropical Analysis System, the European Centre for Medium-Range Weather Forecasts (ECMWF) data archive, and the 1990 Tropical Cyclone Motion experiment (TCM-90). The TCM-90 analyses are provided by the Japan Meteorological Agency and the National Centers for Environmental Prediction and incorporate typhoon boguses of the Geophysical Fluid Dynamics Laboratory and the Japan Meteorological Agency. The monsoon depression developed over northwestern Australia in February 1994. After remaining quasi-stationary for several days after its formation in the monsoon trough, the depression drifted slowly southwestwards along the coast of Western Australia and eventually weakened. The evolution is exemplified by time-height cross-sections of various kinematic quantities as well as the apparent source of potential vorticity, which has been taken into account in the PV equation for the first time. A prominent feature of these diagnostic fields is the impact of convective and diabatic processes on the development. The structure of the depression is very similar to those of the few monsoon depressions that have been documented over the Indian subcontinent. The formation of the depression coincided with the passage of an upper-level middle-latitude trough and a low-level anticyclone to the south, but the extent to which the genesis was influenced by these disturbances is unclear. The equation for the mean tangential wind in a storm-following cylindrical coordinate system is applied to investigate the intensity changes of tropical cyclones and monsoon depressions. In this equation, the symmetric, the resolved asymmetric and the subgrid-scale contributions are fully separated. The tangential wind changes can be interpreted in terms of absolute vorticity flux, angular momentum flux, PV flux or the Eliassen-Palm flux-divergence. The corresponding eddy fluxes are compared, and the impact of convection on the intensity changes as well as the interaction between a monsoon depression and upper-level troughs and ridges is investigated. Analyses of observational data for a monsoon depression that formed near the coast of northwestern Australia in February 1994 show that all terms in the tangential wind equation are important, except for the drift term. These important terms include above all the subgrid-scale terms which are presumed to be largely due to processes associated with deep convection. In the lower and middle troposphere, the main terms contributing to the intensification of the monsoon depression are the radial absolute vorticity fluxes (cyclonic inward fluxes of relative and planetary vorticity; or the corresponding terms that include the Eliassen-Palm fluxes, the radial PV-fluxes, or the angular momentum fluxes) and the vertical advection of tangential wind. In the upper troposphere, the cyclonic tangential wind change can be attributed mainly to the relative vorticity fluxes (anticyclonic outward fluxes of relative vorticity), the vertical advection of tangential wind, and the subgrid-scale contributions. The weakening tendency of the upper-level anticyclone associated with these effects and the channelled, widespread outflow are related to the strengthening of the monsoon depression. The inward movement of the eddy PV-flux-maxima in the upper troposphere reflects the approach of PV anomalies associated with passing mid-latitude troughs. We hypothesize that the convection near the monsoon depression is enhanced in front of the approaching PV anomalies by the reduction of static stability and by the vacuum cleaner effect, and that this influences the intensification of the depression. As a check on the robustness of the findings, the results using BMRC analyses are compared with those using ECMWF analyses. Despite the high diurnal variability, the patterns of the daily-mean symmetric, resolved-asymmetric and unresolved-asymmetric contributions agree relatively well, although the figures from the higher resolution ECMWF analyses show more details with more distinct peaks. The intensity changes of typhoons Flo and Ed, which were strongly influenced by deep convection, have been investigated using the Europa- and the Deutschland-Modell of the Deutscher Wetterdienst. The sensitivity of model forecasts to different initial conditions, typhoon boguses, model resolution and physical parameterizations has been examined. The typhoons Flo and Ed developed east of Guam and drifted northwest and westward, respectively. During the observation period, they were embedded in the monsoon trough and were about 1700 km apart. After 15 September 1990, Flo intensified rapidly to supertyphoon strength and recurved towards Japan. Before weakening over the coast of Vietnam, Ed undertook an unusual, southwestward drift. The effects of the large-scale and subgrid-scale asymmetries on the intensity of Typhoon Flo were not significant despite the nearby TUTT-cell and could not explain the intense deepening phase after 15 September. An inward or outward drift of maximal or minimal absolute eddy-vorticity fluxes was not analysed. The predictions of the asymmetry effects give useful hints about the kind and strength of the effects independently of the grid-resolution and the typhoon bogus incorporated in the start analysis. As in the case of the Australian monsoon depression, the vertical advection of momentum and the subgrid-scale effects are not negligible. For the two typhoons, the Europa- and the Deutschland-Modell showed a modest forecast skill for intensity change. The initial data fields, the incorporated boguses, the model resolution, and the physical parameterizations have a significant influence on the intensity forecasts. The boundary values barely affect the intensity prediction. Compared to operational forecast models, the two models have good skill in predicting typhoon tracks. The track prediction is nearly independent of the grid resolution and the cumulus, radiation and diffusion parameterization applied. Variations in track arise primarily from different boundary conditions and initial analyses including the typhoon boguses used. The model resolution, the initial analysis used, and the typhoon bogus incorporated have nearly no influence on the distribution and size of the rain areas. However, the typhoon bogus used and the model resolution strongly affect the amount of core region precipitation. The intensity of the model typhoons is correlated with the precipitation intensity and the strength of convection. Averaged over the entire typhoon area, the differences in the amount of rain for the two model resolutions is small, however.Die Intensitätsänderungen eines australischen Monsuntiefs und der Taifune Flo (1990) und Ed (1990) wurden mit Hilfe von operationellen Analysen, diagnostischen Studien und numerischen Modellrechnungen untersucht. Die Analysen basierten auf Gitterdaten vom tropischen Analysesystem des australischen Wetterbüros (BMRC), vom Datenarchiv des Europäischen Zentrums für mittelfristige Wettervorhersage (ECMWF) und vom Experiment zur Zugbahn tropischer Zyklone von 1990 (TCM-90). Die TCM-90-Analysen wurden vom Japanischen Wetterdienst (JMA) und vom Nationalen Zentrum für Umweltvorhersage (NCEP) erstellt und enthielten Taifunkeimzellen des Geophysikalischen Labors für Fließdynamik (GFDL) und des Japanischen Wetterdienstes. Das Monsuntief entwickelte sich im Februar 1994 über Nordwestaustralien. Nach seiner Entstehung im Monsuntrog verweilte es für mehrere Tage fast stationär über King Sound. Danach zog es langsam südwestwärts entlang der westaustralischen Küste und schwächte sich schließlich über dem Meer ab. Diese Monsuntiefentwicklung wurde an Hand von Zeit-Höhen- Diagrammen verschiedener kinematischer Größen und an Hand der PV-Quelle, die erstmals in der PV-Gleichung berücksichtigt wurde, veranschaulicht. Charakteristisch für diese diagnostischen Felder war der deutlich erkennbare Einfluß der konvektiven und diabatischen Prozesse auf die Monsuntiefentwicklung. Die Strukturen des australischen Monsuntiefs waren sehr ähnlich zu den Strukturen bei indischen Monsuntiefs. Die Entstehung des Monsuntiefs fand zur gleichen Zeit statt wie der Vorbeizug eines Höhentrogs und eines Antizyklons in der unteren Troposphäre südlich des Tiefs. In wie weit die Entstehung durch diese beiden Wetterstörungen beeinflußt wurde, konnte nicht endgültig geklärt werden. Zur Untersuchung der Intensitätsänderungen von tropischen Wirbelstürmen und Monsuntiefs wurde die allgemeine Gleichung der mittleren, tangentialen Windgeschwindigkeit in wirbelfolgenden Zylinderkoordinaten verwendet. In dieser Gleichung lassen sich die symmetrischen, die aufgelöst-asymmetrischen und die unaufgelöst-asymmetrischen (subskaligen) Beiträge vollständig voneinander trennen. Mit ihr können die Tangentialwindänderungen in Abhängigkeit von den Größen Fluß der absoluten Vorticity, Drehimpulsfluß, PV-Fluß oder Eliassen- Palm-Flußdivergenz angegeben werden. Die jeweiligen Eddyflüsse dieser Größen wurden miteinander verglichen. Die Auswirkungen der Konvektion auf die Intensitätsänderungen sowie die Wechselwirkungen eines Monsuntiefs mit Trögen und Rücken der oberen Troposphäre wurden untersucht. Diagnostische Analysen aus Beobachtungsdaten vom australischen Monsuntief zeigten, daß alle Terme der Tangentialwindgleichung mit Ausnahme des Verlagerungsterms für die Intensitätsänderungen von tropischen Wirbelstürmen und Monsuntiefs von Bedeutung waren. Dies schloß insbesondere die subskaligen Terme mit ein, deren Beiträge vornehmlich von Prozessen in Zusammenhang mit hochreichender Konvektion herrührten. In der unteren und mittleren Troposphäre war die zyklonale Intensivierung des Monsuntiefs vor allem auf die Flüsse der absoluten Vorticity (einwärts gerichtete, zyklonale Flüsse der relativen und planetaren Vorticity bzw. den entsprechenden Termen des Eliassen-Palm- Flusses, des radialen PV-Flusses oder des Drehimpulsflusses) und die vertikale Advektion des Tangentialwindes zurückzuführen. In der oberen Troposphäre erfolgte die zyklonale Tangentialwindänderung vorwiegend aufgrund des Flusses der relativen Vorticity (des auswärts gerichteten, antizyklonalen Flusses der relativer Vorticity), der vertikalen Advektion des Tangentialwindes und der subskaligen Effekte. Die entsprechende Tendenz zur Abschwächung des Antizyklons in der oberen Troposphäre und die kanalisierte, weit ausgedehnte Ausflußströmung waren deutliche Anzeichen für die einsetzende Verstärkung des Monsuntiefs. Das Einwärtswandern der Maxima des PV-Flusses durch Eddies in der oberen Troposphäre spiegelte die Annäherung von PV-Anomalien in Zusammenhang mit vorbeiziehenden Höhentrögen wider. Die Konvektion des Monsuntiefs verstärkte sich vor den herannahenden PVAnomalien aufgrund der reduzierten, statischen Stabilität und aufgrund des Staubsaugereffekts. Auch das Monsuntief konnte sich dadurch intensivieren. Zur Überprüfung der Zuverlässigkeit der Ergebnisse wurden die diagnostischen Felder, berechnet aus den BMRC-Analysen, mit jenen Feldern verglichen, die aus den ECMWFAnalysen bestimmt wurden. Die Strukturen der über einen Tag gemittelten symmetrischen, aufgelöst-asymmetrischen und unaufgelöst-asymmetrischen Beiträge stimmten trotz der hohen täglichen Variationen verhältnismäßig gut überein. Die Abbildungen der ECMWF-Analysen zeigten jedoch aufgrund des geringeren Gitterabstands des Analysemodells mehr Details mit ausgeprägteren Extrema. Die Intensitätsänderungen der Taifune Flo und Ed wurden mit dem Europa- und Deutschlandmodell des Deutschen Wetterdienstes untersucht. Auch diese Taifune wurden stark von hochreichender Konvektion beeinflußt. Die Sensitivität der Modellvorhersagen auf unterschiedliche Anfangsbedingungen, Taifunkeimzellen, Modellauflösungen und physikalische Parameterisierungen wurde überprüft und die großskaligen und subskaligen Asymmetrieeffekte berechnet. Die beiden Taifune Flo und Ed entstanden östlich von Guam und zogen in nordwestliche bzw. westliche Richtung. Während des Beobachtungszeitraums waren sie etwa 1700 km voneinander entfernt in einen Monsuntrog eingebettet. Ab dem 15. September 1990 entwickelte sich Flo sehr schnell zu einem Supertaifun und zog nach dem Abdrehen Richtung Japan. Bevor sich Ed nahe der vietnamesischen Küste abschwächte, vollführte er eine unübliche, südwestliche Zugbewegung. Die Auswirkungen der großskaligen und subskaligen Asymmetrien auf die Intensität des Taifuns Flo waren trotz der benachbarten TUTT-Zelle nicht groß und konnten die starke Eintiefungsphase ab dem 15. September nicht erklären. Auch wurde kein Einwärts- oder Auswärtswandern von maximalen oder minimalen Flüssen der absoluten Vorticity durch Eddies analysiert. Die Vorhersagen der Asymmetrieeffekte gaben unabhängig von der Gitterauflösung und der in der Startanalyse verwendeten Taifunkeimzelle verwertbare Hinweise über die Art und Stärke dieser Asymmetrieeffekte. Wie beim australischen Monsuntief waren die subskaligen Effekte und die vertikale Advektion von Impuls nicht vernachlässigbar. Das Europa- und das Deutschlandmodell zeigten für beide Taifune ein mäßiges Vorhersagevermögen in Bezug auf Intensitätsänderungen. Die Ausgangsdatenfelder, die eingepflanzten Keimzellen, die Modellauflösung und die physikalischen Parameterisierungen hatten einen signifikanten Einfluß auf die Intensitätsvorhersagen. Die Randwerte wirkten sich hingegen kaum auf die Intensitätsprognosen aus. Verglichen mit operationellen Vorhersagemodellen besaßen die beiden Modelle ein gutes Vorhersagevermögen für Zugbahnen. Die Zugbahnvorhersagen waren nahezu unabhängig von der Gitterauflösung und der verwendeten Cumulus-, Strahlungs- und Diffusionsparameterisierung. Abweichungen in der Zugbahn entstanden vor allem durch unterschiedliche Randbedingungen und Ausgangsanalysen, einschließlich der verwendeten Taifunkeimzellen. Die Modellauflösung, die verwendete Ausgangsanalyse und die eingepflanzte Keimzelle hatten kaum einen Einfluß auf die Verteilung und Größe der Regengebiete. Die verwendete Keimzelle und die Modellauflösung wirkten sich hingegen merklich auf die kernnahen Niederschlagsmengen aus. Die Intensität der Modelltaifune war mit der Stärke der kernnahen Niederschläge und der Stärke der Konvektion korreliert. Über das gesamte Taifungebiet gemittelt waren die Unterschiede in der Regenmenge bei unterschiedlicher Modellauflösung hingegen gering