Multivalued current-phase relationship in a.c. Josephson effect for a three-dimensional Weyl semimetal WTe2_2

We experimentally study electron transport between two superconducting indium leads, coupled to a single WTe$_2$ crystal, which is a three-dimensional Weyl semimetal. We demonstrate Josephson current in long 5~$\mu$m In-WTe$_2$-In junctions, as confirmed by the observation of integer (1,2,3) and fractional (1/3, 1/2, 2/3) Shapiro steps under microwave irradiation. Demonstration of fractional a.c. Josephson effect indicates multivalued character of the current-phase relationship, which we connect with Weyl topological surface states contribution to Josephson current. In contrast to topological insulators and Dirac semimetals, we do not observe $4\pi$ periodicity in a.c. Josephson effect for WTe$_2$ at different frequencies and power, which might reflect chiral character of the Fermi arc surface states in Weyl semimetal.Comment: the text is seriously corrected. arXiv admin note: text overlap with arXiv:1801.0955

Signature of Fermi arc surface states in Andreev reflection at the WTe2_2 Weyl semimetal surface

We experimentally investigate charge transport through the interface between a niobium superconductor and a three-dimensional WTe$_2$ Weyl semimetal. In addition to classical Andreev reflection, we observe sharp non-periodic subgap resistance resonances. From an analysis of their positions, magnetic field and temperature dependencies, we can interpret them as an analog of Tomasch oscillations for transport along the topological surface state across the region of proximity-induced superconductivity at the Nb-WTe$_2$ interface. Observation of distinct geometrical resonances implies a specific transmission direction for carriers, which is a hallmark of the Fermi arc surface states.Comment: 5 pages, some misprints has been correcte

Multiple magnon modes in the Co3_3Sn2_2S2_2 Weyl semimetal candidate

We experimentally investigate electron transport in kagome-lattice ferromagnet Co$_3$Sn$_2$S$_2$, which is regarded as a time-reversal symmetry broken Weyl semimetal candidate. We demonstrate $dV/dI(I)$ curves with pronounced asymmetric $dV/dI$ spikes, similar to those attributed to current-induced spin-wave excitations in ferromagnetic multilayers. In contrast to multilayers, we observe several $dV/dI$ spikes' sequences at low, $\approx$10$^4$ A/cm$^2$, current densities for a thick single-crystal Co$_3$Sn$_2$S$_2$ flake in the regime of fully spin-polarized bulk. The spikes at low current densities can be attributed to novel magnon branches in magnetic Weyl semimetals, which are predicted due to the coupling between two magnetic moments mediated by Weyl fermions. Presence of spin-transfer effects at low current densities in Co$_3$Sn$_2$S$_2$ makes the material attractive for applications in spintronics.Comment: final versio

Incorporating model uncertainty into optimal insurance contract design

In stochastic optimization models, the optimal solution heavily depends on the selected probability model for the scenarios. However, the scenario models are typically chosen on the basis of statistical estimates and are therefore subject to model error. We demonstrate here how the model uncertainty can be incorporated into the decision making process. We use a nonparametric approach for quantifying the model uncertainty and a minimax setup to find model-robust solutions. The method is illustrated by a risk management problem involving the optimal design of an insurance contract

Catalogue and Toolbox of Risk Assessment and Management Tools

The ENHANCE project is concerned with analysing and working towards improved public-private partnerships for managing risks from natural hazards. An important issue for such partnerships is the methods, tools and processes available for assessing risk and risk management options. Risk analysis has long provided useful input to decision-making. At the same time, the field of risk analysis is in motion and an enhanced framing of risk analysis and risk management is being embraced following an iterative cycle organized around notions of learning, innovation and transformation. This broadened vision on risk analysis is a key issue for the ENHANCE project as well, which takes many and different perspectives on analysing, understanding, communicating and managing risk. This report lays out the status quo at the outset of the project regarding risk analytical tools, methods and data that are currently used by project partners in ENHANCE. The task overall develops a catalogue of existing risk assessment and management tools and methods to describe the concepts of iterative risk management and further sets up a toolbox, containing individual models and tools to be used by the case studies in their analyses. While work in the cases study, including methodological development, is in process, we find that ENHANCE partners and cases employ a multitude of models, tools and data ranging from impact analysis, different risk modelling techniques to various decision-support methods. A number of tools that encapsulate these methods are also available with the consortium. We suggest the tools and methods in use can be useful starting points for working towards a broader vision of iterative risk management. While the work so far, and this deliverable, have focussed on populating the technical stages of the risk analytical cycle (visually identified as the inner circle), we suggest in the next phase of ENHANCE, additional efforts should be dispensed to better understand adaptive management aspects associated with using these methods and tools, such as learning, innovation and transformation, which we exhibit visually in an outer circle. This report proceeds as follows: We start with laying out key elements of risk analysis and management in section 2, which also describes the new framing organized around the iterative risk-management concept. Methods for assessing risk and evaluating risk management are discussed in section 3. Then we consider methods, models and datasets that are in use in the ENHANCE case studies at the moment (section 4), before section 5 concludes. Finally and importantly, the annex lists more information on cases studies, for which detailed information was received from the project partners

Surface ferromagnetism in a chiral topological semimetal CoSi

Despite the chiral topological semimetal CoSi is known as bulk diamagnetic, it shows unusual surface ferromagnetism of debatable origin. The ferromagnetic ordering has been attributed to the distorted bonds, the superlattice of ordered vacancies, or even to topological surface textures due to the spin polarization in the neighboring Fermi arcs. We experimentally compare magnetization reversal curves for initially oxidized CoSi single crystals and cleaved samples with a fresh, oxide-free surface. While the oxidized CoSi samples do not show sizable ferromagnetism, the fresh CoSi surface gives a strong ferromagnetic response, which is accompanied by the pronounced modulation of the angle dependence of magnetization, as it can be expected for easy and hard axes in a ferromagnet. In addition to the first order reversal curves analysis, this observation allows us to distinguish between different mechanisms of the ferromagnetic ordering in CoSi single crystals. We conclude that the surface states-induced RKKY interaction between distorted bonds near the sample surface is responsible for the strong ferromagnetic multi-domain behavior for freshly cleaved samples

Surface spin polarization in the magnetic response of GeTe Rashba ferroelectric

We experimentally investigate magnetization reversal curves for a GeTe topological semimetal. In addition to the known lattice diamagnetic response, we observe narrow magnetization loop in low fields, which should not be expected for non-magnetic GeTe. The hysteresis is unusual, so the saturation level is negative in positive fields, and the loop is passed clockwise, in contrast to standard ferromagnetic behavior. The experimental hysteresis curves can not be obtained from usual ferromagnetic ones by adding/subtracting of any linear dependence, or even by considering several interacting magnetic phases. The possibility of several phases is also eliminated by the remanence plots technique (Henkel or {\delta}M plots). We explain our results as a direct consequence of the correlation between ferroelectricity and spin-polarized surface states in GeTe, similarly to magnetoelectric structures

Switching ferroelectricity in SnSe across diffusionless martensitic phase transition

We experimentally investigate transport properties of a hybrid structure, which consists of a thin single crystal SnSe flake on a top of 5~$\mu$m spaced Au leads. The structure initially is in highly-conductive state, while it can be switched to low-conductive one at high currents due to the Joule heating of the sample, which should be identified as $\alpha$-$Pnma$ -- $\beta$-$Cmcm$ diffusionless martensitic phase transition in SnSe. For highly-conductive state, there is significant hysteresis in $dI/dV(V)$ curves at low biases, so the sample conductance depends on the sign of the applied bias change. This hysteretic behavior reflects slow relaxation due to additional polarization current in the ferroelectric SnSe phase, which we confirm by direct measurement of time-dependent relaxation curves. In contrast, we observe no noticeable relaxation or low-bias hysteresis for the quenched $\beta$-$Cmcm$ low-conductive phase. Thus, ferroelectric behavior can be switched on or off in transport through hybrid SnSe structure by controllable $\alpha$-$Pnma$ -- $\beta$-$Cmcm$ phase transition. This result can also be important for nonvolatile memory development, e.g. phase change memory for neuromorphic computations or other applications in artificial intelligence and modern electronics