Joule overheating poisons the fractional ac Josephson effect in topological Josephson junctions

Topological Josephson junctions designed on the surface of a 3D-topological insulator (TI) harbor Majorana bound states (MBS's) among a continuum of conventional Andreev bound states. The distinct feature of these MBS's lies in the $4\pi$-periodicity of their energy-phase relation that yields a fractional ac Josephson effect and a suppression of odd Shapiro steps under $r\!f$ irradiation. Yet, recent experiments showed that a few, or only the first, odd Shapiro steps are missing, casting doubts on the interpretation. Here, we show that Josephson junctions tailored on the large bandgap 3D TI Bi$_2$Se$_3$ exhibit a fractional ac Josephson effect acting on the first Shapiro step only. With a modified resistively shunted junction model, we demonstrate that the resilience of higher order odd Shapiro steps can be accounted for by thermal poisoning driven by Joule overheating. Furthermore, we uncover a residual supercurrent at the nodes between Shapiro lobes, which provides a direct and novel signature of the current carried by the MBS. Our findings showcase the crucial role of thermal effects in topological Josephson junctions and lend support to the Majorana origin of the partial suppression of odd Shapiro steps.Comment: Revised article and Supplemental materia

Shape memory properties of Cu-based thin wires obtained by the “in rotating water spinning” technique

Cu-Al-Ni-based cylindrical wires with diameters ranging between 100 and 250 $\mu$m have been successfully produced directly from the melt using the “In Rotating Water Melt-Spinning” (INROWASP) technique. In such a method, a cylindrical jet of molten alloy is ejected into a liquid cooling layer (water) disposed in the inner surface of a rotating drum. This soft cooling medium allows to preserve the cylindrical shape after solidification. Due to the rapid solidification, the martensitic transformation temperatures of the as-prepared wires are depressed in relation to the bulk alloy. Ageing at moderate temperatures (250°C) increases the transformation temperatures of the wires and of the same alloys in bulk form. However, the decrement in the transformation temperatures of the wires still persists, due to their finer grain size. They exhibit superelasticity as well as shape memory properties, both for uniaxial elongation and bending. When biased by a constant aniaxial tensile stress, an elongation up to 2% (at ~ 70 MPa) is attained, in the as-prepared form, upon cooling down the transformation, completely recovered on heating. The recoverable elongation decreases to 1.2% for wires aged 700 h at 520K

Shape memory thin strips produced by the twin roll casting technique

A promising direct method of preparation by rapid solidification, the twin roll casting technique, bas been used for the first time to produce semi-finite shape memory alloys thin strips (200-600 $\mu$m thick). Different NiTi and Cu-Ni-Al based compositions have been tested. Some cracks appeared on these new products but they have been partially or totally suppressed, according to the alloy composition, by optimisation of the parameters of the process and after adding side dams to the wheels. The resulting strip morphology, structure and microstructure have been analyse, taking into account the complex heat and mass flows during the process. Transformation temperatures are in the same range of values that those of the corresponding massive materials

Production of shape memory thin strips by twin roll casting technique

Rapid solidification techniques were first used to obtain amorphous or microcrystalline metallic materials, which required high quenching rates (104-106 K.s-1). Applied to shape memory alloys, the twin roll casting technique allows semi-finished materials (strips) with reduced grain size to be obtained. This is particularly useful for certains shape memory alloys for which shaping is difficult because of their inherent lack of ductility. The melt is cast through a nozzle and solidified between the gap of two rollers rotating in opposite directions. Optimum conditions must be established to obtain thin foils with a smooth surface, not brittle and free of cracks and holes. It is only possible for a limited combination of the following experimental parameters : roll speed, melt temperature, melt flow, ejection pressure and roll gap. In this work, we have characterized (transformation temperatures, microstructures) copper based and Ni-Ti-Hf strips, with a thickness between 150 and 500 µm. For copper based alloys, it has been found that transformation temperatures were in a similar range to those of conventionnally cast alloys, which is not the case of melt spun ribbons whose transformation temperatures dramatically decrease. For Ni-Ti-Hf strips cast with different conditions, transformation temperatures vary : some are close to the conventionnally solidified material but some others are lower

Multicomponent TiNi-based shape memory alloys : General considerations and selection rules for an initial precursor amorphous state

General considerations, which concern the development of new multicomponent shape memory alloys in an initial amorphous state, are discussed. The selection rules for the chemical compositions appropriate for production of both amorphous and potentially shape memory alloys are proposed on a basis of well known three "golden rules" and statements regarding the shape memory phenomena. The production and characterisation of the "AB"-type series amorphous potentially shape memory alloys with "A"=(Ti,Hf,Zr), "B"=(Ni,Cu,Co,Ag,Pd,Al) and the "A:B" ratio varied as 45:55, 50:50 and 55:45 are discussed. The material structure was followed by X ray diffraction and the thermodynamic properties and thermal stability were studied by Differential Scanning Calorimetry. Various heat treatments regimes have been explored for the formation of appropriate microstructures to demonstrate the shape memory property

Effect of the Be and Y on the martensite transformation parameters in TiNi compound

To our knowledge, the effect of Be and Y on the martensite transformation parameters in TiNi-based shape memory alloys was studied occasionally and mainly on a level of the technological additions. Recently, due to the development of non-conventional production technologies applied to the shape memory materials, both metals are found to be the appropriate canditates for production of the potential TiNi-based shape memory alloys in an initially amorphous structural state by means of the melt-spinning and injection casting techniques. First of all, the Be and Y attract attention due to satisfaction of the so-called "golden rules" known for the bulk amorphous alloy systems. We present the result of the experimental study regarding the systematic substitution of the main constituent elements Ti and Ni by Be and Y up to (2-10) at.%. In as-cast condition, all the Ti-Ni-Be and Ti-Ni-Y alloys undergo the dual B2 → R → B19' martensite transformation sequence, well resolved on the cooling run and often overlapping on the heating run. Both the TR and MS transformation temperatures smoothly decrease with the Be or Y content, the slope to be higher for substitution of the Ti than the Ni. The ternary TiNiBe and TiNiY meltspun ribbons produced in the standard technological condition are rather brittle and don't show a good metallic aspect. They are in the crystalline structural state and undergo the martensite transformation sequence similar to the bulk material but in the lower temperature range. The contribution of the chemical composition, microstructure and strain/stress field (caused by the difference in the atomic radii) to the martensite transformation temperatures is considered

Resistance to corrosion an embrittlement of T91 steel in stagnant Pb-Bi of eutectic composition

The resistance to corrosion and embrittlement of T91 steel in stagnant Pb-Bi eutectic was studied in the temperature interval 150-650°C. The degradation of the corrosion resistance manifested itself above 350°C, with Pb-Bi sticking at surface inclusions at 600°C and with localized corrosion effects visible at 650°C. Nevertheless, the specimens aged in Pb-Bi did not exhibit any degradation of mechanical properties during ex situ testing in air at room temperature. On the contrary, a liquid metal embrittlement (LME) effect was observed, when the tensile tests were camed out in situ in Pb-Bi in the temperature interval 300-400°C. The LME effect depends on temperature, strain rate, existence of stress concentrators and especially on the chemical composition of the cover gas. This effect was observed in Pb-Bi under He-4% H$_2$ cover gas, whereas almost no LME effect was detected in Ph-Bi under vacuum. A maximum reduction in energy to rupture (around 30%) was found for notched specimens tested in Pb-Bi under He-4% H$_2$ cover gas at a crosshead displacement rate of 6x10$^{-4}$ mm/s at 350°C

Long flexible melt-spun Ni–Co–Mn–In ribbons with shape memory effect and caloric perfomances above 300 K

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