Induced superconductivity in HgTe based topological insulator nanowires

This thesis describes the studies of Josephson junctions made from topological insulator nanowires. Such nanowires in proximity to conventional superconductors have been proposed as a tunable platform to realize topological superconductivity and Majorana zero modes. The tuning is done using an axial magnetic flux Φ, which allows transforming the system from trivial at Φ=0 to topologically nontrivial when half a magnetic flux quantum Φ=Φ₀/2=h/2e penetrates the cross-sectional area of the wire. In this work, we investigate Josephson junctions based on HgTe nanowires under the influence of a magnetic field. Additionally, we probe the expected transition from trivial to topological superconductivity as a function of the axial magnetic flux. In an out-of-plane magnetic field, some devices studied show a Fraunhofer pattern, i.e. a modulation of the critical current as a function of the magnetic field. The effects of magnetic flux focusing and spin-orbit interaction are taken into account to agree with the theoretically predicted evolution of the pattern. The absence of the pattern in other devices is explained by bad transmissions of the nanowire/superconductor interface or the extreme thinness of some wires. For an axial magnetic field, we also observe a modulation of the critical current for devices with low transmissions. Here, the modulations show periodicities of Φ=h/4e or Φ=h/8e. For devices with high transmission, no modulation occurs, and the critical current monotonously decays with the magnetic field. We relate these findings both experimentally and theoretically to the coupling of the superconducting contacts to the topological insulator nanowire. For a high transmission, all sides of the nanowire become superconducting due to the proximity effect. In contrast, only the interfaces directly covered by the superconductor, i.e. the top and the sides, are proximitized if the average transmission is rather low. Here, different types of transport paths exist while some of them pick up an additional phase induced by the magnetic flux. This additional phase causes a modification of the current-phase relation and, thus, leads to a modulation of the critical current as a function of the magnetic flux. In Josephson junctions, an indication of emanating Majorana bound states is a 4π-periodic current-phase relation. A convenient way to probe the periodicity of the current-phase relation is the measurement of Shapiro steps. In the trivial situation, all Shapiro steps are visible while the odd steps are supposed to disappear if the current-phase relation is 4π-periodic. Hence, we probe the Shapiro step spectrum for different microwave frequencies and intensities. From the suppression of odd Shapiro steps, we extract the 4π- and 2π-periodic fraction of the critical current using both a resistively shunted junction (RSJ) and a resistively and capacitively shunted junction (RCSJ) model. The ratio of the 4π-periodic current on the total critical current depends strongly on the axial magnetic flux. While the total critical current decreases with an increasing flux, the ratio changes from approximately 6% at Φ=0 up to a maximum around Φ=Φ₀/2. The presence of a finite 4π-periodic current at Φ=0 and small magnetic fields is ascribed to Landau-Zener transitions between trivial Andreev bound states causing the 4π-periodic current. A method to distinguish between the trivial and the topological origin of the 4π-periodic currents is achieved by comparing the results for in-plane magnetic fields parallel to the wire as well as perpendicular to the wire. A topological 4π-periodic current is only proposed for the first configuration, while a trivial 4π-periodic current appear for both cases. Thus, our data suggest that the 4π-periodic current, which only appears for parallel magnetic fields ⪎Φ₀/4, is mainly of topological origin. Therefore, our experiments provide an indication for the switching between trivial and topological superconductivity with an axial magnetic flux in topological insulator nanowires