Microwave studies of the fractional Josephson effect in HgTe-based Josephson junctions

The rise of topological phases of matter is strongly connected to their potential to host Majorana bound states, a powerful ingredient in the search for a robust, topologically protected, quantum information processing. In order to produce such states, a method of choice is to induce superconductivity in topological insulators. The engineering of the interplay between superconductivity and the electronic properties of a topological insulator is a challenging task and it is consequently very important to understand the physics of simple superconducting devices such as Josephson junctions, in which new topological properties are expected to emerge. In this article, we review recent experiments investigating topological superconductivity in topological insulators, using microwave excitation and detection techniques. More precisely, we have fabricated and studied topological Josephson junctions made of HgTe weak links in contact with two Al or Nb contacts. In such devices, we have observed two signatures of the fractional Josephson effect, which is expected to emerge from topologically-protected gapless Andreev bound states. We first recall the theoretical background on topological Josephson junctions, then move to the experimental observations. Then, we assess the topological origin of the observed features and conclude with an outlook towards more advanced microwave spectroscopy experiments, currently under development.Comment: Lectures given at the San Sebastian Topological Matter School 2017, published in "Topological Matter. Springer Series in Solid-State Sciences, vol 190. Springer

Ge/Si nanowire mesoscopic Josephson junctions

The controlled growth of nanowires (NWs) with dimensions comparable to the Fermi wavelengths of the charge carriers allows fundamental investigations of quantum confinement phenomena. Here, we present studies of proximity-induced superconductivity in undoped Ge/Si core/shell NW heterostructures contacted by superconducting leads. By using a top gate electrode to modulate the carrier density in the NW, the critical supercurrent can be tuned from zero to greater than 100 nA. Furthermore, discrete sub-bands form in the NW due to confinement in the radial direction, which results in stepwise increases in the critical current as a function of gate voltage. Transport measurements on these superconductor-NW-superconductor devices reveal high-order (n = 25) resonant multiple Andreev reflections, indicating that the NW channel is smooth and the charge transport is highly coherent. The ability to create and control coherent superconducting ordered states in semiconductor-superconductor hybrid nanostructures allows for new opportunities in the study of fundamental low-dimensional superconductivity

Quantum oscillations of the critical current and high-field superconducting proximity in ballistic graphene

Graphene-based Josephson junctions provide a novel platform for studying the proximity effect due to graphene's unique electronic spectrum and the possibility to tune junction properties by gate voltage. Here we describe graphene junctions with a mean free path of several micrometres, low contact resistance and large supercurrents. Such devices exhibit pronounced Fabry-P\'erot oscillations not only in the normal-state resistance but also in the critical current. The proximity effect is mostly suppressed in magnetic fields below 10mT, showing the conventional Fraunhofer pattern. Unexpectedly, some proximity survives even in fields higher than 1 T. Superconducting states randomly appear and disappear as a function of field and carrier concentration, and each of them exhibits a supercurrent carrying capacity close to the universal quantum limit. We attribute the high-field Josephson effect to mesoscopic Andreev states that persist near graphene edges. Our work reveals new proximity regimes that can be controlled by quantum confinement and cyclotron motion

MESOSCOPIC SUPERCONDUCTOR SEMICONDUCTOR HETEROSTRUCTURES

A summary is given of recent results on carrier transport in mesoscopic conductors with superconducting electrodes. Three-dimensional transport in the diffusive limit is studied with crystalline silicon membranes sandwiched between two niobium electrodes or between one electrode superconducting and one normal. At low temperatures, inelastic scattering is negligible in the intermediate silicon layer. At finite voltages the distribution of electrons over the energies in the silicon is found to be strongly nonthermal, with details depending on the interplay between Andreev scattering and elastic scattering at the interfaces. At small voltages, well below the gap-voltage, transport is phase-coherent. A supercurrent is found if both electrodes are superconducting, provided the membrane is thin enough. If only one electrode is superconducting or for thick membranes an enhanced conductance is observed, which decreases with increasing voltage and magnetic field. Two-dimensional transport and the ballistic regime are being studied by using InAs- and GaAs-based heterostructures. Various interesting theoretical predictions have been made and some novel phenomena have been discovered experimentally. Interesting new phenomena have also been found in mesoscopic normal metals with superconducting electrodes

MESOSCOPIC SUPERCONDUCTOR SEMICONDUCTOR HETEROSTRUCTURES

A summary is given of recent results on carrier transport in mesoscopic conductors with superconducting electrodes. Three-dimensional transport in the diffusive limit is studied with crystalline silicon membranes sandwiched between two niobium electrodes or between one electrode superconducting and one normal. At low temperatures, inelastic scattering is negligible in the intermediate silicon layer. At finite voltages the distribution of electrons over the energies in the silicon is found to be strongly nonthermal, with details depending on the interplay between Andreev scattering and elastic scattering at the interfaces. At small voltages, well below the gap-voltage, transport is phase-coherent. A supercurrent is found if both electrodes are superconducting, provided the membrane is thin enough. If only one electrode is superconducting or for thick membranes an enhanced conductance is observed, which decreases with increasing voltage and magnetic field. Two-dimensional transport and the ballistic regime are being studied by using InAs- and GaAs-based heterostructures. Various interesting theoretical predictions have been made and some novel phenomena have been discovered experimentally. Interesting new phenomena have also been found in mesoscopic normal metals with superconducting electrodes