We report strong electron-electron interactions in quantum wires etched from an InAs quantum well, a material known to have strong spin-orbit interactions. We find that the current through the wires as a function of the bias voltage and temperature follows the universal scaling behavior of a Tomonaga-Luttinger liquid. Using a universal scaling formula, we extract the interaction parameter and find strong electron-electron interactions, increasing as the wires become more depleted. We establish theoretically that spin-orbit interactions cause only minor modifications of the interaction parameter in this regime, indicating that genuinely strong electron-electron interactions are indeed achieved in the device. Our results suggest that etched InAs wires provide a platform with both strong electron-electron and strong spin-orbit interactions. * sato@meso.t.u-tokyo.ac.jp; Contributed equally to this work † matsuo@ap.t.u-tokyo.ac.jp; Contributed equally to this work

We demonstrated dominant Cooper pair splitting in a ballistic double nanowire Josephson junction.

Two aspects of p-wave pairing in metals are discussed. First the group-theoretical classifications of p-wave states in metals with strong spin-orbit scattering and cubic, hexagonal tetragonal symmetry is reviewed. In the second part the depairing effect associated with normal impurities is shown to be dependent on the form of the p-wave pairing states. States with lines of zeros have no critical concentration for the onset of a finite density of states at the Fermi energy while states with no zeros or only point zeros have critical concentrations.

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We report on half-integer Shapiro steps observed in a gate-tunable short ballistic InAs nanowire Josephson junction. We observed the Shapiro steps of the short ballistic InAs nanowire Josephson junction and found the half-integer steps in addition to the conventional integer steps. In this Josephson junction device the junction transmission can be varied with gate voltage. From measurements of the gate voltage and temperature dependences of the Shapiro steps, the origin of half-integer steps is assigned to the skewness of the current phase relation in the short ballistic Josephson junctions. These results will contribute to establish and control the superconductivity physics in the short ballistic semiconductor nanowires.