Josephson junctions are the basic building blocks of superconducting qubit architectures, and Josephson junctions made from semiconductors are interest for search for topological states. A novel direction is the realization of systems with multiple superconducting terminals. If the superconducting terminals are placed close to each other, the Andreev Bound states living between pairs of electrodes can hybridize and form a states connected to more than two electrodes. The simplest system consists of 3 superconducting electrodes placed in a linear array and by the two junctions inbetween them. This system is called Andreev molecule and is of central interest to the field. If the Josephson junctions are realized in a semiconducting system, quantum dots can be formed in the junctions, which allows to study the role of Coulomb interaction as well. Finally, in multiterminal Josephson junctions, by controlling the phase difference between the superconducting terminals, a synthetic Weyl metals can be realized: in the space of phase differences Weyl points should appear in the Andreev spectrum, similarly to the k-space of real Weyl semimetals.

Multiterminal Josephson junctions will be realized in InAs 2DEG, that are covered with epitaxial aluminum. The InAs has a large SOC allowing also to study the topological aspects of the Josephson junctions. The systems could by studied using supercurrent measurements, tunnel probe experiments or by coupling them two superconducting resonators and using so-called two-tone spectroscopy.  During the PhD work the candidate will realize semiconducting/superconductor using nanofabrication techniques. The measurements will be done at ultra-low temperatures and in collaboration with several European universities.