Lecturer: Julia Meyer (Univ. Grenoble-Alpes)
Abstract: Topological phases of matter have attracted much interest in recent years. Starting with gapped phases such as topological insulators and superconductors, more recently gapless topological phases possessing topologically protected band crossings have been discovered. Here we show that n-terminal Josephson junctions may provide a straightforward realization of tunable topological materials in n-1 dimensions, the independent superconducting phases playing the role of quasi-momenta. In particular, we find Weyl points in the Andreev bound state spectrum of 4-terminal junctions. The topological properties of the junction may be probed experimentally by measuring the transconductance between two voltage-biased leads, which we predict to be quantized. Further, the analogy between the spectrum of Andreev bound states in an n-terminal Jospehson junction and the bandstructure of an n-1-dimensional material opens the possibility of realizing topological phases in higher dimensions, not accessible in real materials.