Towards Topological and High-Dimensional Synthetic Band Structures in 2DEG-Based Multiterminal Josephson Junctions

Hybrid superconductor-semiconductor multiterminal Josephson junctions (MTJJs) provide a rich playground for realizing and probing novel quantum phenomena. In particular, the ability to control both the super/semi coupling and superconducting phase at each terminal has driven a significant recent effort to realize in MTJJs a form of synthetic matter, where the phase-dependent energies of Andreev or Yu-Shiba-Rusinov bound states in the mutual scattering region form a sort of pseudo-band structure. Not only is this artificial band structure predicted to become topologically nontrivial when suitably tuned, but its dimension may be made arbitrarily high through the addition of additional terminals, making MTJJs a potential simulator for Bloch Hamiltonians in greater than three dimensions. We present here our recent experimental progress towards realizing such artificial band structures in 2DEG-based material platforms.