Exploring the Energy Spectrum of a Four-Terminal Josephson Junction: Toward Topological Andreev Band Structures

Hybrid multiterminal Josephson junctions (JJs) are expected to harbor a novel class of Andreev bound states (ABSs), including topologically nontrivial states in four-terminal devices. In these systems, topological phases emerge when ABSs depend on at least three superconducting phase differences, resulting in a three-dimensional (3D) energy spectrum characterized by Weyl nodes at zero energy. Here, we realize a four-terminal JJ in a hybrid Al/InAs heterostructure, where ABSs form a synthetic 3D band structure. We probe the energy spectrum using tunneling spectroscopy and identify spectral features associated with the formation of a tri-Andreev molecule, a bound state whose energy depends on three superconducting phases and, therefore, is able to host topological ABSs. The experimental observations are well described by a numerical model. The calculations predict the appearance of four Weyl nodes at zero energy within a gap smaller than the experimental resolution. These topological states are theoretically predicted to remain stable within an extended region of the parameter space, well accessible by our device. These findings establish an experimental foundation to study high-dimensional synthetic band structures in multiterminal JJs and to realize topological Andreev bands.