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

Tommaso Antonelli1,2,*, Marco Coraiola1,*, David Christian Ohnmacht3, Aleksandr E. Svetogorov3, Deividas Sabonis1, Sofieke C. ten Kate1, Erik Cheah2, Filip Krizek2, Rüdiger Schott2 et al.

Juan Carlos Cuevas4,5, Wolfgang Belzig3, Werner Wegscheider2, and Fabrizio Nichele1,†

  • *These authors contributed equally to this work.
  • †Contact author: fni@zurich.ibm.com
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Phys. Rev. X 15, 031066 – Published 9 September, 2025

DOI: https://doi.org/10.1103/qd3y-f912

Abstract

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.

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Popular Summary

One of the biggest challenges in building quantum devices is making them resistant to noise, which can easily disrupt fragile quantum states. Topology offers a powerful solution because topological states are expected to be protected against disturbances. Theory predicts that special topological states called Weyl nodes can form in semiconductor-superconductor devices if they include at least four superconducting terminals. In this work, we take an important experimental step toward realizing such states by building and studying the essential element of this system.

We design a device where three energy states are confined between four superconducting terminals. By carefully tuning three independent superconducting phases, we observe that the energy states strongly interact and form a new collective state that depends on all phases at once. This behavior matches theoretical predictions and is similar to how electronic bands appear in solid-state crystals. In fact, our device effectively acts as a simulator of a 3D band structure, allowing us to study models of condensed matter physics in a controlled quantum circuit.

Our calculations suggest that Weyl nodes are already present in the band structure of this device, though detecting them directly will require experiments with finer energy resolution. Importantly, the predicted Weyl states remain stable under a wide range of conditions, making them promising for future applications. This demonstration shows that synthetic band structures can be engineered in superconducting devices, paving the way for electronic Weyl simulators and, ultimately, more robust quantum technologies based on topological protection.

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Phys. Rev. X 15, 031066– Published 9 September, 2025
  • Received 14 January 2025
  • Revised 5 May 2025
  • Accepted 7 August 2025
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