Topological Superconductivity in Synthetic Dimensions

Speaker: Wolfgang Belzig (Department of Physics, University of Konstanz, 78567 Konstanz, Germany)
Event: Quantum Technology Workshop 2026
Slides (PDF)

Superconductivity is a macroscopic quantum phenomenon characterized by a complex order parameter that has both an amplitude and a phase. Coupling multiple superconductors introduces additional phase parameters that can be considered synthetic dimensions. The phases control quantum states in such systems, which can be considered quantum objects living in synthetic dimensions. For example, topological objects such as Weyl singularities exist only in three dimensions and offer a route toward novel quantum states that are topologically protected. In this talk, I will explain the basics of the underlying microscopic process, Andreev reflection, which leads to phase-dependent Andreev bound states. These topological states are of fundamental interest because they can host Weyl nodes, store robust quantum information, and realize more exotic topologies. I will present examples and discuss the current state of experimental research. Besides their fundamental importance, these states offer new perspectives for superconducting quantum bits.

[1] R. L. Klees, G. Rastelli, J. C. Cuevas, and W. Belzig, Microwave spectroscopy reveals the quantum geometric tensor of topological Josephson matter, Phys. Rev. Lett. 124, 197002 (2020)

[2] H. Weisbrich, R.L. Klees, G. Rastelli, and W. Belzig, Second Chern Number and Non-Abelian Berry Phase in Superconducting Systems, PRX Quantum 2, 010310 (2021).

[3] M. Coraiola, D. Z. Haxell, D. Sabonis, H. Weisbrich, A. E. Svetogorov, M. Hinderling, S. C. ten Kate, E. Cheah, F. Krizek, R. Schott, W. Wegscheider, J. C. Cuevas, W. Belzig, and F. Nichele, Phase-engineering the Andreev band structure of a three-terminal Josephson junction, Nat. Commun. 14, 6784 (2023).

[4] D. C. Ohnmacht, V. Wilhelm, H. Weisbrich, W. Belzig, Non-hermitian topology in multiterminal superconducting junctions, Phys. Rev. Lett. 134, 156601 (2025).

[5] T. Antonelli, M. Coraiola, D. C. Ohnmacht, A. E. Svetogorov, D. Sabonis, S. C. ten Kate, E. Cheah, F. Krizek, R. Schott, J. C. Cuevas, W. Belzig, W. Wegscheider, F. Nichele, Exploring the energy spectrum of a four-terminal Josephson junction: Towards topological Andreev band structures, Phys. Rev. X 15, 031066 (2025).