Wolfgang BELZIG | Higher-dimensional topology in multi-terminal superconducting structures

Wolfgang Belzig, University of Konstanz, Germany

Topology is ultimately unveils the roots of the perfect quantization observed in complex systems. The 2D quantum Hall effect is the celebrated archetype. Remarkably, topology can manifest itself even in higher-dimensional spaces defined by control parameters playing the role of synthetic dimensions. However, so far, a very limited number of implementations of higher-dimensional topological systems have been proposed, a notable example being the so-called 4D quantum Hall effect. In this talk I will show that mesoscopic superconducting systems can implement higher-dimensional topology and represent a formidable platform to study a quantum system with a purely nontrivial second Chern number [1]. I further demonstrate that the integrated absorption intensity in designed microwave spectroscopy [2] is quantized and the integer is directly related to the second Chern number. Finally, I discuss that these systems also possess a non-Abelian Berry phase or exotic topologies like tensor monopoles.

[1] 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) [2] 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)