Second Chern Number and Non-Abelian Berry Phase in Topological Superconducting Systems

Year: 2021

Authors: Weisbrich H., Klees R.L., Rastelli G., Belzig W.

Autors Affiliation: Univ Konstanz, Fachbereich Phys, D-78457 Constance, Germany; Univ Konstanz, Zukunftskolleg, D-78457 Constance, Germany; Univ Trento, INO CNR BEC Ctr, I-38123 Povo, Italy; Univ Trento, Dipartimento Fis, I-38123 Povo, Italy

Abstract: Topology ultimately unveils the roots of the perfect quantization observed in complex systems. The two-dimensional quantum Hall effect is the celebrated archetype. Remarkably, topology can manifest itself even in higher-dimensional spaces in which control parameters play the role of extra, 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 four-dimensional quantum Hall effect. Here we 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. We demonstrate that the integrated absorption intensity in designed microwave spectroscopy is quantized and the integer is directly related to the second Chern number. Finally, we show that these systems also admit a non-Abelian Berry phase. Hence, they also realize an enlightening paradigm of topological non-Abelian systems in higher dimensions.

Journal/Review: PRX QUANTUM

Volume: 2 (1)      Pages from: 010310-1  to: 010310-18

More Information: The authors are grateful for funding provided by the DFG through SFB 767 and Grant No. RA 2810/1.
KeyWords: mesoscopic superconductivity, Andreev Reflection, topological superconductors, Josephson effect
DOI: 10.1103/PRXQuantum.2.010310