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

TL;DR

This paper demonstrates that mesoscopic superconducting systems can realize higher-dimensional topological phenomena, including a quantized second Chern number and non-Abelian Berry phases, through microwave spectroscopy.

Contribution

It introduces a novel platform using superconducting systems to explore 4D topological effects and non-Abelian Berry phases, previously limited in implementation.

Findings

Quantized integrated absorption intensity related to second Chern number

Implementation of non-Abelian Berry phase in superconducting systems

Potential for studying higher-dimensional topological phenomena

Abstract

Topology 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 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 4D 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.