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.4 MoreReceived 9 July 2020Accepted 15 December 2020DOI:https://doi.org/10.1103/PRXQuantum.2.010310Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasTopological materialsTopological phases of matterTopological superconductorsPhysical SystemsQuantum dotsSuperconductorsCondensed Matter, Materials & Applied Physics
Highlights
Topology explains the origin of phenomena that at first glance appear extremely fragile
We demonstrate that the integrated absorption intensity in designed microwave spectroscopy is quantized and the integer is directly related to the second Chern number
We propose systems formed by multiterminal SC contacts embedding quantum dots and that are characterized by a nontrivial second Chern number
Summary
Topology explains the origin of phenomena that at first glance appear extremely fragile. Majorana-based qubits illustrate the idea of holonomic quantum computation in a paradigmatic way that is based on the concept of a generalized non-Abelian Berry phase in a degenerate ground-state subspace [10]. The concept of the 2D quantum Hall effect has been extended to the 4D quantum Hall effect with the quantized nonlinear Hall response determined by the second Chern number [38] Even though this situation does not naturally arise in solid-state systems due to limited dimensionality, there are several possibilities to create the 4D space artificially. The difference in the oscillator strengths for different circular polarizations integrated over the 4D parameter space corresponds to the integration of the local Berry curvature and, the result will be directly related to the second Chern number
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