Six-dimensional quantum Hall effect and three-dimensional topological pumps

Year: 2018

Authors: Petrides I., Price H., Zilberberg O.

Autors Affiliation: Swiss Fed Inst Technol, Inst Theoret Phys, CH-8093 Zurich, Switzerland; Univ Birmingham, Sch Phys & Astron, Birmingham B15 2TT, W Midlands, England; Univ Trento, INO CNR BEC Ctr, I-38123 Povo, Italy; Univ Trento, Dipartimento Fis, I-38123 Povo, Italy.

Abstract: Modern technological advances allow for the study of systems with additional synthetic dimensions. Using such approaches, higher-dimensional physics that was previously deemed to be of purely theoretical interest has now become an active field of research. In this work, we derive from first principles using a semiclassical equation-of-motion approach the bulk response of a six-dimensional Chern insulator. We find that in such a system a quantized bulk response appears with a quantization originating from a six-dimensional topological index: the third Chern number. Alongside this unique six-dimensional response, we rigorously describe the lower even-dimensional Chern-type responses that can occur due to nonvanishing first and second Chern numbers in subspaces of the six-dimensional space. Last, we propose how to realize such a bulk response using three-dimensional topological charge pumps in cold atomic systems.

Journal/Review: PHYSICAL REVIEW B

Volume: 98 (12)      Pages from: 125431-1  to: 125431-11

More Information: H.M.P. received funding from the Royal Society and from the European Union Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 656093: SynOptic. I.P. and O.Z. acknowledge financial support from the Swiss National Foundation.
KeyWords: Magnetic Bloch Bands; Berry-phase; Semiclassical Dynamics; Conduction Electrons; Hofstadter Spectrum; Chern Number; Edge States; Transport; Curvature; Quantization
DOI: 10.1103/PhysRevB.98.125431

Citations: 60
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