Four-dimensional topological lattices through connectivity

Thanks to recent advances, the 4D quantum Hall (QH) effect is becoming experimentally accessible in various engineered set-ups. In this paper, we propose a new type of 4D topological system that, unlike other 2D and 4D QH models, does not require complicated (artificial) gauge fields and/or time-rev...

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Bibliographic Details
Published inarXiv.org
Main Author Price, Hannah M
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 09.06.2020
Subjects
Broken symmetry
Honeycomb construction
Lattices
Photonics
Physics - Optics
Physics - Quantum Gases
Topology
Two dimensional models
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Summary:Thanks to recent advances, the 4D quantum Hall (QH) effect is becoming experimentally accessible in various engineered set-ups. In this paper, we propose a new type of 4D topological system that, unlike other 2D and 4D QH models, does not require complicated (artificial) gauge fields and/or time-reversal symmetry breaking. Instead, we show that there are 4D QH systems that can be engineered for spinless particles by designing the lattice connectivity with real-valued hopping amplitudes, and we explain how this physics can be intuitively understood in analogy with the 2D Haldane model. We illustrate our discussion with a specific 4D lattice proposal, inspired by the widely-studied 2D honeycomb and brickwall lattice geometries. This also provides a minimal model for a topological system in Class AI, which supports nontrivial topological band invariants only in four spatial dimensions or higher.
ISSN:2331-8422
DOI:10.48550/arxiv.1806.05263