Four-dimensional topological lattices through connectivity

Abstract

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.

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Cited by in corpus (16)

• Topological Photonics
• Circuit Implementation of a Four-Dimensional Topological Insulator
• 4D spinless topological insulator in a periodic electric circuit
• Hyperbolic band topology with non-trivial second Chern numbers
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• Revealing Chern number from quantum metric
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• Zeros of Green Functions in Topological Insulators
• Linking topological features of the Hofstadter model to optical diffraction figures
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• Even spheres as joint spectra of matrix models
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• Geometry induced quantum Hall effect and Hall viscosity