Revealing the boundary Weyl physics of the four-dimensional Hall effect via phason engineering in metamaterials

Abstract

Quantum Hall physics has been theoretically predicted in 4-dimensions and higher. In hypothetical 2n-dimensions, the topological characters of both the bulk and the boundary are manifested as quantized non-linear transport coefficients that connect, respectively, to the n-th Chern number of the bulk gap projection and to the n-th winding number of the Weyl spectral singularities on the (2n-1)-dimensional boundaries. Here, we introduce the concept of phason engineering in metamaterials and use it as a vehicle to access and apply the quantum Hall physics in arbitrary dimensions. Using these specialized design principles, we fabricate a re-configurable 2-dimensional aperiodic acoustic crystal with a phason living on a 2-torus, giving us access to the 4-dimensional quantum Hall physics. Also, we supply a direct experimental confirmation that the topological boundary spectrum assembles in a Weyl singularity when mapped as function of the quasi-momenta. We also demonstrate topological wave steering enabled by the Weyl physics of the 3-dimensional boundaries.

References in corpus (2)

• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump

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• Topological Insulators with Hybrid-order Boundary States
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• Curved vortex surfaces in four-dimensional superfluids: II. Equal-frequency double rotations
• Curved vortex surfaces in four-dimensional superfluids: I. Unequal-frequency double rotations
• Classifying the Dynamics of Architected Materials by Groupoid Methods