Tensor-Monopole-Induced Topological Boundary Effects in Four-Dimensional Acoustic Metamaterials

Abstract

<p>Gauge field theory provides the mathematical and conceptual framework to describe and understand<br>topological singularities such as Weyl points and magnetic monopoles. While singularities associated with<br>vector electromagnetic gauge fields have been well studied, those of higher-form tensor gauge fields, like the<br>four-dimensional (4D) tensor monopoles predicted by string theory, have remained largely theoretical or<br>limited to experimental demonstration in pure synthetic dimensions, thereby not allowing investigations of<br>the associated boundary effects. Here, we present a 4D system with tensor monopoles using engineered<br>acoustic metamaterials. Our momentum space combines three real momentum dimensions and a geometric<br>parameter as the fourth. By varying this fourth momentum, we experimentally reveal two distinct<br>topological surface states in 3D subsystems: Fermi-arc surface states in a gapless subsystem and Diraccone<br>surface states in a gapped subsystem. Our work introduces a novel platform for exploring new<br>topological structures associated with tensor gauge field and topological phenomena in higher dimensions.<br></p>