Curtis Rasmussen | Searcharxiv

arXiv2026

Topological Acoustic Metamaterials with Synthetic Magnetism: Observation of Hofstadter Spectrum and Topological Edge States

Architected materials are increasingly used to implement topological dynamics, yet realizing the gauge fields and symmetries that protect the topology with purely passive elements remains the central practical challenge. Here we turn a previously proposed theoretical strategy into an integrated platform that accepts a theoretical model as input and returns a passive acoustic metamaterial with identical dynamics. We demonstrate it experimentally on the Hofstadter model at $θ= 2π/3$, fabricating a spin-Chern insulator whose two sectors carry Chern numbers $C_s = \pm 1$, and observe the predicted helical edge states.

cond-mat.mes-hall↗

arXiv2024

Hyperbolic Space Spectral Characteristics in a Network of Mechanical Linkages

We investigate the dynamic properties of elastic lattices defined by tessellations of a curved hyperbolic space. The lattices are obtained by projecting nodes of a regular hyperbolic tessellation onto a flat disk and then connecting those sites with simple linkages. Numerical and experimental investigations illustrate how their vibrational spectral properties are characterized by a high density of modes that are localized at the domain boundaries. Such properties govern the propagation of waves induced by broadband inputs. This suggests the potential for applications seeking the protection of bulk media from boundary-incident perturbations. We uncover the boundary-dominated nature of an exemplary hyperbolic lattice through the evaluation and analysis of its integrated density of states and vibrational spectrum. The dynamics of the lattice are also contextualized by comparing them with those of continuous disks characterized by Euclidean and hyperbolic property distributions, which confirms that the lattice retains the boundary-dominated spectrum observed in the hyperbolic plane. We then numerically investigate the response of the lattice to transient pulses incident on the boundary and find that edge-confined wave propagation occurs. The modal and transient pulse propagation behavior of the lattice is experimentally validated in a milled aluminum sample. By leveraging hyperbolic geometry, our mechanical lattice ushers in a novel class of mechanical metamaterials with boundary-dominated wave phenomena reminiscent of topologically protected systems suitable for applications in advanced wave control.

physics.app-ph↗