Topological gaps in 2D locally resonant meta-structures via twisting

Quasi-periodic structures are known to support topological gaps forming a fractal spectrum that resemble the Hofstadter butterfly. While most studies dwell on a variety of 1D quasi-periodic structures, research in 2D quasiperiodic domains and their topologies has been scarce. It was recently shown that twisted bilayered lattices are quasi-periodic systems that host higher dimensional topological phases akin to the 4D Quantum Hall effect, which are characterized by a second Chern number. Herein, we present a reconfigurable 2D elastic plate featuring arrays of resonators with tunable on-site frequency. The resonators are arranged according to a fixed square lattice, while their frequencies are modulated by a second twisted lattice. We demonstrate that the procedure opens topological gaps characterized by second Chern numbers, whose higher dimensional topological states are controlled by the phason of the modulation. Experiments are conducted on elastic plates whose tunable resonators allows for agile reconfiguration, and preliminary results are discussed. The existence of non-trivial gaps and localized modes in 2D non-periodic systems open new avenues for wave localization and transport exploring higher dimensional topologies.