Trapped State at a Dislocation in a Weak Magnetomechanical Topological Insulator

Topological insulators are characterized by an insulating bulk and symmetry-protected bound states on their boundaries. A "strong"topological insulator is characterized by robust conducting states on all boundaries protected by certain internal symmetries. A "weak"topological insulator (WTI), however, requires lattice translation symmetry, making it more sensitive to disorder. However, this sensitivity gives rise to interesting characteristics, such as anisotropic edge modes, quantized charge polarization, and bound states appearing at dislocation defects. Despite hosting interesting features, the sensitivity of WTIs to disorder poses an experimental confirmation challenge. Here we realize a two-dimensional (2D) magnetomechanical metamaterial and experimentally demonstrate the unique features of a WTI. Specifically, we show that the 2D WTI is anisotropic and hosts edge modes only on certain edges, as well as hosting a bound state at a dislocation defect. We construct the 2D WTI from stacked 1D Su-Schrieffer-Heeger chains for which we experimentally show the different gapped phases of the 1D model.